Copyright ©1996 by Paul Niquette. All rights reserved.
I have posed this thought
friends and associates, to university audiences and
The answers I invariably hear are of the form: The
net nine balls into the vase at each step; after an
infinite number of
steps, there must be an infinite number of balls in the
See Off on a Tangent
Off on a Tangent
onsider the trigonometric tangent of a 90-degree angle.
As a transcendental function, the tangent does something mighty strange in the vicinity of 90 degrees.
Mathematicians shrug. "What do you
expect from a discontinuous
function?" they explain.
This puzzle is a ball-in-the-vase version of the famous paradox [seemingly contradictory statement but nevertheless true] attributed to Zeno of Elea, a Greek mathematician and philosopher who lived back in 5th century BC (long before numbered balls). We have come across this fellow Zeno before (see Hand Over Hand). Another version of this paradox was discovered in the solution to Rational Roots.