Math Is Fun Forum

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Math Terms - Visually Described ?

I can give some examples of matrices are used to perform transformations on a line or points. This will help you to see a little bit of how it is done. If that is okay with you?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

SuperLynx

Member

Registered: 2009-06-28

Posts: 335

Re: Math Terms - Visually Described ?

I would like some examples, and make them understandable

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Math Terms - Visually Described ?

Hi;

To rotate a line around the origin 90°

That is the transformation matrix. Draw a line from (0,0) to (1,1).

Multiply the transformataion matrix and the point (1,1) to rotate it.

We used θ = 90° to get the new point (1,-1). Draw the new line (0,0) , (1,-1) and tell me what you see.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

SuperLynx

Member

Registered: 2009-06-28

Posts: 335

Re: Math Terms - Visually Described ?

Whoa do you know of another way to explain it, start basic and then work my way up

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Math Terms - Visually Described ?

Hi Superlynx;

That is the basic thing, just follow my instructions in that post. Draw the lines as I have indicated.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Math Terms - Visually Described ?

Hi Superlynx;

Where did she go? Please draw those lines, you don't have understand the matrix math right now. Like baking bread. You don't have to know what the origins of yeast are. You do not have to understand the biochemistry. But you do have to add the yeast, that is mandatory. Graph those two lines in your program. Tell me what happened.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

SuperLynx

Member

Registered: 2009-06-28

Posts: 335

Re: Math Terms - Visually Described ?

You want me to draw a matrix line ???

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Math Terms - Visually Described ?

Hi;

Nope, draw two lines.

One line between (0,0) and ( 1,1)

and then draw another line between (0,0) and (1,-1)

Will see you a little later!

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

SuperLynx

Member

Registered: 2009-06-28

Posts: 335

Re: Math Terms - Visually Described ?

I don't quite know how to do that in this program.  That is the problem I can do some other things but if I get told to design something specifically I don't know yet which is why I want to learn another way so I can relate it, if possible.

Sarah Rebekah 13

Guest

Re: Math Terms - Visually Described ?

Hi SuperLynx.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Math Terms - Visually Described ?

Hi SuperLynx and Sarah;

Do you know how to use graph paper?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

SuperLynx

Member

Registered: 2009-06-28

Posts: 335

Re: Math Terms - Visually Described ?

Yes, but I don't have any

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Math Terms - Visually Described ?

Okay then you will have to graph them here.

http://itools.subhashbose.com/grapher/index.php

Find this and I will explain further. In order to get a feel for these translations so you can understand them you will have to see the graphic. You have a nice graphic program, my suggestion again is to learn how to use it or download a simpler one.

For now see if you can understand the above coordinate grapher.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

SuperLynx

Member

Registered: 2009-06-28

Posts: 335

Re: Math Terms - Visually Described ?

I understand it to a extent but the 1,2,3,4 for X & Y is a little confusing.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Math Terms - Visually Described ?

If you are at the front screen enter 4 as the number of points. Set graph area to 400, 700. Then enter the points:

0   0
1   1
0   0
1   -1

You will see the results of the matrix translation.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

SuperLynx

Member

Registered: 2009-06-28

Posts: 335

Re: Math Terms - Visually Described ?

You have a nice graphic program, my suggestion again is to learn how to use it or download a simpler one

I thought you were going to suggest a simpler one, so I can understand it easier then move up ?

Sarah Rebekah 13

Guest

Re: Math Terms - Visually Described ?

Hi Bobbym.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Math Terms - Visually Described ?

Hi Sarah!

Hi SuperLynx;

I thought you were going to suggest a simpler one, so I can understand it easier then move up ?

That was your first mistake, trying to predict what I would do next. I don't even know. What I don't know is what do you mean by simpler. Simpler problems or a simpler program?

Anyway, did you plot those 4 points and take a look at them, because that is a simple transformation of a line around the origin, It was done by matrix algebra! (Post # 79)

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

SuperLynx

Member

Registered: 2009-06-28

Posts: 335

Re: Math Terms - Visually Described ?

Simpler problems or a simpler program?

Simpler program, but for now I'm fine to stick with this program

I plotted those four points and all that occurred was a horizontal triangle ??

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Math Terms - Visually Described ?

Hi SuperLynx;

Nope, that is not all you see, you see line A rotated 90° ( around the origin ) to line B by a matrix transformation! Specifically by this one when θ = 90°

(0,0)(1,1) became (0,0)(1,-1)

You should get this:

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

SuperLynx

Member

Registered: 2009-06-28

Posts: 335

Re: Math Terms - Visually Described ?

A Matrix goes in the opposite direction ? If

then

correct?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Math Terms - Visually Described ?

Hi SuperLynx;

Nope, it doesn't work like that.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

SuperLynx

Member

Registered: 2009-06-28

Posts: 335

Re: Math Terms - Visually Described ?

Oh, then you're going to have to explain a little more

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Math Terms - Visually Described ?

Hi SuperLynx;

Please don't jump ahead. I haven't explained to you what is happening. Right now you are just looking at some pictures.

Let's rotate the line (0,0),(2,3) by 180°

So we get (-2,-3). Plot the line (0,0)(2,3) and then plot the line (0,0)(-2,-3). What happened?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

SuperLynx

Member

Registered: 2009-06-28

Posts: 335

Re: Math Terms - Visually Described ?

What I get is a diagonal line as seen in the image.