CTK Insights

The altitudes of a triangle concur at a point - the orthocenter of the triangle. There are multitudes of proofs, each shedding light of a different hue on the existence of the orthocenter. Collecting these proofs was an enjoyable undertaking, and edifying, too. Not until a few days ago, when I came across another problem, [...]

Imagine a pyramid with no symmetries or regularities whatsoever. To construct a pyramid like that, pick a plane, four arbitrary points in the plane and one point outside. The lines (or rays) joining the latter to the four points in the plane serve as the edges of a slanted and likely irregular pyramid. However, the [...]

Indeed, is it possible to miss the New Year moment? The question is not meant to account for a possible tragic circumstance and is being asked plainly and candidly. Assuming you are in good health on December 31 of one year and remain healthy on January 1 of the next year, is it possible to [...]

It's hard to overestimate the influence Alcuin of York (c. 732-804) had on Western civilization. He also left the earliest known European collection of puzzles, Propositiones alcuini doctoris caroli magni imperatoris ad acuendos juvenes - Propositions by Alcuin Teacher to the Great Emperor Charles to Sharpen up the Young. The collection consists of 53 problems [...]