Visualising solids

The second half of the chapter is about seeing solids, and the book starts by asking you to do it in your head.

The inventor Nikola Tesla worked like this. He said: 'I do not rush into actual work. When I get an idea I start at once building it up in my imagination. I change the construction, make improvements, and operate the device entirely in my mind.' It is what you do when you imagine a cartoon character fully before you draw a single line.

So, no paper for these. Picture your own name written out, and read the letters backwards, by seeing them, not by sound. Then try a friend's name.

Now picture a square. Cut off all four corners, each cut joining the midpoints of two sides next to each other. What shape is left? Can the four cut corners be put together into another square?

Two more: mark each side of an equilateral triangle into thirds and cut off each corner up to the marks. What shape appears? Now do the same to a square.

The big idea: when you look at a solid object, what you really see is its profile, its outline from where you are standing. Move, and the outline can change completely.

You see this in photos and shadows, and in cartoons, where a character runs through a wall and leaves a hole shaped exactly like their outline.

So ask: which solid, seen from which direction, leaves a square hole? A circular one? A triangular one? Harder: which solid gives a rectangle from one side and a circle from another? A circle and a triangle? A trapezium and a circle? And once you have an answer: is it the only one? Often it is not.