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# Tesla Multiplication 3D interactive applet

This multiplication diagram, purportedly by the brilliant inventor Nikola Tesla, contains some interesting patterns.

(Click to see full-size image)

There are various patterns highlighted around the edge of the spiral, like a hexagon for multiples of 2 and a diamond for multiples of 3.

I was fascinated by this multiplication chart, and in the following applet I present the hihglighted patterns in a 3D animation.

## The applet

### Things to do

First, choose some of the low numbers (2, 3 or 4) to see the simple patterns mentioned around the edge of the spiral in the above image.

Next, choose 5 so you can see the star shape. The prime 7 will give you a similar shape.

Then see how 6, 12, 18 give us straight lines when seen from above.

You can see the animation from either above, or as a "chase cam".

You can change the speed of the animation using the "minus" or "plus" buttons.

After the animation finishes each time (gets close to, or reaches 144), you can interact with the resulting 3D graph. You can:

• Drag the curve left-right and up-down to see the axes and point P from different angles
• Change each of the x-, y-, and z-values of the point P by using the sliders around the 3D graph.
• Zoom in and out using the mouse wheel (or 2-finger pinching, if on a mobile device)
• Pan the whole graph left and right using the right mouse button and dragging (or 3-finger swipe on a mobile device)

speed