Math Terms - Visually Described ?

bobbym · 2010-08-27 00:19:02

You should see two lines, one pointing to the right and going up and the other pointing to the right going down. Please try again.

SuperLynx · 2010-08-27 07:16:51

Can you explain to me without going though these graph sessions what Matrix can do ?

bobbym · 2010-08-27 07:29:58

Hi SuperLynx;

Yes, I already have. But it will have little or no meaning. Take a little look at these pages.

http://www.mathsisfun.com/geometry/transformations.html

Here is what we just started:

http://www.mathsisfun.com/geometry/reflection.html

And this is basically what you just finished.

http://www.mathsisfun.com/geometry/translation.html

This is all of it.

http://www.mathsisfun.com/geometry/congruent.html

A couple of simple matrix transformations are making those objects on his pages appear to be moving. We are covering rotations, reflections and dilations.

Check this out also and have a little fun:

http://www.mathsisfun.com/geometry/images/symmetry.swf

SuperLynx · 2010-08-27 07:53:53

That is helpful but do you have something like this for Matrix ?

bobbym · 2010-08-27 07:59:16

Hi SuperLynx;

A matrix is just a rectangular box filled with numbers. When you were graphing the 4 points . You were seeing the result of the matrix transformations. You put the points into a matrix and then multiplied them by another matrix and you are done. I wanted you to have a graphic or visual understanding of what the terms dilation, shearing, translation, rotation and reflection mean.

Please spend some time on the links I have provided. They will enhance your understanding. The last one or symmetry artist is a gem!

SuperLynx · 2010-08-27 08:50:11

I understand symmetry, theres gotta be a way I can understand where the light bulb goes off.

bobbym · 2010-08-27 08:55:09

Hi SuperLynx;

Might be trying to ingest too much too quick. I am going to send you to a site where you can experiment a little more. Come back here with any questions you have.

http://www.mathwarehouse.com/transforma … n-math.php

SuperLynx · 2010-08-27 10:01:48

That is helpful but specifically on Matrix, I'm understanding programming language codes as in Arrays, slowly but it's Matrix.

bobbym · 2010-08-27 13:01:33

Hi;

Many graphics programs contain matrix instructions. It is all done for you. Also we haven't gone over any matrix algebra so it is natural to be confused.

SuperLynx · 2010-08-27 14:43:01

I want to understand 3x3 matrix but the plotting points on graphs isn't making me understand.

bobbym · 2010-08-27 17:31:46

Hi SuperLynx;

Confucius wrote:

Before you can understand 3 x 3 you must understand 2 x 2

Did you play around on those sites? Cause that will help.

Oh and by the way, let's say you don't get it.
Even after everything that I do.
Just think of all the fun you will have had looking at my posts.

SuperLynx · 2010-08-28 01:33:22

Can you at least try a different method for me to understand Matrix ? This method is not even slowly helping I have taken a look at those sites the information presented on those sites I knew how it worked.

bobbym · 2010-08-28 01:40:49

Hi SuperLynx;

A matrix 3 x 3 or 50 x 50 is just a rectangular grid of numbers. There is nothing magical about them. As I have said the rotation around the origin or any other point is done by multiplying 2 matrices they could be 2 x 2, 3 x 3 or more. Until we plot them the numbers have no meaning.

We are doing a little 2 D graphics using matrices. This is the particular area of them that you wanted to know something about. I have distilled it to what I think is the simplest form. I have made some changes so that you would not be confused.

If you want to understand something other than graphics and matrices then tell me now.

SuperLynx · 2010-08-28 02:12:11

If you want to understand something other than graphics and matrices then tell me now.

No, I don't.

A matrix 3 x 3 or 50 x 50 is just a rectangular grid of numbers. There is nothing magical about them. As I have said the rotation around the origin or any other point is done by multiplying 2 matrices they could be 2 x 2, 3 x 3 or more. Until we plot them the numbers have no meaning.

Oh that is what Matrix do is multiply one set of numbers within the matrix by another set.

23 45 12
84 91 2
14 4 16

bobbym · 2010-08-28 02:22:30

Hi;

Oh that is what Matrix do is multiply one set of numbers within the matrix by another set

That is only one thing they can do. You can add 2 matrices or subtract or take the inverse or transpose
or take the determinant. Remember post #2. But yes matrix multiplication does the rotations around a central
point.

SuperLynx · 2010-08-28 03:13:03

That is only one thing they can do. You can add 2 matrices or subtract or take the inverse or transpose
or take the determinant. Remember post #2. But yes matrix multiplication does the rotations around a central
point.

Basically you can add,subtract, multiply all the numbers within the matrix ? What do you mean that a matrix multiplication does the rotations around a central point ? What is the central point?

bobbym · 2010-08-28 03:44:16

The origin was our central point. (0,0).

SuperLynx · 2010-08-28 11:33:40

If you had a 3x3 matrix where would it's centre point be?

bobbym · 2010-08-28 14:32:07

The center of a 3 x 3 is in matrix talk is 2,2. The element in the second row and the second column. Why is that important? It is not what I mean by the origin or (0,0).

lindsey8555 · 2010-08-29 00:17:34

hello:

please wait a minute, before that one, this one is a piece of cake only.

there are 8 cats in a box of shoe, and there are 3 kittens with each cats. how many legs are all in that box ?

_________________________________ easy right ? )

bobbym · 2010-08-29 00:33:02

Hi lindsey8555;

SuperLynx · 2010-08-30 08:32:43

I found a few web sites, I'm going to try to figure this out !

bobbym · 2010-08-30 08:56:57

Okay, if you get stuck come back here.

SuperLynx · 2010-12-20 04:16:04

Hi, I wanted to add to this thread what the following terms mean:

What are therules for adding, subtracting and dividing two 3x3 matrices ?
What is the difference between a 3x3 matrix and a 4x4 matrix ?
How do you convert a 3x3 matrix to X,Y,Z ?:)

bobbym · 2010-12-20 09:59:26

Hi SuperLynx;

We went over this before but maybe you have forgotten.First you cannot divide matrices. There is no matrix division in linear algebra, instead you have multiplication by the inverse.

3X3 refers to the number of rows and columns. First number are rows and the next number is columns. So 3X3 means 3 rows by 3 columns. Here is a 3X3 matrix. The numbers in the boxes are arbitrary.

And here is a 4X4

You should remember we covered the basic matrix operations in an earlier post. Here they are again:

There is also a direct sum for two matrices but you will not need it right now or maybe ever.

We also covered XYZ. I told you that unless you are willing to cover the math first 3D graphics will be difficult to understand.
I taught you modulo and clamp and how to rotate and translate points in a cartesian system. I say the same things now that I said then, you have 2 choices.

1) Many graphic programs and languages will create 3D forms for you. They use templates, you do not have to know much math. But you must know the language or the program intimately.
That means experience in using them. You must gain this for yourself, I cannot just hand it to you. You must practice with the commands and the help section that the program provides.

2) The math is also something you learn by experience. You left in the middle of what we were doing, I assume because you thought there was some shortcut way. I hoped you would find it so you could show me this shortcut, I have never found any shortcut way to learn math. I no longer believe there is one.

Yes, I know I am scolding you. Did you get any help from that 3D forum you went to? If you would have stayed here we would have been done by now, instead we have to begin again.

Math Is Fun Forum

#151 2010-08-27 00:19:02

Re: Math Terms - Visually Described ?

#152 2010-08-27 07:16:51

Re: Math Terms - Visually Described ?

#153 2010-08-27 07:29:58

Re: Math Terms - Visually Described ?

#154 2010-08-27 07:53:53

Re: Math Terms - Visually Described ?

#155 2010-08-27 07:59:16

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#156 2010-08-27 08:50:11

Re: Math Terms - Visually Described ?

#157 2010-08-27 08:55:09

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#158 2010-08-27 10:01:48

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#159 2010-08-27 13:01:33

Re: Math Terms - Visually Described ?

#160 2010-08-27 14:43:01

Re: Math Terms - Visually Described ?

#161 2010-08-27 17:31:46

Re: Math Terms - Visually Described ?

#162 2010-08-28 01:33:22

Re: Math Terms - Visually Described ?

#163 2010-08-28 01:40:49

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#164 2010-08-28 02:12:11

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#165 2010-08-28 02:22:30

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#166 2010-08-28 03:13:03

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#167 2010-08-28 03:44:16

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#168 2010-08-28 11:33:40

Re: Math Terms - Visually Described ?

#169 2010-08-28 14:32:07

Re: Math Terms - Visually Described ?

#170 2010-08-29 00:17:34

Re: Math Terms - Visually Described ?

#171 2010-08-29 00:33:02

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#172 2010-08-30 08:32:43

Re: Math Terms - Visually Described ?

#173 2010-08-30 08:56:57

Re: Math Terms - Visually Described ?

#174 2010-12-20 04:16:04

Re: Math Terms - Visually Described ?

#175 2010-12-20 09:59:26

Re: Math Terms - Visually Described ?

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