Favorite Numbers

During this past summer's vacation, we had a discussion about favorite numbers. Mine is pi. I like it's shape -- sort of Stonehenge-ish. When I think of pi I think of roundness and harmony. I like thinking about curved surfaces. Two parallel lines can intersect on a curve. Triangles placed on a curve have more than 180 degrees when their angles are added together! Pi is great.

Gravity Well's favorite number is square root of two. It fascinates him that we can travel simply 1 unit (rational number) to the right, 1 unit up (rational number) but to go straight back to our starting point (Pythagorean theorem) we have to travel an irrational number of units 1.41421...

Which can be represented as,

....
Which is wonderfully similar to another favorite of Gravity Well's, PHI=1.618... (golden ratio)

Which can be represented as,

Also, approaches 2 if you keep going... And shows up a lot in Trigonometry.

....

Esh's favorite number is e. It describes many things in the mathematical world, from Euler's identity to continually compounded interest. And in calculus, the derivative of e^x is e^x, and the derivative of ln(x) is 1/x. So simple, but so elegant.