A circle is a curve of constant width. As you rotate a circle its width doesn't change. Does any other shape have this property?
Why yes! The Reuleaux polygons all do. The simplest and best known of which is the Reuleaux Triangle.
How do you draw a Reuleaux triangle?
Draw an equilateral triangle, and then inscribe 3 arcs, each centred on a point of the triangle and travelling between the other two points.
lt 30 repeat 3 [ fd 100 lt 120 lt 60 arc 100 60 rt 60 ]
Or, draw three circles, where the centre of each circle touches the outside of the other two:
What can you do with this special shape?
You can make a drill bit that drills a square hole! (The Harry Watt square drill bit, where the drillbit needs to be mounted in a special chuck which allows for the bit not having a fixed centre of rotation)
You can build rotary engines! *
You can make a bike that has non-circular wheels but still gives a smooth ride.
- Regarding rotary engines:
The Wankel rotary engine isn't quite Reuleaux shaped. It says on wikipedia:
The four-stroke cycle occurs in a moving combustion chamber between the inside of an oval-like epitrochoid-shaped housing, and a rotor that is similar in shape to a Reuleaux triangle with sides that are somewhat flatter.
Can you write a program that draws a Reuleaux polygon of any number of sides?
- Smooth-riding Bike with Reuleaux Triangle back-wheel and Pentagonal front-wheel
- Rolling with Reuleaux
- Mathworld: Reuleaux Triangle
- Wikipedia: Reuleaux Triangle