Math Terms - Visually Described ?

bobbym · 2010-08-17 11:35:55

Hi SuperLynx;

Not exactly, what happened is the line in the the first quadrant was rotated clockwise by 180 degrees. Making the bigger line you see.

SuperLynx · 2010-08-17 12:14:37

I made the line bigger, Ok I don't quite get it.

bobbym · 2010-08-17 12:18:33

Hi;

See the line above the origin. Picture it being rotated like the second hand of a clock. rotated from 2:00 to 8:00. That's the bottom line!

SuperLynx · 2010-08-17 13:56:15

A Matrix rotates ???

bobbym · 2010-08-17 13:59:56

The line rotates like the second hand of a clock. The matrix causes the transformation from one set of points to another.

SuperLynx · 2010-08-18 02:39:37

Give me another example so I can slowly understand.

bobbym · 2010-08-18 03:14:51

Let's rotate around the origin the line (0,0) ( 4,5) by 30° So θ = 30°

We get the line (0,0)(5.96,2.33)

Set the graph area to 600,500 and graph those lines.

SuperLynx · 2010-08-18 03:57:54

I don't understand, when you say to rotate around the origin ? Set the Graph to X=600 and Y=500 ?

bobbym · 2010-08-18 04:05:42

On the right under appearance set graph area to 600 X 500.

The top line is like the second hand of an old clock. As it moves thirty degrees it becomes the second line. The origin does not move here. The line goes around it. (4,5) became (5.96,2.33). That's a change. The (0,0) stayed (0,0), no change. The line is rotating like a clock hand.

Look here:

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

See the big hand. That is what we are doing. 1 move at a time. Notice it revolves around the center. Just like ours.

SuperLynx · 2010-08-18 05:39:18

In this case the Matrix rotated around the origin, in other words that is just one thing that a matrix can do, which is rotate around it's origin ?

bobbym · 2010-08-18 09:20:49

Hi SuperLynx;

Nope, matrices don't revolve, else they would get dizzy. It is the points they are acting on that are transformed or moved around to different parts of the graph or screen.

Did you look at the clock? Did you see that our lines are just two different positions of that big hand? Graphically you already know enough to make an arrow move all the way around the origin, just like the second hand.

in other words that is just one thing that a matrix can do, which is rotate around it's origin ?

They do a lot more, we are just looking at the simplest one.

SuperLynx · 2010-08-18 13:19:16

Alright, give me another example where one thing controls another which I know matrix can do but break it up so I can understand

bobbym · 2010-08-18 13:36:09

Hi;

Now with t = 120

So plot the line (0,0)(0,5) and then plot the line (0,0),(4.333,-2.5)

Set graph area 400 X 600 and uncheck show axes.

SuperLynx · 2010-08-18 23:26:03

I get the graph seen in the image, but I don't understand other then I've plotted some points.

bobbym · 2010-08-19 01:21:38

Hi SuperLynx;

Please plot the lines again. That is not correct.

(0,0)
(0,5)
(0,0)
(4.333,-2.5)

but I don't understand other then I've plotted some points.

This is part of your difficulties, We will have to cover some trigonometry.

SuperLynx · 2010-08-19 02:47:23

I hope this is right, other wise you know a simpler program I could start off with and build up eventually ?

bobbym · 2010-08-19 03:05:30

Hi;

other wise you know a simpler program I could start off with and build up eventually

I really don't know of anything simpler than this page that I have sent you to. Anything simpler would have no features at all.

That picture is almost correct, you forgot to set graph area 400 X 600 and uncheck show axes.

SuperLynx · 2010-08-19 03:33:23

What is happening now it seems like all I'm doing is moving points around and making lines.

bobbym · 2010-08-19 03:50:47

That's what the matrix transformation does. This is the basis for motion on the screen. Did you draw the set of points with set graph area 400 X 600 and uncheck show axes?

SuperLynx wrote:

What is happening now it seems like all I'm doing is moving points around and making lines.

I am only going over more of these examples for 2 reasons. First, because you asked for more.

SuperLynx wrote:

Alright, give me another example where one thing controls another which I know matrix can do but break it up so I can understand smile

And second because you do not understand them well enough to move on yet.

SuperLynx · 2010-08-19 06:19:26

That's what the matrix transformation does. This is the basis for motion on the screen. Did you draw the set of points with set graph area 400 X 600 and uncheck show axes?

Yup

From what I understand so far I'm plotting from a origin then one line is going one way the other is going another way while at the same time the origin can control both directions of the lines if I were to rotate the origin ?

bobbym · 2010-08-19 11:21:01

Hi SuperLynx;

The origin is not rotating. It stays fixed. The end point of the line is being rotated around the origin like a planet goiing around the sun. Also don't think of it as two lines. It is one line in two different positions. One clock handle can tell lots of different times.

Did you draw the points with the settings I gave you? If you did you will see that the line went from 12:00 to 4:00. Why?

SuperLynx · 2010-08-19 11:51:36

Did you draw the points with the settings I gave you? If you did you will see that the line went from 12:00 to 4:00. Why?

I changed the line position formally it was at 12 now it's at 4 ?

bobbym · 2010-08-19 12:15:44

Hi SuperLynx;

Remember how much we rotated the line pointing at 12:00? 120° was the amount. 1 / 3 of a circle which is 360°. Now it is pointing to 4:00. Go to the clock page.

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

Press the right button for the hour hand 4 times. That is what you have done over here.

SuperLynx · 2010-08-19 12:58:41

We've rotated around the point of origin ?

bobbym · 2010-08-19 13:03:40

That's right, just like a clock hand does. The hands rotate around the center.

Math Is Fun Forum

#101 2010-08-17 11:35:55

Re: Math Terms - Visually Described ?

#102 2010-08-17 12:14:37

Re: Math Terms - Visually Described ?

#103 2010-08-17 12:18:33

Re: Math Terms - Visually Described ?

#104 2010-08-17 13:56:15

Re: Math Terms - Visually Described ?

#105 2010-08-17 13:59:56

Re: Math Terms - Visually Described ?

#106 2010-08-18 02:39:37

Re: Math Terms - Visually Described ?

#107 2010-08-18 03:14:51

Re: Math Terms - Visually Described ?

#108 2010-08-18 03:57:54

Re: Math Terms - Visually Described ?

#109 2010-08-18 04:05:42

Re: Math Terms - Visually Described ?

#110 2010-08-18 05:39:18

Re: Math Terms - Visually Described ?

#111 2010-08-18 09:20:49

Re: Math Terms - Visually Described ?

#112 2010-08-18 13:19:16

Re: Math Terms - Visually Described ?

#113 2010-08-18 13:36:09

Re: Math Terms - Visually Described ?

#114 2010-08-18 23:26:03

Re: Math Terms - Visually Described ?

#115 2010-08-19 01:21:38

Re: Math Terms - Visually Described ?

#116 2010-08-19 02:47:23

Re: Math Terms - Visually Described ?

#117 2010-08-19 03:05:30

Re: Math Terms - Visually Described ?

#118 2010-08-19 03:33:23

Re: Math Terms - Visually Described ?

#119 2010-08-19 03:50:47

Re: Math Terms - Visually Described ?

#120 2010-08-19 06:19:26

Re: Math Terms - Visually Described ?

#121 2010-08-19 11:21:01

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#122 2010-08-19 11:51:36

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#123 2010-08-19 12:15:44

Re: Math Terms - Visually Described ?

#124 2010-08-19 12:58:41

Re: Math Terms - Visually Described ?

#125 2010-08-19 13:03:40

Re: Math Terms - Visually Described ?

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