CTK Insights

Sam Loyd's Fifteen is a famous conundrum from the end of the 19th century. As the recent investigation by Jerry Slocum and Dic Sonneveld has revealed, attributing the puzzle to Sam Loyd is justified only partially. Repeated claims to the contrary notwithstanding, Sam Loyd has not invented the puzzle. He is certainly responsible for creating [...]

Here is a curious diagram I cam across in H. Jacobs' Geometry. (Jacobs, in turn, credits a 1901 publication.) The diagram that presents all possible kinds of triangles could serve as a great poster. As you can see, all possible triangle classes do appear there. The diagram is curious in that its dimensions (up to [...]

Two fractions a/b and c/d are equal (or often equivalent) only if ad = bc. The same cross-multiplication helps compare two fractions. For simplicity I shall assume all integers positive. Thus, a/b > c/d if and only if ad > bc. This is a simple and, for small numbers, not an overly difficult test. However, [...]

Once in a while an NCTM publication stuns me. They just published solutions to the July 15 problem of finding proportions between areas in a square: One solution is absolutely beautiful.                                             The solution [...]

I am a proud parent: my 11 years old son takes a 7th grade Algebra 1 Honors class. Judging by the homework assignments and my kid's notes, the 6th grade math teacher was rather inept in the subject matter. The topics came one after another with no indication of any relationship between any two. To [...]

Hamas PLC Speaker Ahmad Bahr gave a speech broadcast by Al-Aqsa TV (Hamas/Gaza) on September 5, 2010. Here is the mathematical part: It is said that Omar [Ibn Al-Khattab] wished to become a martyr. It is said that one day, Omar addressed the people: 'In the Garden of Eden, there is a palace – hear [...]

The list of the 2010 Fields Prize Winners is now available on the web. There are two articles, The laudations and The work profile, that introduce each of the winners and throw light on their mathematics. The laudations is an extensive math biography, the work profile is a popular rendition of the winner's achievement. This [...]

Here is a simple problem I found in a recent book from MAA (C. Alsina, R. B. Nelsen, Charming Proofs, p. 89.) Geometric constructions of a square inscribed in a triangle are well known. There are two ways to inscribe a square into a right isosceles triangle: Which square has the larger area? The problem [...]

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 [...]