CTK Insights

As Galileo has famously said, "Mathematics is the language with which God has written the universe." But what problems! The new book is a collection of physical puzzlers, often with counter intuitive manifestations, which, for all that, admit rigorous explanation supported by physical intuition. Say, you are in a spacecraft orbiting a planet. You turn [...]

For a prime , two integers are both divisible by with the probability , because this only happens when the two integers have the residue 0 (one out of available residues) modulo . Two integers are mutually prime if they have no common nontrivial factors, prime facors in particular. Assuming divisibility by one prime is [...]

Here are a few engaging problems that many a student will be able to solve and, if not, would be able to appreciate the simplicity of a missed solution. Without a measuring tape, is it possible to cut a half-meter piece from the rope of 2/3 m length? Solution What is the digital root of [...]

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, [...]

Going through the old issues of the Mathematics Magazine, I have stumbled on the following note by Dawn Lindquist (Vol. 78, No. 3, Jun., 2005, p. 245) Mathematicians in the market for a car today have many choices. While analytic geometers might be drawn to the Ford Focus and algebraists may assume the Isuzu Axiom [...]