Need help to develop Pythagoras theorem-

Hi i need help to develop proofs 2,3,4
of pythagoras theorems in java as demonstrations
These are applets can anyone help me with it or give me an idea of how to go about developing it -
the site is the following
http://www.uni-koeln.de/ew-fak/Mathe/Projekte/VisuPro/pythagoras/pythagoras.html
then double click on the screen to make it start

Pardon my ASCII art, but I've always liked the following, simple, geometric proof:
     a                   b
---------------------------------------+
|       |                                |
a|   I   |              II                |
|       |                                |
---------------------------------------+
|       |                                |
|       |                                |
|       |                                |
|       |                                |
|       |                                |
b| IV   |              III               |
|       |                                |
|       |                                |
|       |                                |
|       |                                |
|       |                                |
|       |                                |
---------------------------------------+It almost goes without saying that I+II+III+IV == (a+b)^2, and II == IV == a*b,
I == a*a and III == b*b, showing that (a+b)^2 == a^2+a*b+a*b+b^2.
I hope the following sketch makes sense, stand back, ASCII art alert again:     a                   b
---------------------------------------+
|               .             VI         |
|     .                 .                |a
| V                               .      |
|                                        +
|                                        |
|   .                                    |
b|                                     . |
|                                        |
|                  IX                    |
| .                                      |
|                                    .   |b
|                                        |
+                                        |
|      .                                 |
a|               .                  . VII |
| VIII                   .              |
---------------------------------------+
                 a                    bThe total area equals (a+b)^2 again and equals the sum of the smaller areas:
(a+b)^2 == V+VI+VII+VIII+IX. Let area IX be c^2 for whatever c may be.
V+VII == VI+VIII == a*b, so a^2+b^2+2*ab= c^2+2*a*b; IOW a^2+b^2 == c^2
Given this fundamental result, the others can easily be derived from this one,
or did I answer a question you didn't ask?
kind regards,
Jos

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