Math Terms - Visually Described ?

SuperLynx · 2010-08-20 08:39:12

Are you saying that a basic thing a matrix does is rotate around a origin ? Do you have another example, that goes into more depth of matrix?

bobbym · 2010-08-20 11:11:04

Hi SuperLynx;

Are you saying that a basic thing a matrix does is rotate around a origin ? Do you have another example, that goes into more depth of matrix?

Nope. A matrix is a rectangular array of numbers. It does not rotate. The values ( lines in this case ) are transformed. The lines are rotating aroung the origin like a clock hand does.

I think you need a few more of this type, as you are still a little shaky about them.

SuperLynx · 2010-08-21 04:14:40

Nope. A matrix is a rectangular array of numbers. It does not rotate. The values ( lines in this case ) are transformed. The lines are rotating around the origin like a clock hand does.

I don't understand how since a 3x3 Matrix is 3 rows of 3 relates to your clock hand example? I'm trying to relate what you're saying to what is on this page

bobbym · 2010-08-21 07:16:16

Hi SuperLynx;

We are doing pure math here, truthfully I have no idea what they are doing. Our matrices are 2 x 2 and 2 x 1. With it we are moving a line around a central point. With just that we could create a graphic of clock hands, speedometer, tachometer etc,

You originally asked to understand a matrix. This is what we are working on. You wanted to know how a matrix could act upon certain graphical objects. I am showing you the simplest graphical object, a straight line.

SuperLynx · 2010-08-22 02:30:51

We are doing pure math here, truthfully I have no idea what they are doing. Our matrices are 2 x 2 and 2 x 1. With it we are moving a line around a central point. With just that we could create a graphic of clock hands, speedometer, tachometer etc,

Within that page they are using a 3x3 Matrix, could you give me an example of a 3x3 matrix ? After you help me understand a 2x2 Matrix and a 2x1 and what is the difference between a 2x1 Matrix ?

You originally asked to understand a matrix. This is what we are working on. You wanted to know how a matrix could act upon certain graphical objects. I am showing you the simplest graphical object, a straight line.

I was informed that a matrix can control one aspect of another, as seen on that page I posted that is what I'm trying to understand Unless I won't be able to understand until after understanding 2x1 and 2x2 Matrix ?

bobbym · 2010-08-22 03:07:26

Hi SuperLynx;

First you have to understand a little bit more of what we are doing here. Then you might be able to move on to whatever they are doing. Till then , do you have any questions about rotations around the origin?

SuperLynx · 2010-08-22 03:11:16

How was the rotation around origin laid out ? This is a 2x2 Matrix correct?

bobbym · 2010-08-22 04:05:08

This is the whole process. With t = 30°.

The point (-2,-3) is transformed into the point (-3.23205, -1.59808). This means that the line (0,0) ( -2,-3) bcomes the line (0,0) (-3.23205, -1.59808).

Now please plot:

0,0
-2,-3
0,0
-3.23205, -1.59808

You should see that the bottom line has been rotated or moved up by 30 degrees. It is now the top line!

SuperLynx · 2010-08-22 04:58:10

Correct, what was it before so I can compare ?

bobbym · 2010-08-22 10:29:24

Two points determine a line. (0,0) and (-2,-3) are a line segment. The bottom hand that looks like it is pointing to 7:00 moved 1 hour ( 30 degrees ) and is now pointing at 8:00.

SuperLynx · 2010-08-22 11:53:56

Arrrgh I'm still not understanding.

bobbym · 2010-08-22 11:55:29

Hi;

What are you having a problem with? Which part in particular.

SuperLynx · 2010-08-23 11:19:48

What I have done is been plotting points on a curve. Yet I'm not understanding what I'm doing when I change the positions. You mentioned we are working with a 2x2 matrix in this case

0,0
0,0
0,0
0,0

Is that all a 2x2 matrix does it in this case change the position ?

2,2-2,2
2,2-2,2

That is just an example of a 2x2 Matrix setup correct?

bobbym · 2010-08-23 11:27:22

Hi SuperLynx;

Relax, you are getting ahead of yourself. Take a look at post #135. Now go to the clock page.

http://www.amblesideprimary.com/amblewe … clock.html

Press the 5 minute button, the one on the right. Press it till the big hand is pointing at 7:00. That is the first line. The big hand represents the first line in your graph. Now press the button 1 more time. The big hand will be pointing at 8:00. 30 degree rotation did that. That is the second line in your graph. The transformation changed it from pointing at 7:00 to pointing at 8:00.

Notice the center of the clock. The big hand revolves around it. That is (0,0), the origin. It does not move. The other point moves, that is what causes the rotation.

SuperLynx · 2010-08-23 12:38:01

Notice the center of the clock. The big hand revolves around it. That is (0,0), the origin. It does not move. The other point moves, that is what causes the rotation

Do you mean that when the bigger hand on the clock moves the smaller hand moves but it moves more slowly behind it ? If is this correct then when a matrix is a 2x2 and you move one thing the other thing will lag behind it ?

bobbym · 2010-08-23 12:42:47

Nothing to do with the hour hand (smaller hand). Just concentrate on how the big hand is moving. It went from 7:00 to 8:00. That is all we are changing. Did you look at the clock page? Anything that big hand does on that page I can duplicate right here. That was done by a matrix transformation similar to ours.

SuperLynx · 2010-08-23 14:01:34

You can duplicate what the clock did with these lines, alright what is next ?

bobbym · 2010-08-23 14:04:08

If you understand what happened with one line around the origin, then we can go to the next transformation. One question. If the big hand was pointing at 12:00 (straight up ) and I rotated it 120° what is it pointing at now? I am going on a little munch break, see you soon.

SuperLynx · 2010-08-26 14:42:04

One question. If the big hand was pointing at 12:00 (straight up ) and I rotated it 120° what is it pointing at now? I am going on a little munch break, see you soon.

It would be at 12:20 approx.

bobbym · 2010-08-26 14:45:55

Hi SuperLynx;

That's correct! It would be pointing at the 4.

SuperLynx · 2010-08-26 22:54:38

Alright onto the next transformation

bobbym · 2010-08-26 23:01:50

Plot the points (0,0) ( 1,1 ) and (0,0),(1,-1) and tell me what you see.

annething1010 · 2010-08-26 23:52:47

hi, got a lot of problems with my math instructor, does anyone here have the same concern?

bobbym · 2010-08-26 23:54:26

Hi annething1010;

Welcome to the forum. I don't know your math instructor. But if I did I am sure I would have problems with him.

SuperLynx · 2010-08-27 00:10:17

The graph looks like it's pointing at 9:00

Math Is Fun Forum

#126 2010-08-20 08:39:12

Re: Math Terms - Visually Described ?

#127 2010-08-20 11:11:04

Re: Math Terms - Visually Described ?

#128 2010-08-21 04:14:40

Re: Math Terms - Visually Described ?

#129 2010-08-21 07:16:16

Re: Math Terms - Visually Described ?

#130 2010-08-22 02:30:51

Re: Math Terms - Visually Described ?

#131 2010-08-22 03:07:26

Re: Math Terms - Visually Described ?

#132 2010-08-22 03:11:16

Re: Math Terms - Visually Described ?

#133 2010-08-22 04:05:08

Re: Math Terms - Visually Described ?

#134 2010-08-22 04:58:10

Re: Math Terms - Visually Described ?

#135 2010-08-22 10:29:24

Re: Math Terms - Visually Described ?

#136 2010-08-22 11:53:56

Re: Math Terms - Visually Described ?

#137 2010-08-22 11:55:29

Re: Math Terms - Visually Described ?

#138 2010-08-23 11:19:48

Re: Math Terms - Visually Described ?

#139 2010-08-23 11:27:22

Re: Math Terms - Visually Described ?

#140 2010-08-23 12:38:01

Re: Math Terms - Visually Described ?

#141 2010-08-23 12:42:47

Re: Math Terms - Visually Described ?

#142 2010-08-23 14:01:34

Re: Math Terms - Visually Described ?

#143 2010-08-23 14:04:08

Re: Math Terms - Visually Described ?

#144 2010-08-26 14:42:04

Re: Math Terms - Visually Described ?

#145 2010-08-26 14:45:55

Re: Math Terms - Visually Described ?

#146 2010-08-26 22:54:38

Re: Math Terms - Visually Described ?

#147 2010-08-26 23:01:50

Re: Math Terms - Visually Described ?

#148 2010-08-26 23:52:47

Re: Math Terms - Visually Described ?

#149 2010-08-26 23:54:26

Re: Math Terms - Visually Described ?

#150 2010-08-27 00:10:17

Re: Math Terms - Visually Described ?

Board footer