This design below shows, visually, how one and zero are related to each other (i.e. by rotation). Here is a mathematical proof for the same idea.

**A proof that one equals zero. **

Consider two non-zero numbers x and y such that

x = y.

Then x^{2} = xy.

Subtract the same thing from both sides:

x^{2} – y^{2} = xy – y^{2}.

Dividing by (x-y), obtain

x + y = y.

Since x = y, we see that

2 y = y.

Thus 2 = 1, since we started with y nonzero.

Subtracting 1 from both sides,

1 = 0.

Hmmm… Clearly something is wrong with this proof. Can you figure out what it is?

Thanks to Mudd Math Fun Facts for the proof above.