Tuesday, August 31, 2010

jQuery.LocalScroll 1.2 released

A new major update of jQuery.LocalScroll has seen the light.
Two minor releases were added after it and is now at 1.2.2. I'll detail them all together:

Optimizations

  • Replaced a $('[name='+name+']') for a document.getElementsByName(name) to critically improve perfomance.
  • Small improvements to make the code shorter.

Fixes

  • The last argument received by onBefore when scrolling the window, is no more $(window) but the real element being scrolled.

Changes

  • Renamed the option 'persistent' to 'lazy', the latter seemed more adequate. Using 'persistent' will still work (backwards compatibilty)

Features

  • Added the option 'stop', if true (default), each event will stop any previous animations of the target.
  • Added the option 'lock', if true, the plugin will ignore events if already animating.
  • Added $.localScroll.hash( settings ); which will scroll to the given element if the URL contains a valid hash.
  • Removed the option 'cancel' that wasn't working well, and added the option 'hash'. It does what 'cancel' was meant to do, but in a different way.
    After a scroll, the hash( #some_id ) of the link is added to the URL.
    Note:This setting is not compatible with options like offset and margin, as the browser will natively scroll in the end.
    If you use the option 'target'(to scroll an overflowed element) and the window has overflow, setting the hash will scroll the window as well. So my advice is:
    only use 'hash' when scrolling the window.
jQuery.ScrollTo is now at 1.3.2, it has a new option called 'over', check its demo to see it in action.
jQuery.LocalScroll 1.2.x requires jQuery.ScrollTo 1.3.1 or higher.

Links

Downloads

I really advice using the minified versions. The code is optimized for those releases. Source versions should only be used to learn.


setting up equations for given situations

Nested radicals, smoothness, and simplification

I saw an expression involving a nested radical, namely

\phi = \sqrt{ 1 + \sqrt{ 1 + \sqrt{ 1 + \sqrt{ 1 + \cdots } } } }
.

(Write φ = (1 + φ)1/2 and solve for φ.) The Wikipedia article on nested radicals led me to Simplifying Square Roots of Square Roots by Denesting. The authors tell us that:

The term surd is used by TeX as the name for the symbol √ Maple has a function called surd that is similar to the nth root defined here; like all good mathematical terms, the precise definition depends upon the context. In general, a mathematical term that does not have several conflic! ting definitions is not important enough to be worth learning.

This reminds me of a couple things that happened in my class yesterday. First, I was defining what it means for a curve to be smooth; our definition was that the curve given by the vector function r(t) is smooth if r'(t) is continuous and never zero, except perhaps at the endpoints of the interval over which it's defined. (This makes smoothness a property of a parametrization, which is a bit counterintuitive. I suppose that one could define a curve -- as an abstract set of points -- to be smooth if it has a smooth parametrization. Although I haven't worked it out, I assume that if a curve has a smooth parametrization, the arc-length parametrization is smooth.) One of the students said "but the professor said 'smooth' means something else!" I'm not sure if the professor actually said "smooth means X" or if he said "some people think smooth means X", but i! t's a good point. (In particular, "smooth" often seems to mea! n that a function has infinitely many continuous derivatives.)

Second, the article is about using computer algebra systems to simplify expressions like
\sqrt{5 + 2 \sqrt{6}} = \sqrt{2} + \sqrt{3}

where the left-hand side is "simpler"; sometimes my students worry that they are not presenting their answer in the simplest form. While I'll accept any reasonably simple answer (unless the problem statement specifies a particular form), it is remarkably difficult to define what "simple" means.

One rule I have figured out, though, is that 4x - 4z - 8 = 0 should be simplified to x - z - 2 = 0 by dividing out the common factor. In general, given a polynomial with rational coefficients, one probably wants to multiply to clear out the denominators and then divide by an! y common integer factor of the new coefficients, so the resulting coefficients are relatively prime integers. The article addresses this sort of "canonicalization" in the context of nested radicals. I keep telling my students that they should keep that sort of thing in mind, especially since our tests will be mostly multiple-choice.

(Sometimes I'm tempted to define "simplest" as "requires the fewest symbols"... but how does one prove that some 100-character expression one has written can't be written in 99 characters? And how do you count something like "f(x, y)= (x+y)1/2 - (x-y)1/2, where x = foo and y = bar?" ("foo" and "bar" are supposed to be very complicated expressions.) Do you plug foo and bar into the original equation and then count the characters, or do you count the actual characters that are between the quotation marks?)

polynomial simplifier

Can Flat Plane Carving Have Any Roundness To It ?

One question Iam ask hundreds of times is this question .. Can a flat plane figure have any roundness to its shape ? .. Well lets let the masters of flat plane show us ..
Observe the three carvings below ... They are Axel Peterssons .. Sevens and Harley Refsal .. All master's of flat plane carving .. Now observe the figures closely .. Is there any roundness at all in their work .. The answer is of course there is .. look at the head of the figure in the grey suit .. doesnt his head have roundness ? Is it completely flat in nature ? No ..of course not ... Look at Axel Peterssons figure of the gentlem! an with the cane .. Is his hat rounded at the top ? Yes of course it is ...
So can a flat plane figure have any roundness at all ? YES ! It Can ...
The confusion lies in the term Flat Plane .. So often people associate the term with everything has to be 100 % flat .. no exceptions and thats just not true ..
Flat Plane carving is more a style of carving rather then a absolute term ... The old style carvers had access to few tools and primitive style .. and If you observe the carvings below .. you see a certain style of rough knife work that is the trademark of flat plane carvers .. The large or small flat knife cuts that create the character of the figure in the face and body alike .. And then finishes with little sanding and the knife cuts visible to the observer .. The style is the key .. not the word flat ..
So if anyone tells you .. You cant see any roundness in a flat plane carving .. Tell them the masters work tells different
Gene






plane figures

Current Obsession: Emoticons

Emoticons are graphical or textual representations of the writers' emotion or facial expression because it's so difficult to express your feelings in words. I guess it's acceptable to use emoticons in text messages and while chatting on the internet, but please don't use them in your exams.

Here are some emoticons that you should never use in your exams:

1. Facial expressions:
:) - smiley face
:D - big smile
:{ - guy with mustache
:{> - guy with mustache and beard
XD - smile so much until your eyes can't open
;o)- clown winking at you
>.< - upset about something
(",) - smiling
T___T - I think this means crying
o_0 - shocked

2. There are also emoticons for hand gestures and actions. For example:
\m/ - rock on
..l.. - middle finger
\/ - peace
\\// - the Vulcan salute, live long and prosper
O/\O - two people high five-ing (or Heil Hitler-ing) each other
\O/ - waving! /flailing both arms frantically
~\O/~ - waving/flailing both arms frantically because you can't swim
~^~~\O/~ - waving/flailing both arms frantically because there's a shark chasing you
(`-´)> - salute
(",)> - HL saluting
_| ̄|○ - doggy style/give up/lady doing push ups
>--(^.^)--< - stretching hands out, presumably to hug someone

3. You can use the hand gesture emoticons in conjunction with faces. I like to use a cute cat's face. Here are a few:
=^.^= - cute cat face
A=^.^= - cat praying/putting hands together and apologizing/clapping
\/=^.^= - cat doing the 'peace' sign
\\//=^.^= - cat doing the vulcan salute. LOL, my classmate invented this emoticon
..l..=^.^= - cat giving you the finger
d=^.^= - cat giving you the thumbs up
d=^.^=b - cat giving you two thumbs up/cat wearing earphones

4. Aimster emoticons
These are emoticons that look like Aimster. M! ost of them are derived from the cute cat emoticons that I wro! te about earlier, just change the cat face to the Aimster face
-____- - Aimster face (her face really looks like this)
\_n_(-____-)_n_/ - Aimster flexing her muscles
..l..(-___-) - Aimster giving you the finger
A(-____-) - Aimster praying/putting hands together and apologizing/clapping
\/(-___-) - Aimster doing the 'peace' sign
\\//(-___-) - Aimster doing the Vulcan salute
d(-___-) - Aimster giving you the thumbs up
d(-___-)b - Aimster giving you two thumbs up/wearing earphones
O---\_(-___-)_/^ - Aimster playing badminton, she has a badminton racket in her right hand and a shuttlecock in her left hand
O---\_n_(-___-)_n_/^ - Aimster flexing her muscles while playing badminton
\m/(-___-)\m/ - Aimster doing the 'rock on' sign at a rock concert
*\(-___-)/* - Aimster cheerleading/holding pom poms/holding sparklers
3(-____-)3 - Aimster with 'rambut maggi'
~&~(-____-)~&~ - Aimster with pigtails
0(-____-)0 - Aimster ! with Princess Leia style cinnamon buns/big ears
(-____-)> - Aimster saluting
(-____-") - Aimster sweating
>--(-___-)--< - Aimster with outstretched arms, presumably to hug Jinat (this emoticon was invented by Aimster)

5. Miscellaneous
*\(",)/* - cheerleader. I like this emoticon, a classmate taught it to me
¯\(o_O)/¯ - I don't know
@}-;-`-- - rose
<3 - heart lying on its side
(_l_) - ass
(_x_) - kiss my ass/qin wo de pi gu. I learnt this from boss.

We'll see how long this emoticon obsession lasts. Make sure you don't use these emoticons in your exam. Spread the word.

middle finger smiley text

Play Rags to Riches -Mean, Median, Mode, and Range

Play a game of Rags to Riches with Mean, Median, Mode, and Range.

math mean median

Precalculus problems

Is there anything which seem to be tough these days? I personally feel there is nothing such word called "Impossible". Like for example when we need help in completing our calculus homework, its make within in seconds with the help of internet.

A very interesting example to explain you guys, earlier we use to look around for math tut ions which will help us, look for banners which tells us where we need to go if we need math help. But now its so simple with the help of internet.

Do you know how internet makes it easy for us? We have so many sites which gives us online calculus homework help and makes it easy for us.

Not alone calculus any subject it gives us help. I was looking for solved precalculus answers for ! my sister the other day and i got it within no minutes. Make use of the internet completely and score very good marks in your examinations.

help with precalculus

PASS TAKS Math 5th, 6th, 7th, 8th Blog Welcome!

Welcome to my blog. Bookmark, subscribe to and/or follow this blog because it is updated often with awesome Math links and videos.

Please leave general questions, comments, concerns, and feedback in this post. It will remain at the top of the blog. Please let me know if this blog is helpful to you.



help with math problems

A Guide to Earn GOLD

If you are tired of trying to figure out who to trust, if you are tired of trying to figure out what voice to listen to for guidance, if you are tired of trying to be in the right place at the right time, whatever that means. Explore the world and see all the wonders. Give gold a try. It sounds like it may be right for you. Over the last 10 years gold has outperformed virtually every other investment out there. From stocks to bonds to real estate, there has not been any other investment that not only provides an above average return but also the feeling of security associated with just leaving your money in a savings account. Gold prices here are much worthy. You are assured of the quality and in time the prices will become higher and higher.

Gold is precious, though this time it is not that popular compare to real estate business. Bu! t it is a good business venture; you can earn much on this kind of business. Gold price will eventually go higher and higher as time pass by. A very good investment. Here are the The current five participants who fix the price of gold:

  • Scotia-Mocatta - successor to Mocatta & Goldsmid and part of Bank of Nova Scotia
  • Barclays Capital - Replaced N M Rothschild & Sons when they abdicated
  • Deutsche Bank - Owner of Sharps Pixley, itself the merger of Sharps Wilkins with Pixley & Abell
  • HSBC - Owner of Samuel Montagu & Co.
  • Societe Generale - Replaced Johnson Matthey and CSFB as fifth seat

In our world right now, it’s always ! right to find something you can have in the future. For me GOL! D is the answer.


free online tutoring for algebra

Shout Out To Briana For Joining The Club


double middle finger text

Obstacles

I have not posted anything for a long time. I have finished my freshman year of college. Boy o Boy was it the the toughest year for me. I learned a lot of lessons for example, living with a roommate and handling all my finances. I have never mentioned that I went through foster care at age sixteen until I emancipated. Recently I gave a speech for the Faith in Motion event in my community. It is explained further on page 3 of the link. I received a lot of compliments after I gave the speech. I am so happy that others understood how much I meant each word about the importance of social services. Right now I am going through a big obstacle to pass my current classes. I am glad that I was able to use what I learned in my speech class because the experience boosted my energy to keep going since I never gave up on myself before (pre- and during foster care). It is important to be patient with yourself and also of o! thers. We must understand each other's differences if we are to have peace. My experience in foster care is a long one. I like short and to the point posts so I am going to take time to write a long essay form of my experience in foster care then I will post it to scribd (hopefully it will still be free service) so that my followers could read it (I hope I have a following ). I will post it as soon as it is done. In the mean time I will post more experiences of growth,hardship and of course.... learning.

course compass answers

Math best websites

Math
100th Day Activities
Suggested Activities for 100th Day - Across the curriculum ideas planning the 100th day of school activities.
100th day of school from Delmar, Maryland
The 100th Day of School from A to Z Teacher Stuff
300 Celebration Ideas from Joan Holub
Counting to 100 - worksheet with blanks for students to fill in the numbers
AAA Math - Practice sessions for all types of basic skills such as word and number match, fractions, adding, comparing numerals, and more.
APlus Math - Games, worksheets, flashcards and hidden picture activiti! es using basic math operations.
Beginning Addition - This site is for beginners using most-familiar fingers as manipulatives. Audio announces numeral for reinforcement. Audio reply when numeral is selected for the answer.
Color By Number - Use the correct color to go with the number and create a picture. (numbers 0-5)
ColorCount - Click on the number of animals to match the numeral.
Cool Math has some activities to help parents get their kids ready for Kindergarten. Actually they recommend that these activities be continued grade 1.
Flash Cards - print out and use in your classroom
Fractions - A simple practice for c! hildren first learning fractions. Using fourths, this page demonstrates how the colored section is the key to the top number and the total boxes (4) are the key to the bottom number.
Fractions - lessons teaching beginning fractions.
Fractions - Create your own bar fractions to explain the concept. Use the arrows at the top to add or subtract pieces on the bar.
Fraction Match - match pictures with their fraction counterparts
Daily Graphing Lessons for Kindergarten - Many graphing ideas from Marcia Goudie in CA. This is a Geocities site and may not work through the filters of! some school systems.
ABC List of things to Graph - These are just a few things that teachers and elementary students can use to chart data.Be sure to check the underlined links.
Greater Than/ Less Than - Whole class activity on practicing this concept.
Harcourt School Publishers - (Kindergarten activities to go along with the Math Advantage series) Take a look at their first grade and second grade pages also!
Kindergarten Math Lessons - lessons, activities, worksheets and more
K-1 Math Activities! - activities for young student classified by StandardsMagnetic Numbers - Can you come up with the correct number sentences for these numbers? Unscramble the number sentences in addition, subtraction and multiplication.
Math Lessons - K-1st Grade math lessons, many with technology components
Math Lingo - Play tic tac toe while learning positional words, more, less and many more math terms.
Missing Numbers - worksheet
Money Count - Imagine taking your piggy bank and emptying it out on the floor... well now you can.
Money - Worksheets containing recognition, counting and comparing money.
The Money Page - Multiple links to activities and worksheets dealing with the counting of money.
Number Chart - (interactive 100 number chart) Use this to show number patterns and much more! the chart can be printed
Number Dice - empty template
Number Dice - dice with black dots
Number Dice - dice with white dots
Number Dice - dice with white numbers
Number Dice - dice with black numbers
Number Dic! e - dice with fingers
Number Jigsaw puzzles - print these off for your students.
Number Sheets - Worksheets in Zaner-Bloser style or Dnealian style for each numeral 1-10.
Number Table- Numbers to 100 - print and put on students desk for review
Number Wallcards with fingers - hang up on the wall in your classroom
Number Word Poster - print and put on students desk for review
Ordinals - An online game to practice ordinal numbers up to tenth. First through tenth is written out in words and objects appear. Student is to select ordinal word that corresponds with last object.
Ruler- Using a ruler - (worksheet format) Use a ruler to measure each object and write results.
Shapes - (pre-school) identify shapes and colors
Shapes Poster for Printing - print and put on students desk for review
Silver Burdett Ginn - On-line activities categorized by grade level.
Smiley Clock - Create a face for Smiley Clock by telling the correct time. Tell time by picking one from three choices. The clock gains eyes, nose, mouth and hair if you select the correct time. (2nd grade and higher)
Sorting by Size Activity - An apple game that allows students to match apples to appropriate baskets. (Shockwave required)Sortin g Pumpkins - Good activity for beginning mouse skill drills. Move pumpkins and group according to size or color.
Subtraction - Although this is basically a counting site, introduction to subtraction can be taught here by bringing down a number of spiders then clicking on the button to make them disappear. The number at the corner keeps track of how many are there as you add and subtract spiders!
Tangram Puzzles - Interactive puzzles; tasks that involve virtual manipulatives afford many students an entry into mathematics that they might not otherwise experience
Telling Time - Set the clock and Mr. Clock will tell you the time. (good for beginners)
Time - This site has worksheets that can be printed, but can al! so be used in a total class group, answering the problems as a team. It provides practice on the hour, half hour, quarter hour and minutes.
Time: blank worksheet - let students fill in times dictated
What time is it? - An interactive game practicing the hour and half hour on an analog clock.
Writing Numbers - Shows the strokes to write numbers. Select a number at the bottom to see an animation of the strokes to write a number.

bar graph template for kids

Number Problem 9

This is a algebra number word problem which was asked by a anonymous person in the ask question section which read, "One number is 5 more than another.their sum is 53.what are the two numbers?"


Number Problem 9 Solution Here!


algebra word problem help

The Advanced Algebra Tutor

advanced algebra math  tutor

The Advanced Algebra Tutor is a 7 hour course spread over 2 DVD disks that picks up where the Algebra 2 Tutor DVD ends and continues to teach the student core concepts in Algebra. The material in this DVD is sometimes taught at the end of Algebra 2 and is always taught in College Algebra. Every topic is taught by working example problems that begin with the easier problems and gradually progress to the harder problems. Every problem in taught in step by step detail ensuring that all students understand the content. Read more on next page.
download

algebra tutor free

Finance Problem 1

An anonymous poster recently asked the following algebra finance word problem:

"An employee's new salary is $19,110 after getting a 5% raise. What was the salary before the increase in pay?"



Finance Problem 1 Solution Here





algebra math answers

Solving Simple Linear Equations

A lot of students seem to find it difficult to solve equations. The act of solving equations is all about doing the same thing to both sides of the equation and making sure you end up with the letters on one side and the numbers on the other side of the equation.

For Example:

Find the value of y in these equations:

y + 3 = 10
Subtract 3 from both sides
y = 7

y – 3 = 10
Add 3 to both sides
y = 13

3) 4y + 5 = 21
Subtract 5 from both sides
4y = 16
Divide both sides by 4
y = 4

In the first equation we subtracted 3 because it was + 3. So the general rule is to use the inverse operation.


Solving Linear Equations

Help!

Here's the deal:  I'm working on curriculum for my school and Algebra 2 is making my eyes cross.  I think the major problem is the state of Virginia is in a transition year between "old" Standards of Learning (SOLs), and "new" ones.  This year is supposed to be the year that we're still teaching and assessing the old SOLs, but we're supposed to teach the new ones, too.  Those of you that teach Algebra 2 already know that there's an enormous amount of information to cover in a short period of time.  To give you context, our school teaches it as a semester-long block course.  There's only so much a brain can handle in one day, though! 

Here's the first draft of my skills list and structure...I'm not sure what to do about the old vs. new SOLs (my skills list is based on the old SOLs because that is what will be assessed).

Note:  Gray items are not included in old or new SOLs but might be necessary for student understanding
          Blue items are being taken out of the SOLs starting next year
          Red items are new to the SOLs starting this year

Unit 1 Algebra 1 Review/Solving Equations


1 Solve multi-step equations and inequalities
2 Matrix +/-
3 Solve compound inequalities
4 Solve absolute value equations
5 Solve absolute value inequalities

Unit 2 Polynomial Review/Add Depth

6 Factor trinomial a = 1
7 Factor trinomial a > 1
8 Factor special cases (sum/diff of cubes, diff of squares, perfect square trinomials)
9 Factor out GCF first (factor completely)
10 Exponent rules
11 +/- polynomials
12 Multiply polynomials
13 Divide polynomials

Unit 3 Rational Expressions

14 Identify undefined values
15 Simplify rational expressions by factoring and canceling out common factors
16 Multiply and divide fractions
17 Multiply and divide rational expressions
18 Add and subtract fractions
19 Add and subtract rational expressions
20 Simplify complex fractions
21 Solve rational equations

Unit 4 Radicals, Radical Equations and Complex Numbers

22 Simplify numbers under radical
23 Simplify monomials under radical
24 Multiply and divide radicals
25 Add and subtract radicals
26 Nth roots to rational exponents and vice versa
27 Simplify expressions with nth roots and rational exponents
28 Solve radical equations
29 Simplify square roots with negative terms inside radical using i
30 Add and subtract complex numbers
31 Powers of i
32 Multiply complex numbers

Unit 5 Functions (intro)

33 Domain and range of relations (from ordered pairs, mapping, graph, table)
34 Identify relations that are functions and one-to-one
35 Given graph and a value k, find f(k)
36 Given graph, find zeros
37 Given graph and a value k, find where f(x)=k

Unit 6 Linear Functions


38 Slope from graph, equation, points
39 Graph from equation
40 Equation from graph
41 x- and y- intercepts
42 Determine whether lines are parallel, perpendicular, or neither from equation or graph
43 Write equations for parallel and perpendicular lines given line and point off the line
44 Graph linear inequalities

Unit 7 Systems


45 Solve systems of equations by graphing
46 Multiply Matrices using a graphing calculator
47 Inverse matrix method of systems
48 Systems of equations word problems
49 Graph systems of linear inequalities
50 Linear programming max/min problems

Unit 8 Functions (reprise)

51 Function math (addition, subtraction, multiplication, division)
52 Function composition, find a value i.e. f(g(3))
53 Function composition, find the function i.e. f(g(x))
54 Find an inverse function by switching variables

Unit 9 Quadratics

55 Graph from vertex form, identify max/min and zeros
56 Solve by factoring
57 Solve by Quadratic Formula (including complex solutions)
58 Determine roots using the discriminant
59 Write equation for quadratic given roots
60 Quadratic systems
61 Polynomials: relating x-intercept, zeroes and factors
62 End behavior for polynomials

Unit 10 Exponential/Logarithmic functions

63 Exponential growth or decay from function
64 Sketch base graph of exponential/log functions
65 Exponential to log and vice versa
66 Data analysis/curve of best fit for linear, quadratic, exponential and log

Unit 11 Transformations and Parent Functions

67 Graph absolute value functions
68 Horizontal and vertical translations of linear, quadratic, cubic, abs value, exponential and log
69 Reflections and stretching of linear, quadratic, cubic, abs value, exponential and log
70 Combinations of transformations on parent functions
71 Identify parent graphs of parent functions
72 Identify equations of parent functions

Unit 12 Conics

73 Identify a conic from graph
74 Identify a conic from equation

Unit 13 Variations

75 Write equation for direct, inverse and joint variation problems
76 Find the constant of variation

Unit 14 Sequences/Series

77 Write n terms of an arithmetic sequence
78 Find the sum of a finite arithmetic series
79 Write n terms of geometric sequence
80 Find sum of geometric series
81 Use formulas to find nth term
82 Identify sequence/series as arithmetic, geometric or neither

Unit 15  Statistics

83 Determine probabilities associated with areas under the normal crve
84  Compute permutations and combinations

 
If you made it this far, here's my call for help:  Anyone have advice/suggestions for how to make this work and/or a better way to organize the information into cohesive units that seem to occur in a somewhat logical order?  There is and will continue to be an emphasis on function families and transformations (as there should be).  I find it difficult to express on paper how each function category needs to be a resting place, but they are all connected in the ways that transformations apply.  Any ideas?
 
...oh...and I'm going to be teaching one section of deaf students and one section of blind students...in case that makes a difference

**edit:  I've added links to the old and new Virgina SOLs for Algebra 2 if anyone's interested**

Rational Expressions and How to Simplify Expressions

Week as of May 17th to May 21st

This week we will continue working with Polynomials. Adding, Subtracting, Multiplying and Dividing.
Students will be given review packet so they can review what we covered during 7th grade.
We will be making our ITBS exams from the 18,19 and 20th so I will not be able to meet with some of the class sections. I strongly recommend to visit the blog to check your daily assignments.
Thursday May 20th Pre-Algebra Test 7-3
Friday May 21st Pre-Algebra 7-1, 7-2, 7-4
Have a wonderful week!!!!!!

Pre algebra two step equations

statistics - standard normal curve


Download: Statistics_Normal_Distribution.zip

This sketch can be used to discuss various aspects of the normal curve. Normal curves have a specific nature to them that is brilliantly captured by Sketchpad. Every combination of Mean (mu) and Standard Deviation (sigma) yields a graph with the same area, and this sketch provides a look at the changes that take place in order to satisfy such a constraint. The calculations of area were made ! using trapezoidal estimates and summed iteratively as described in Sketchpad's sample calculus sketches. There are four pages: Normal Distribution with sliders, Standard Normal Distribution with z-scores, Confidence Intervals, and Standard Normal Distribution with a calculation of the shaded region corresponding to P( a < Z < b ).

Keywords: normal distribution, normal curve, N(0,1), mu, sigma, mean, standard deviation, z-score, probability, density curve, standardize, standard normal, normal random variable, confidence interval, CI, z*, statistics

Normal to the Curve

Logarithms and Ropes (as found in Mathematician's Delight)

I recently got a copy of Mathematician's Delight, by W. W. Sawyer. I had loved his book Vision in Elementary Mathematics, so I knew I'd like this one. I found out about it through a blog I stumbled upon in my wanderings, where the blogger included this:*
Nearly every subject has a shadow, or imitation. It would, I suppose, be quite possible to teach a deaf ... child to play the piano. ... [The child] would have learnt an imitation of music, and would fear the piano exactly as most students fear what is supposed to be mathematics.

What is true of music is also true of other subjects. One can learn imitation history - kings and dates, but not the slightest idea of the motives behind it all; imitation literature - stacks of notes on Shakespeare's phrases, and a complete destruction of the power to enjoy Shakespeare.
I think that idea, of a shadow subject, will stick with me, and become more powerful for me over time.


Logarithms
I've told my students Logarithms were invented in a time when calculators didn't exist, and scientists were looking at lots of data about the planets, trying to discover patterns. Napier invented a way to do multiplication by adding and division by subtracting, a second application of which allows powers and roots to also become questions of addition and subtraction. I don't think this is enough of an introduction to this strange concept.

How did Napier dream this up? Sawyer gives us a glimmering of the sort of inspiration Napier might have had, with this marvelously concrete model for Logarithms:
We are all familiar with machines which [we] use to multiply [our] own strength - pulleys, levers, gears, etc. Suppose you are fire-watching on the roof of a house, and have to lower an injured comrade by means of a rope. It would be natural to pass the rope round some object, such as a post, so that the friction of the rope on the post would assist you in checking the speed of your friend's descent. In breaking-in horses the same idea is used: a rope passes round a post, one end being held by a person, the other fastened to the horse. To get away, the horse would have to pull many times harder than the man.

The effect of such an arrangement depends on the roughness of the rope. Let us suppose that we have a rope and a post which multiply one's strength by ten, when the rope makes one complete turn. What will be the effect if we have a series of such posts? A pull of 1 pound at A is sufficient to hold 10 pounds at B, and this will hold 100 pounds at C, or 1000 pounds at D.

Thus, 108 will represent the effect of 8 posts. ... The number of turns required to get any number is called the logarithm of that number. ... So far we have spoken of whole turns. But the same idea would apply to incomplete turns. ... Accordingly, 101/2 will mean the magnifying effect of half a turn. ... The logarithm of 2 will be that fraction of a turn which is necessary to magnify your pull 2 times. (page 70)

I had to put the book down here, to ask myself why half a turn wouldn't magnify the pull 5 times - half of ten. As I thought about that, I wanted to know if there would be an easy way, either a thought experiment or a very simple physical experiment (i.e., no special equipment), to prove that this relationship must be multiplicative. That is, how do we know the friction of the rope doesn't just add to our pulling force, so that a certain amount is added at each turn? (Can anyone help me with this?)

If we've decided that the relationship must be multiplicative, then we know that two half turns must multiply to have the effect of one whole turn, and that would mean we need the number that multiplied by itself gives ten. To get to this thought, I had to imagine two posts near one another, with the rope halfway around one, and then halfway around the next.

Why haven't I seen this before?!

I haven't read any more of the book yet, because I keep needing to think more about this cool idea. I look forward to more pedagogical delights as I keep reading this book, and maybe others he wrote. (One list is at the bottom of this page.)



___
*W. W. Sawyer wrote this book in 1943, long before feminists began to analyze the effect of using the male for the generic. Although Sawyer uses 'man' and 'he' in a generic sense in other sections (which I've taken the liberty of changing in the second quote I've used), perhaps he was trying to avoid that in this story by calling the deaf child of his music example 'it'. I had real trouble with that, and didn't know how to fix it without messing with his meaning, so I left the meat of the example out. You can go here to see it.

Logarithms

Simplifying Radical Expressions

My Algebra I students are having lots of problems with simplifying radical expressions. It seems that they have run across a concept that eludes them. I am posting about this topic to provide several more examples.

√18

First, we find the prime factorization of 18. If you need help with this concept, go here.

√18 = √(2•3•3)

Since the 3 is repeated twice, we can pull it out from under the square root symbol. Therefore,

√18 = 3√2

Now my students would be asking what happens if you have variables?

√24x3y2

√24x3y2 = √(2•2•2•3•x•x•x•y•y)

Pull out everything that is repeated twice - 2, x, y. Leave everything else under the radical symbol.

2xy√(6x)

! Some other places to visit for more details on this concept are here and here and here.

If you are one of my students and would like some extra credit, please visit those sites and comment here on whether or not they were helpful.

How to simplify radicals with variables

Help!

Here's the deal:  I'm working on curriculum for my school and Algebra 2 is making my eyes cross.  I think the major problem is the state of Virginia is in a transition year between "old" Standards of Learning (SOLs), and "new" ones.  This year is supposed to be the year that we're still teaching and assessing the old SOLs, but we're supposed to teach the new ones, too.  Those of you that teach Algebra 2 already know that there's an enormous amount of information to cover in a short period of time.  To give you context, our school teaches it as a semester-long block course.  There's only so much a brain can handle in one day, though! 

Here's the first draft of my skills list and structure...I'm not sure what to do about the old vs. new SOLs (my skills list is based on the old SOLs because that is what will be assessed).

Note:  Gray items are not included in old or new SOLs but might be necessary for student understanding
          Blue items are being taken out of the SOLs starting next year
          Red items are new to the SOLs starting this year

Unit 1 Algebra 1 Review/Solving Equations


1 Solve multi-step equations and inequalities
2 Matrix +/-
3 Solve compound inequalities
4 Solve absolute value equations
5 Solve absolute value inequalities

Unit 2 Polynomial Review/Add Depth

6 Factor trinomial a = 1
7 Factor trinomial a > 1
8 Factor special cases (sum/diff of cubes, diff of squares, perfect square trinomials)
9 Factor out GCF first (factor completely)
10 Exponent rules
11 +/- polynomials
12 Multiply polynomials
13 Divide polynomials

Unit 3 Rational Expressions

14 Identify undefined values
15 Simplify rational expressions by factoring and canceling out common factors
16 Multiply and divide fractions
17 Multiply and divide rational expressions
18 Add and subtract fractions
19 Add and subtract rational expressions
20 Simplify complex fractions
21 Solve rational equations

Unit 4 Radicals, Radical Equations and Complex Numbers

22 Simplify numbers under radical
23 Simplify monomials under radical
24 Multiply and divide radicals
25 Add and subtract radicals
26 Nth roots to rational exponents and vice versa
27 Simplify expressions with nth roots and rational exponents
28 Solve radical equations
29 Simplify square roots with negative terms inside radical using i
30 Add and subtract complex numbers
31 Powers of i
32 Multiply complex numbers

Unit 5 Functions (intro)

33 Domain and range of relations (from ordered pairs, mapping, graph, table)
34 Identify relations that are functions and one-to-one
35 Given graph and a value k, find f(k)
36 Given graph, find zeros
37 Given graph and a value k, find where f(x)=k

Unit 6 Linear Functions


38 Slope from graph, equation, points
39 Graph from equation
40 Equation from graph
41 x- and y- intercepts
42 Determine whether lines are parallel, perpendicular, or neither from equation or graph
43 Write equations for parallel and perpendicular lines given line and point off the line
44 Graph linear inequalities

Unit 7 Systems


45 Solve systems of equations by graphing
46 Multiply Matrices using a graphing calculator
47 Inverse matrix method of systems
48 Systems of equations word problems
49 Graph systems of linear inequalities
50 Linear programming max/min problems

Unit 8 Functions (reprise)

51 Function math (addition, subtraction, multiplication, division)
52 Function composition, find a value i.e. f(g(3))
53 Function composition, find the function i.e. f(g(x))
54 Find an inverse function by switching variables

Unit 9 Quadratics

55 Graph from vertex form, identify max/min and zeros
56 Solve by factoring
57 Solve by Quadratic Formula (including complex solutions)
58 Determine roots using the discriminant
59 Write equation for quadratic given roots
60 Quadratic systems
61 Polynomials: relating x-intercept, zeroes and factors
62 End behavior for polynomials

Unit 10 Exponential/Logarithmic functions

63 Exponential growth or decay from function
64 Sketch base graph of exponential/log functions
65 Exponential to log and vice versa
66 Data analysis/curve of best fit for linear, quadratic, exponential and log

Unit 11 Transformations and Parent Functions

67 Graph absolute value functions
68 Horizontal and vertical translations of linear, quadratic, cubic, abs value, exponential and log
69 Reflections and stretching of linear, quadratic, cubic, abs value, exponential and log
70 Combinations of transformations on parent functions
71 Identify parent graphs of parent functions
72 Identify equations of parent functions

Unit 12 Conics

73 Identify a conic from graph
74 Identify a conic from equation

Unit 13 Variations

75 Write equation for direct, inverse and joint variation problems
76 Find the constant of variation

Unit 14 Sequences/Series

77 Write n terms of an arithmetic sequence
78 Find the sum of a finite arithmetic series
79 Write n terms of geometric sequence
80 Find sum of geometric series
81 Use formulas to find nth term
82 Identify sequence/series as arithmetic, geometric or neither

Unit 15  Statistics

83 Determine probabilities associated with areas under the normal crve
84  Compute permutations and combinations

 
If you made it this far, here's my call for help:  Anyone have advice/suggestions for how to make this work and/or a better way to organize the information into cohesive units that seem to occur in a somewhat logical order?  There is and will continue to be an emphasis on function families and transformations (as there should be).  I find it difficult to express on paper how each function category needs to be a resting place, but they are all connected in the ways that transformations apply.  Any ideas?
 
...oh...and I'm going to be teaching one section of deaf students and one section of blind students...in case that makes a difference

**edit:  I've added links to the old and new Virgina SOLs for Algebra 2 if anyone's interested**

How to simplify radicals with fractions

Basic Information related to GATE Exams

..........................................................................................................................................................................
Graduate Aptitude Test in Engineering (GATE) is an all-India examination administered and conducted jointly by the Indian Institute of Science and seven Indian Institutes of Technology on behalf of the National Coordinating Board - GATE, Department of Education, Ministry of Human Resource Development (MHRD), Government of India. The GATE committee, which comprises of representatives from the administering institutes, is the sole authority for regulating the examination and declaring the results. GATE is conducted through the constitution of eight zones. The zones and the corresponding administrative institutes are:
Zone 1 - Indian Institute of Science Bangalore
Zone 2 - Indian Institute of Technology Bombay
Zone 3 - Indian Institute of Technology Delhi
Zone 4 - Indian Institute of Technology Guwahati
Zone 5 - Indian Institute of Technology Kanpur
Zone 6 - Indian Institute of Technology Kharagpur
Zone 7 - Indian Institute of Technology Madras
Zone 8 - Indian Institute of Technology Roorkee

Admission to postgraduate programmes with MHRD and some other government scholarship/assistantship at engineering colleges/institutes in the country are open to those who qualify through GATE. GATE qualified candidates with Bachelor's degree in En! gineering/ Technology/ Architecture/ Pharmacy or Master's degr! ee in an y branch of Science/Mathematics/Statistics/Computer Applications are eligible for Master/Doctoral programmes in Engineering/Technology/Architecture/Pharmacy as well as for Doctoral programmes in relevant branches of Science. To avail the scholarship, the candidate must secure admission to such a postgraduate programme, as per the prevailing procedure of the admitting institution. GATE qualification, however, is not required for candidates with Master's degree in Engineering /Technology/Architecture/Pharmacy, who may be seeking scholarship/ assistantship for relevant doctoral programmes.

Some institutions specify GATE as the mandatory qualification even for admission of self-financing students to postgraduate programmes. GATE qualified candidates are also eligible for the award of Junior Research Fellowship in CSIR Laboratories and CSIR sponsored projects. Some government organizations prescribe GATE qualification as a requirement for applying to the post of a Scie! ntist / Engineer.
.........................................................................................................................................................................

continuity differentiability

Application of Derivatives

On Friday, our class started talking about the application of derivatives. To start off, Mr. K showed us this slide:


Mr. K then asked us when was the car moving fastest. The class decided that the car was moving fastest during t2, because the slope of the tangent line was the steepest at that point. During the interval [t1,t2], it is clear that the car is speeding up during that interval because the slope of the tangent lines are getting steeper going from t1 to t2. The car is definitely slowing down on the interval [t2,t3] as we can see that the slope of the ! tangent lines are decreasing.



Now this was a tough graph to decipher. The AP Calculus students had no problem understanding this one, but to those of us who aren't taking AP, this was kind of difficult. I myself found it quite confusing at first, but after clarification, I understand it. Now, you have to find the derivative of f in this graph to find out where is f ' is positive. First we have to find out where the tangent lines in f are zero. Looking at the ! function f, we can cl! early se e that the tangent lines are zero in -2 and +2. This means that f ' will have roots at -2 and +2. Then, we look when the tangent lines of f are approaching zero. There are 2 instances in this graph. The first instance is from (-∞, -2]. The slope from that domain is increasing, since it's coming from a negative value to zero. But that still doesn't solve our problem since f ' is still negative at that point. Then, from (-2, 2) in f, we can see that the slope is increasing until (0,0) and it starts to decrease until it reaches (! 2,3), where it becomes zero. At this point, f ' is positive as the slopes of the tangent lines from (-2, -1) to (0,0) are increasing from zero and reaches its maximum at (0,0), and then it starts to decrease from (0,0) until it reaches (2,3) where the slope is zero. This then solves the first question which asks where is f ' positive, which is from (-2, o) to (2,0).

Now to find out where f '' is positive. From the graph, we can see that f is some kind of a cubic function, so we know that its derivative will be a quadratic function. Now, the derivative of a quadratic function is a straight line, so now we know that f '' is a straight line. Looking at the shape of f ' (say it is -2x2), it is definitely a negative quadratic function because it has a maximum, not a minimum. We then h! ave to find out the derivative of f '' which is represented as -2x2 (However, it IS NOT -2x2, it's just a representation). Using the power rule, we can determine that the derivative of f ', which is f '', is -4x. From this we can see that the function is positive at quadrant 2.

The critical numbers (which is another term for the roots) of f are -2 and 2.


This is a little difficult...
For a! ), f is increasing w! herever f ' is positive.
For b), f(0) is negative.

Well, that was all we talked about last class. Mr. K tried to squeeze in one more slide but we ran out of time.

The next scribe is Kristin.

problems on application of derivatives

Catia v4 questions


 

  1. What does '/CLN' command do?
  2. What do you mean by 'cold start' and 'warm start'?
  3. Name any 5 licenses of CATIA?
  4. Name any 2 Translators in CATIA?
  5. How do you see more than one model simultaneously (in one screen)?
  6. What is the procedure and/or how do you 'renumber'?
  7. What is the difference between tangent continuity and curvature continuity?
  8. How do! you grab a picture from main window?
  9. What is the difference between AUXVIEW and AUXVIEW2?
  10. What is DETAIL?
  11. What do you (or how do you) do hatching in drafting?
  12. How do you draw centrelines of circle in draft?
  13. What are (/is) the tools used to capture 2D-3D models?
  14. How do you parameterize the geometry in your model?
  15. What is 'PARTEDITOR'?
  16. What is 'skin'? How so you create?
  17. Does (/will) geometry constraining in sketcher help in parameterizing?
  18. What is the command for creating thin walled solids?
  19. What is the difference between SURF1 and SURF2?
  20. Name any 3 methods of creating 3 points curve?
  21. What is the difference (/what does this command do) LIM2+SURF+extrapolate and SURF+GEO+ extrapolate?
  22. Give any 3 functions of FORMTOOL?
  23. How do you give skin command?
  24. What is 'LAW'?
  25. Name any 3 functions of LIM2?
  26. What is 'spine'?
  27. What is '/anadia'?
  28. What is the full form of NURBS?
  29. What does BLENDSURF do?
  30. Give any 2 (or what are the) functions of UTILITY?
  31. What is 'INTERFER'?
  32. If given die direction how will you check minimum draft angle in the SURF (surface) model?
  33. What checks will you perform between surfaces with common boundary?
  34. What is the differ! ence bet ween '*role' file and '*save' file?
  35. Can data be model history be exported between 2 different CAD systems?
  36. What is 'FTRCLASS' command?
  37. Which module is used for surfacing with history in CATIA?
  38. What is Class 'A' Surfaces?


 


 


 

A1_Q2-060804


 

1) /CLN- This is the Cat Clean command used to clean the model for any unwanted geometery and to pack the model to compress the size of the model.


 

2) COLD START means it will start the CATIA workwindow in the normal way, whereas WARM START means if your system closed abruptly, without saving, it will start from that particular file in which you were working, maybe with some loss of data.


 

3)ADD,FREE FORM DESIGN,SPA,SHIP DESIGN,AERO SPACE


 

4)IGES,VDAFS


 

6)We renumber with the command Identity

Identity-------> Renumber


 

7)Tangent Continuty is the surface will be tangent to the existing surface, whereas curvature continuty means surface will follow the curvature of the curve.


 

8)go to tools + screen grab and select the area.


 

9)AUXVIEW is used to create/modify the frames of different views, whereas AUXVIEW2 is used to create the views.


 

10) Detail function is used if you have a assembly to create, and there are some common parts in different locations, then you can create a detail and use it in the master workspace wherever needed.


 

11) For doing hatching go to PATTERN+SELECT+HATCHING then select the boundary of the required view till you get the symbol \"c\", then press \"YES\" twice.


 

12) For creating centerlines of circles in draft, first you can select POINT+LIMITS ! and select the circle; you will get the center point. And then select LINE+HORIZONTAL+Symmetrical; you will get the horizontal line; and then Select LINE+VERTICAL+Symmetrical, you will get the vertical line.


 

14) Auxview2+USE in the popup window; select Parameter Tab, and you can do the parameterization, whatever you want.


 

15)PARTEDITOR is the history of all the work you have done, and you can use the parteditor to change and update the solid.


 

16)For creating SKIN, first you need the faces; once you have faces then you can select LIMIT2+CREATE+SKIN and select the faces from which you want to create skin. Everytime you select the face it should be the adjacent face which you have selected earlier, and the! y will be merged together. Once all the faces are selected the! n press \"YES\" twice; the skin is created. Now you can use this SKIN to create the solid.


 

19)SURF1 is used for the planner curves, whereas SURF2 you can use for the intricate curves where you need the tangency constraints and curvature constraints.


 


 


 


 

1) Name any 3 methods of creating a 3 point curve?

Ans:    1) Functions Arc, Spline, Curve2+Circle+ThreePT


 

2) What is the difference (/what does this command do) LIM2+SURF+EXTRAPOLATE AND SURF+GEO+ EXTRAPOLATE?

Ans:    2) Lim2 w! ill extend an existing surface (a percentage of the original length) and attempt to maintain curvature. Use with care because the theoretical extension loses accuracy over distance. Surf+GeoExtra will create a surface extension that is linear and tangent to the existing surface at a given length (it also offers the option to concatenate the two surfaces). Isoparms may be distorted using this process.


 

3) Give any 3 functions of FORMTOOL?

Ans:    3) Filleting of skins, limiting of skins and offseting of skins.


 

4) How do you give the skin command?

Ans:    4) Too vague to answer.


 

5) ! What is "LAW"?

Ans:    5) Laws are used to add precise control to surfaces created with Surf2. Radius, Area, Angle and Parameter values can be specified.


 

6) Name any 3 functions of LIM2?

Ans:    6) Creation of faces and volumes. Also used for surface breaks and concatenates. Other uses as well.


 

7) What is "spine"?

Ans:    7) A Spine is the \"backbone\" or support for a Surf2 surface. It dictates the orientaion of a surface as it relates to generating curves.


 

8) What is "/anadia"?

Ans:    8) Anadia is an analysis tool that allows you to save and update specific analysis processes. Used mainly for surface analysis.


 

9) What is the full form of NURBS?

Ans:    9) Too vague to answer.


 

10) What does BLENDSURF do?

Ans:    10) Blensurf allows you to create curvature continous (class A) fillets relatively easily.


 

11) Give any 2 (or what are the) functions of UTILITY?

Ans:    11) Many Utility functions. Commonly used to import and export CATIA files. Also used to process IGES and STEP file formats.


 

12) What is "INTERFER"?

Ans:    12) Another analysis tool.


 

13) If given die direction, how will you check minimum draft angle in the SURF (surface) model?

Ans:    13) One way is to use the Tools pull down menu and select Analyze+Draft (you must also indicate a direction and which elements to be analyzed). Moldpart can also do this along with many other cool bells and whistles (it helps you design the draft surfaces). There are other ways to check drafts as w! ell.


 

14) What checks do you perform between surfaces with common boundaries?

Ans:    14) Continuity of connection, tangency and curvature mainly.


 

15) What is the difference between a "*role" file and a "*save" file?

Ans:    15) These are files created by CATIA in order to maintain a temporary version of the files in use. If CATIA were to crash, a warm start would try to access these files to re-establish your CATIA session.


 

16) Can data model history be exported between 2 different CAD systems?

Ans:  ! ; & #160;16) It depends on which two systems are being used. V4 models, unless you are sending them to V5, usually have their history stripped from the model.


 

17) What is the "FTRCLASS" command?

Ans:    17) Used to create solid features that can be stored and accessed from a library. Used in conjunction with the Param3D function.


 

18) Which module is used for surfacing with history in CATIA?

Ans:    18) Sorry on this one. I can't remember the designation as I use AL3 (basically, everything).


 

19) What are Class "A" Surfaces?

Ans:    19) Surfaces that when connected have tangent and curvature continuous properties with their adjoining surfaces. Example: the curvature value along the boundary of Surface A matches the curvature value of the adjacent boundary of Surface B. This is the simplest explanation.


 

20) What is a "Layer"? What is the use of it? And how do you create Layers?

Ans:    20) Think of layers as transparencies on an overhead projector (in the old days before Powerpoint). Different categories of objects can be assigned to various layers. Then you create Filters which instruct CATIA to display only those layers you wish to see at a given point in time.


 


 


 

J ust some Answers………………………. If it helps,


 

  • Four arcs.
  • CRV or Curves is that curve which is continous in curvature and tangency.

CCV or Composite curve is that curve which is a combination of more than one curve and is not continous in curvature and tangency.

  • The hiearchy of making a complex solid design is: Freefirm Surface (Face, Surface, Skin)

|

                  &! #160;                  |

                                     Closed volume

                                     |

                                     |

      !  &# 160;                             Solid


 

  • Face --- *fac, Surface ---- *sur, Volume------ *vol, Skin--- *ski, Draw axis---- *axd, Dittos-----*dit, Curves----*crv.


 

  • Volume element is the collection of the surfaces (faces, surfaces, skin) placed next to each other such that they form a closed space or volume.


 

  • ALPHA-numeric winodow :- alt+


 

  • A face bounded by lines and curves on a plane is known as planar face.


 

    A face created from ! surface may or may not be planar depending upon the shape of surface.


 

  • SURF1 function helps in creating simple individual building surface shapes. i.e they are of definite shape that can be represented by mathematical equations.


 

    SURF2 function helps in creating complex shape using different conditions available. It can not be represented by mathematical equations.


 

  • A functional surface is the surface of the solid.
  • Surface element is represented in CATIA by * sur and the isoparametric curves(optional)
  • surface model are created out of the surface by various methods like offset, ..........


 

    S! olid mod els are created out of simple indivisual building blocks or regular shaped solids like PRISM, CYLINDER, CUBE, CONE, PYRAMIDS etc.


 

  • Smoothness of surface can be checked by TOOL+ANALYSE+CURVATURE.


 

    three colour comes up on the surface GREEN------>smooth surface. BLUE & RED ----->not smooth surface indicating depression at that region


 

  • Connect---> It is the surface fillet created between the two surfaces(face, skin, or surface)


 

    Corner---> It is the surface fillet created at the corner created by three surface (face, skin or surface) meeting each other.


 

  • Surfaces---> It is a support which include used portions to be machined as faces.


 

    Faces---> They are the planes or surfaces bound by lines and curves

    Skins----> It is the collecton of freeform surfaces (face, or surface) which are placed next to each other.


 

  • SPINE - indicates the direction of surface formation.
  • LAW is the function used to define a condition for creating a surface.

    LAW is a defined values along a curve or surface for the surfaces to be formed under different operations.


 

The different types of LAW's a! re:-

1)! 0;    Radius law- to draw variable fillet.

2)    Area law - to define area of the surface element.

3)    Angle law - to draw variable angle while sweeping a contour over a spine.

4)    Param - To define parameters.


 

  • The CONNECT & CORNER under SURF1 functions are used for filleting surfaces.


 

    CONNECT is used for filleting at a command edge of surfaces.

    see fig. page9

    CORNER is used for filleting at a common vertex of the surfaces.

    see fig. page9


 

  • Master Workspace is the default workspace which is displayed when CATIA is started. The main design and modelling is carried out in this space.

    A master Workspace is the space in which the main modelling is done or the initial workspace when CATIA is started.

    Additional workspace can be created by clicking WSP icon in the tool pallete and giving user defined names. This can also be defined workspace under DETAIL function.


 

    Additional workspace can be created by following this methods

    DETAIL+CREATE+W.SP! ACE

 &! #160; 60; followed by keying some name.

    We can switch to the additional workspace on the master workspace by following methods:

i)    Click on workspace present on tool bar

ii)    enter to get the list of workspace available

iii)    Select the workspace required

iv)    close the workspace list box.


 

  • whenever a particular body occures in the modelling several time, instead of creating each time, it is better to create in DETAIL workspace and copy it into the master workspace to wherever necessary.


 

    There are two way of doing it:-

i)    DITTO---> It copies the detail to the master workspace. The changes made on this solid in DETAIL workspace is reflected on the master workspace i.e those solids are associated.

ii)    COPY---> Here the change made in the DETAIL workspace is not reflected on the master workspace. i.e they are isolated from each other.


 

    [ The DITTO under detail function, the modification made on DITTO is reflected in the main model where it is used, but in the case of copy under DETAIL function only the DITTO is changed for corresponding modification and not the DITTO copied in the main model.]


 

  • Extens! ion of assembly file - .asm
  • Different constraints in assembly:

The constraints available are:-

    i) Axis coincident constraint.

    ii) Surface contact constraint.

    iii) Surface offset constraint.

    iv) Angular constraint.

    v) Snap constraint.


 

  • AUXVIEW                    

    i) The changes made are automatically |

    updated                    |

                        |

    ii) The views shows the hidden lines

  •     AUXVIEW2

i) It needs updation.

            | ii) The views does not show the hidden lines.

            


 

  • When AUXVIEW2+DROP [command is given for a view, it loses all its links with the parent model and in future cases, whenever any modification done on the parent model cannot be updated on the earlier dropped views)command is used on any view, it get completly isolated from the solid model in the space mode.


 

    No command works on it except the delete function


 

  • SURF1 function is used for creating canonic surfaces or simple surfaces.

    eg:- Ruled surfaces, Cylindrical surfaces, Spherical surfaces etc...


 

    SURF2 function is used to create complex freedorm surfaces.


 

  • A! functional surface is a surface extracted from a solid to manipulate the model.
  • Surface element in CATIA is represented by isoparams along and across the boundary of the surface element.


 

  • Surfaces are closed boundary elements with out any holes in between.

    Faces are superform of surfaces which may or maynot have holes inside it.

    Skin is a combination of adjacent faces.


 

  • The smoothness of a surface is checked by analysing the curvature and tangent continous of the surface. The curvature & tangency of surface analysed will have the following options.


 

    1)the boundries between sur! face are not joined, then the surface are not tangent continous.

    2)


 


 

  • Surface degree is the measured along and across the surface element. i.e along 'u' and 'v' directions.


 

    the surface degree denotes the oscillations and smoothss of the inside surface curves.


 

  • Featured based design is the design based on the company's customisation of product feature and [arameters.
  • SOLIDM - SOLID MOCK-UP:- This is an approsimate solid and was used in the earlier version of CATIA.
  • SOLIDE - EXACT SOLID:- As the name indicates, the solid formed are exact fulfill! ing all the conditions defined by the user.


 

  • A constraint element in CATIA is one in which the parameters of the element cannot be changed.
  • Local function window is an window consisting of the follwing sub. functions


 

1)STD - This is used to check the visualisation of the partmodel by checking on/off for the sections

2)2D - Settings for draw mode & space 2D

3)3D - Settings for space 3D mode

4)COL - Setting the colour of the background.

5OFF - To come out of local function window.


 


 


 

1. ! 60;   What is the difference between point/int ! lim-on a nd lim-off?


 

    lim-on: Creates the point by intersection & Projection can be done

    with in the limits of the Selected elements.


 

    Lim-off: Creates the point by intersection & Projection can be done

    Outside the limits of the Selected elements.


 

2.     What is the difference between surf1/geo extra and limit2/extrapol?


 

    Geo-extra: extrapolates a new surface which is in the form of ruled

         Surface.

    Extrapolate: creates non-ruled surface thus changing original surface

         Definition.


 

3.    &#! 160;What is the use of formtool function?


 

    Used to:

    a. to connect skin(or face) elements - connect

    b. to relimit skin(or face) elements - relimit

    c. to break skin(or face) elements - break


 

4.    What is the difference between face, surface and skin?


 

    a. Faces are infinitely thin elements that represent the bounded exterior

     defn. of a part. Faces can be planar or built on existing surfaces.


 

    b. Skin are infinitely thin elements that are incorporate or group a series

     of faces together to completely define a feature of part.


 

    c. S! urfaces are infinitely thin elements that are used to define a! bounded

     contour in space. Surface is parent.


 

5.     What is hlr and nhr explain?


 

    Hidden line removal

    No hidden line removal

    Purpose : Visualisation of solids in different modes.


 

6.    What is the difference between isolate and separate?


 

    Isolate: Deletes logical links between elements.

    Separate: Separates lines , curves & faces from their links with other

     elements ex: A curve is considered as separate when it is linked

     to only one surface.


 

7.    Is it possible to change pattern as required to exis! ting pattern?


 

    Yes


 

8.     What is the difference between parametric and nonparametric modeling?


 

    a. Relational model is parametric. i.e. one to one relation.

     If any change in dimension that may reflects on other dimensions.


 

    b. Developing a solid by using surface, face, solid primitives etc.,

     There is no one to one relation.


 

9.     Which is the better to split the solid a) surface b) plane c) face?


 

    Plane


 

10.     What is the difference between spine and spline?


 

    a. Spine: Creates a ! curve passing thro' point on a plane & normal to

!

&# 160;    one or more other planes.


 

    b. Spline: Creates a curve passing thro' several points having tangential

     & curvature contuinuity.


 

11.     How you will delete the surface if the face is created by surface?


 

    First erase face & then surface.


 

12.    What are master w/s and detail w/s?


 

    Master w/s: Model w/s

    Detail w/s: We can have any no. of detail w/s, that can be called in

    model w/s.


 

13.     What is difference between curve1 project and combine?


 

    Project: Perpendicular projecti! on of a curve on to plane, surface, face

etc,.

    Combine: Unspecific projection of a curve on to plane, surface, face etc,.


 

14.     Is it possible to split by using sewing operation


 

    Yes


 

15.     Diff. b/w surf1 connect & surf2 fillet


 

    Connect: Creates a fillet surface that connects two existing surfaces,

    Planes, or planar faces.

    Fillet: Creates a fillet surface that connects two existing surfaces,

    Planes, or planar faces using spine.


 

16.     What is functional surface


 

    A FSUR is an element that defines a fac! e on a solid. The displayed in

  &! #160; 60;non-hidden mode.


 

17.     Purpose of IUA


 

    IUA: Interactive users application, used to customize the CATIA users

command.


 

18.     How you will convert ccv into crv


 

    Using limit1 è Appr ccv

    i.e., Approximate compound curve or composite curve.


 

20.     How you are setting attribute to a particular file


 

    Standardization of model file by Permanent setting of layers, graphics

etc,.

    as per Company standards for their project.


 

21.     Is it possible to do shell operation to sphere


 

 &#! 160;  Yes


 

22.     Difference between surf1+cylinder & surf1+depth


 

    Cylinder: Extending a curve thro' space in a linear direction with

    given length.Surface created length is equal to PAI * D.


 

    Depth: Extending a curve thro' space in linear direction with given length.


 

23.     How many types of environment is available to start Catia


 

    a. From desktop [motif]

    b. From console [dterm]


 

24.    Mention different starting modes in catia. explain each briefly?

    Normal, Cold, quick, warm start respectively


 

25.   ! ; what does Adjust function is used for?


 

26.    what are functions used to make "balloon with leader"?


 

27.    what is difference b/w surf1+concanten+crv & surf1+concanten+ccv?


 

28.    what is difference b/w solide+intersect/subtract+trim all/trim elem 1/no

trim?


 

29.    what is difference b/w limit2+break & surf2+divide ?


 

30.    Mention 5 primitives solids in solide function ?


 

31.    Give two eg. for feature based primitive & contour based primitives ?


 

32.    what is use of Markup function ?


 

33.    what is required for to find massproperties of a surface model? And what

is used for finding the massprope! rty.


 

34.    Difference between sewing and split


 

35.    what is the difference b/w tranfor+affinity & tranfor+scaling ?


 

36.    what is parameter is asked for curve1+crv+crv ?


 

37.    what is importance of tree in catia ?


 


 

1.    What is the difference between ccv and crv?


 

2.     What is difference between solid, surface and wireframe modeling?


 

3.     What r the types of modelings?


 

4.     What is the difference between solide and solidm?


 

5.     What is the difference between surf1/geo extr and limit2/extra! pol?


 

6.     ! ;What is the use of formtool function?


 

7.     Using 3-points how many circles can create?


 

8.     What is the use of adjust command?


 

9.    Explain solide/operation/subtract & intersect/trim all: trim el1: no

trim?


 

10.    What is the difference between face, surface and skin?


 

11.    What are the solid primitives?


 

12.    What is hlr and nhr explain?


 

13.     What are the translators and explain?


 

14.    What is the use of LAW function?


 

15.    What is the use of layer function?


 

16. ! 0;  What is the use of merge function?


 

17.    What is the difference between isolate and separate?


 

18.    Is it possible to change pattern as required to existing pattern?


 

19.    What is the difference between parametric and nonparametric

(hybrid)modeling?


 

20.    Which is the better to split the solid a) surface b) plane c) face?


 

21.    What is the difference between spine and spline?


 

22.    How you will delete the surface if the face is created by surface?


 

23.    What is the difference between affinity and scaling?


 

24.    What is CSG tree explain?


 

25.    What a! re maste r w/s and detail w/s?


 

26.    What are nurbs, B-ref, brazier curves?


 

27.    What is difference between curve1 project and combine?


 

28.    What is difference between curve1 project and reflect?


 

29.    While creating solid model shell is first operation or fillet?


 

30.    What are the types of starting modes?


 

31.    What are the CATIA sessions?


 

32.     Mention the ways to start the CATIA


 

33.     Is it possible to split by using sewing operation


 

34.     Is it possible to appr. Surface using isoparameter


 

35.     Diff. B/w surf1 connect & surf2 fillet


 

36.     What is functional surface


 

37.     Difference between point projection and unspecific projection


 

38.     Difference between curv2 mono and multi tangent


 

39.     Purpose of iua


 

40.     Catia element


 

41.     Difference between sewing and split


 

42.     How drawing will be extracted ---- aux2 or spc-drw2 [if related to

surface spc-drw]


 

43.     Difference between line bisect and line median


 

44.     How you will convert ccv into crv


 

45.     Exp! and IGES ,DXF,CATIA,IUA,STEP


 

46.     Catia file format


 

47.     How you are setting attribute to a particular file


 

48.     Difference between tangential continuity and curvature continuity


 

49.    Necessity of using filters in layer


 

50.     List out the command used for the surface modeling


 

51.     What are different types of modules available with Catia package


 

52.     Catia models requires at least ____co-ordinate axis system


 

53.     What are different types of co-ordinate system


 

54.     Which one is not a sub function of transfor in! space mode ---

    (a)project (b) affinity (C)symmetry (d)scaling


 

55.     Symbol is function of draw mode


 

56.     Detail is function of draw & space mode


 

57.     Is it possible to do shell operation to sphere


 

58.     Difference between surf1+cylinder & surf1+depth


 

59.     How many types of environment is available to start Catia


 

60.     How many layers are present Catia


 

61.     How many types of working space are there in Catia


 

62.     How many operations can we done by using sewing command of solide


 

63! .     What is the importance of pulling di! rection in case of sweep


 

64.     Symbol can be defined in detail work space


 

65.     Difference between limit1+appr ccv & curv2+approxm


 

66.     Necessity of using filter in layer


 

67.     What is the difference between point limit-on and off?


 


 


 


 


 


 


 

CLASS -A

Here is a further understanding of Class-A surfacing based on experiences with two automotive companies and whites goods manufacturers. They independently hav! e the same definition for the classification.

 The physical meaning:

 Class A refers to those surfaces, which are CURVATURE continuous to each other at their respective boundaries. Curvature continuity means that at each "point" of each surface along the common boundary has the same radius of curvature.

 This is different to surfaces having;

 Tangent continuity - which is directional continuity without radius continuity - like fillets.
Point continuity - only touching without directional (tangent) or curvature equivalence.

 In fact, tangent and point continuity is the entire basis most industries (aerospace, shipbuilding, BIW etc etc). For these applications, there is generally no need for curvature.

 
By ! definition:

 Class ! A surfac e refers to those surfaces which are VISIBLE and abide to the physical meaning, in a product. This classification is primarily used in the automotive and increasingly in consumer goods (toothbrushes, PalmPC's, mobile phones, washing machines, toilet lids etc etc etc). It is a requirement where aesthetics has a significant contribution. For this reason the exterior of automobiles are deemed Class-A. BIW is NOT Class-A. The exterior of you sexy toothbrush is Class-A, the interior with ribs and inserts etc is NOT Class-A.


The consequence:


 

The consequence of these surfaces apart from visually and physically aesthetic shapes is the way they reflect the real world. What would one expect to see across the boundary of pairs of point continuity, tangent continuity and curvature continuity surfaces when reflecting a straight and dry tree stump in the desert????!

* Point Continuity (also known as G0 continuity) - will produce a reflection on one surface, then at the boundary disappear and re-appear at a location slightly different on the other surface. The same reflective phenomenon will show when there is a gap between the surfaces (the line markers on a road reflecting across the gap between the doors of a car).


 

* Tangent Continuity (also known as G1 continuity) - will produce a reflection on one surface, then at the boundary have a kink and continue. Unlike Point continuity the reflection (repeat REFLECTION) is continuos but has a tangent discontinuity in it. In analogy, it is "like" a greater than symbol.

 
 

* Curvature Continuity (also known as G2 continuity, Alias can do G3!) - this will produce the unbroken and smooth ref! lection across the boundary.

 60;
 

Please do not believe me! This is the real physical world. Look at your cars rounded hood reflecting lines on the road or trees. Look at ripples of water that are not turbulent, reflection is everywhere but all blend into each other, as there is also curvature continuity everywhere.

 
 

Still not convinced - For an analytical approach, you may simply prove this point using any rendering package (eg. CATIA V4 VST), Neon textures in 4D Navigator or DMU Navigator (V5), using the traditional CURVE1+REFLECT or /ANADIA in V4 CATIA and of course the neon-tray dynamic reflect curve facility in V5.

 
 


What about CATIA??

 
 

Traditionally CATIA has been used to create the "engineer! ing" side of most designs, rather then the exterior "aesthetic" shell (ie Class-A). These traditional yet awesome tools (like SURF2) are geared for this kind of engineering work. The best example being BIW in the automotive industry.

 
 

Functions like SURF2 and FORMTOOL carve up even the most difficult inner panel structures into reality. This is why, historically, CATIA took an early strangle hold (amongst other reasons like a great capacity in all aspects of DMU and integration across disciplines).

 
 

CATIA comes from the aerospace industry. The exterior of aeroplanes (whose panels buckle between frames and expand with every land-takeoff cycle) has very little "need" for curvature continuity and has 100% engineering factors driving its design (aerodynamics and structures).

 
 

Tha! t is, th ere is zero styling in the design of an aircraft body. The fact that aeroplanes looks good and "smooth" is by virtue of its operation (streamlined as possible), their general cleanliness and most importantly the distance that one generally views them. If one was to look carefully down the fuselage of an aircraft on the ground, there is nothing smooth about it!

 
 

Having the capability to cater for these industries in an engineering and process capacity with existing function and not requiring the ability to create Class-A, has made CATIA the de-facto standard for the aerospace and automotive industries.

 
 

As for Class-A, automotive manufacturers have utilised either or combinations of Alias and/or ICEM Surf (or others) to achieve these goals in a productive manner (remember the word productive). Alias has! the ability cover the entire industrial design process from Sketches TO Surfaces on sketches TO Surface manipulation and build and further onto rendering and animation.

 
 

In retrospect, CATIA V4 can create Class-A surfaces with (1) compromise (eg. this deviation is OK, because it can be polished by the toolmaker) and (2) an idiosyncratic approach by the CATIA operator - ie, it can be done but not as easily as with Alias or ICEM Surf.

 
 

Historically, its been "difficult" of Dassault to create software in V4 to easily create Class-A surfaces due to the use of Bezier (polynomial) based mathematics. There is nothing against Bezier based surfaces though. They are excellent for creating the engineering surfaces we have all come to love (BIW etc) utilising intelligent use of multi-patch surface methodology. I! n fact, I doubt NURBS surfaces could do a better job.

 
 

And without a doubt, V5, with its new architecture and use of Bezier and NURBS surfaces will go along way in being able to confidently and more importantly competently producing these Class-A surfaces for an ever growing aesthetic minded world.

 
 


And what about V4 CATIA??

 
 

CATIA V4 currently has the ability to create curvature continuous surfaces in two categories.

 
 

Surfaces:

 
 

a. Using SURF2 and SKIN (GSM) functions to sweep and loft as "long" a surface as possible. This will generally produce a curvature continuous surface with minimum deviation.

 
 

b. Intelligent use of SPINES and LIMIT curves when using SURF2 and SKIN to closely match curvature across boundaries.

 
 

c. Utilising conic surfaces and conic curve approximations to mimic curvature conditions.

 
 

d. For parts with large variations within its shape cause techniques a and b to struggle. For this reason, we may take three approaches.

 
 

d1. Create "unstressed" surfaces to the point of struggle and fill in the blank with blend surfaces and curvature continuity. This is very much situation dependant.

 
 

d2. Use ARC's and PATCHES's - ARC's and! PATCHES have the peculiar yet great ability to

 
 

* not go through all their constraints (good for the styling end of the design process)
* the ability to deform a arc or patch to a point
* the ability to deform the boundary of a patch to an arc whilst maintaining the opposing continuity.
* most importantly - the ability to reduce or increase degrees of arcs and patches to maximise or localise deformations.

 
 

I have found these most useful.

 
 

e. Utilise NURBSCRV and NURBSSRF when and arc or patch refuses to go close enough to the constraints of interest.

 
 


Blends:

 
 

These are a curious family of sur! faces. One can utilise two functions within CATIA V4.

 
 

The first is the ubiquitous BLENSURF functions, which allows a point/tangent/curvature continuos blend between any two curves on any part of any plane, FSUR, RSUR, surface, face or skin. OR automatically creating bi-rail curves along two surfaces at particular "radii" and placing a point/tangent/curvature continuous blend between them. Tensions and connectivity locations are also adjustable.

 
 

Although it is a great tool, one issue with Blensurf is its inability to blend around a large angle. For instance, if one constructs two segment surfaces to each other at right angles with a gap between them and then placing a curvature continuos surface to connect them. The result is very suprising. The surface comes off one with curvature continuity, takes! the shortest route to the other and then blends with curvatur! e again. It is not the expected shape in the blend, when comparing it to the curves created using CURVE2+CONNECT with curvature from the isoparametric curves of each surface.

 
 

The reason for this is that Blensurf creates purely mathematical curvature. For the correct shape, mathematical and isoparametric curvature is required. Guess what my friends, Dassault are already on the ball, this is possible using GSM's SKIN function blend and V5 GSD blends.


 


 


Question answers on intersecting angles between curves