## A short proof of Pythagorean Theorem via Silverlight

Press Next step to navigate thru the Yellow-Green-Blue-Red triangles. Here follows a description of the first 4 steps. The next 4 ones are quite similar.

Step 1: The Yellow triangle has half the area of the Left square .

Step 2: The Green triangle has the same area with the previous Yellow one. We just moved the bottom corner along a parallel to its top Base.

Step 3: The Blue triangle is equal to the previous Yellow one. We rotated by 90 degrees counterClockwise.

Step 4: The Red triangle has the same area with the previous Blue one. We just moved the bottom corner along the blue parallel to its top Base.

The above small Silverlight application was created trying to understand and learn the new WPF-Silverlight framework of Microsoft. Another motivation was to demonstrate the theorem to my small son. Because, as the great American physicist Richard Feynman has said, "we understand what ever we can make ..."

## A tribute to Isaac Newton

Drag the ball and let it fall down. You will see a simple simulation of gravity

We all have seen apples or balls falling down to the ground. BUT Isaac Newton was the first to explain WHY the ball falls down and not flying around. In few words, this is due to gravitational force which causes a constant accellaration (g) downwards.

On every clock tick the velocity (v) increases by a constant amount (g) and the travelled distance icreases by the amount of the velocity. if (V) is the Velocity, (t) the time and (H) the distance, this is expressed in mathematics:

dV/dt = g ⇔ V = g × t , H = ( g × t² ) / 2

The above small Silverlight application was created trying to understand and learn the new WPF-Silverlight framework of Microsoft. Another motivation was to demonstrate the gravitational forces to my small son and introduce him to the wonderful world of animation. We should learn, as if we would live for ever.