CTK Insights

Theorem For any greater than is irrational. The following proof has been submitted by Richard Ehrenborg, University of North Carolina, Charlotte and published in the American Mathematical Monthly (May 2003, 423) with a remark that the proof was found by William Henry Schultz, at the time an undergraduate at UNC-Charlotte. The proof has been reproduced [...]

Elsewhere we proved that the sequence (1) is convergent to 2. With this in mind, it is possible and meaningful to shorten the description of this fact to   Expressions like that serve an example of infinite nested radicals. They are realized in terms of limits, if those exist, and are understood as the shorthand [...]

Years ago I came across a problem of flipping several items simultaneously: There are 7 glasses on a table–all standing upside down. It is allowed to turn over any 4 of them in one move. Is it possible to reach a situation where all the glasses stand right side up. The solution is rather obviously [...]

Charles Lutwidge Dodgson – better known to broad public as Lewis Carroll – has developed an algorithm to calculate the exact date of Easter Sunday for every year until 2499. In this he bested the great Carl Friedrich Gauss who also found it a sufficiently important occupation. Gauss devised a formula that gave the correct [...]

Three ropes have been fastened to a horizontal plunk, tangled a little as if one tried to make a braid and, lastly, loosely attached to an auxiliary plank to keep them braided. Down below there is a third plank. The task is to attach three additional ropes to the first ones at one end and [...]

A human hand carries five fingers; two hands have ten of them. Undoubtedly, this fact is responsible for the universal adoption of the decimal system. Children learn to count by counting fingers, first to 5 on one hand and then to 10 on two hands. However, there is a simple way to count to 10 [...]

George G. Szpiro, author of Numbers Rule: The Vexing Mathematics of Democracy, from Plato to the Present is a mathematician and journalist living in Switzerland. Numbers Rule focuses on key figures in the development of democracy and on the mathematics of voting, elections, and apportionment that they developed. Szpiro pays particular attention to the paradoxes [...]

The fact that π exists is due to the similarity of all circles. The ratio of the circumference to the diameter would not be constant otherwise. The simple idea of similarity is commonly being reported as overly hard on children. I am confident that the problem must lie with the manner of presentation and not [...]

This is a Math teachers at play carnival, issue # which I am going to reveal shortly. See if you can make it from what is known as a single image stereogram. Try focusing your eyes behind the screen. In this month issue: What is the number of this issue? Sad news Interesting and relevant [...]

V. Arnold in an article Innumeracy and the Fires of the Inquisition narrates the following episode: A flier that was distributed during a forum (the paper has been written in 1998) of the mathematical section of RAS (Russian Academy of Sciences) contained a QA section. The answer given to the question of how much is [...]