The Disc Problem (doc | pdf)

A can of soup, a coin, and a piece of spaghetti are all cylinders even though they look very different.  One might say the coin is more “disc-like” than the spaghetti.

1.   Given the variety of cylinders you have: Devise a definition of disc-ness that allows you to say which object is the most disc-like and which is the least.
2.   Write a formula (or algorithm or algebraic sentence) which expresses your measure of disc-ness. You may introduce any labels and definitions you like and use all the mathematical language you care to.
3.   Make any measurements you need, and calculate a numerical value of disc-ness for each of the six items.
4.   Discuss whether these numbers seem reasonable in light of your notion of disc-ness.
5.   How would you change your answers to these questions if you were asked to write a formula for cylinder-ness rather than disc-ness?