2014.05.18


+-------------------------------------------------------+
|        C                                              |
|       /| .                                            |
|      /90    .                                        |
|     /  |         .                                    |
|    /   |             .                                |
|   /    |                 .                            |
|  /  90|90                  .                        |
| A------D------------------------B                     |
|                                                       |
|      AD AC                                            |
| cosA=--=-- -> AB*AD = AC*AC = AC^2                    |
|      AC AB                                            |
|                                                       |
|      BD BC                                            |
| cosB=--=-- -> AB*BD = BC*BC = BC^2                    |
|      BC AB                                            |
|                                                       |
| then Pythagoras wondered what would sum of those give | rus:     .
| AC^2 + BC^2 = AB*AD + AB*BD = AB(AD+BD=AB)            |
|                             = AB^2                    |
+-------------------------------------------------------+
                           ||
                          \  /
+-------------------------------------------------------+
| some AB^2 in xy-coords = (Ax-Bx)^2 + (Ay-By)^2        | rus:    2D-
|                                                       |
|            y                                          |
|            |   B                                      |
|            |   |                                      |
|            |   |                                      |
|            |   |                                      |
|            |   |                                      |
| -x---------0---------x                                |
|            |90y                                      |
|    A-------|xxxy                                      |
|            |                                          |
|            |                                          |
|            |                                          |
|           -y                                          |
+-------------------------------------------------------+
                           ||
                          \  /
+-------------------------------------------------------+
| z-coord implies depth/height/left-right moves         | rus: z- -   //-
| some AB^2 in xyz-coords = (Ax-Bx)^2 + (Ay-By)^2 +     |         3D-
|                         + (Az-Bz)^2                   |
|                                                       |
|     y                     y                           |
|     |                     |                           |
|     |                     |                           |
|     |                     |                           |
|     |                     |                           |
|     |                     |                           |
|     0---z--z--x    =      0---z--B--x                 |
|    /   z  z              /   z                        |
|   /   z..B              /   A   90                   |
|  /   z                 /                              |
| z   A   90           z                               |
+-------------------------------------------------------+

