CTK Insights

Jeffrey Samuelson twitted a question to which I am happy to provide an answer, or two. Question Find an integer N such that N(N+1)(2N+1) is NOT divisible by 6. If no such integer exists, prove why. Since the question is about the properties of a product modulo 6, it seems proper to investigate the dependency [...]

When Tennyson wrote The Vision of Sin, Babbage read it. After doing so, it is said he wrote the following extraordinary letter to the poet: "In your otherwise beautiful poem, there is a verse which reads: 'Every moment dies a man, Every moment one is born.' "It must be manifest that, were this true, the [...]

(Borrowed from http://www.boingboing.net/2011/03/21/how-to-make-a-hamant.html)

Simple mathematics may be rather impressive even on an early developmental level. The "1089 prediction" is one of the better known tricks that may be presented to the 3-4 grade audience. David Acheson describes it thus: Think of a three-digit number. Any three-figure number will do, so long as the first and last figures differ [...]

March 14 is practically an official π day. Why is that? March is the fourth month of the widely accepted Gregorian calendar and, not incidentally, π ≈ 3.14. There are dissenting voices that claim July 22 as a more appropriate day for the celebration because 22/7 (≈ 3.14286) is a better approximation to the real [...]

I cannot recollect which book it was but I do remember it was a book by a famous mathematician who wrote in Introduction that to write a book is the best way to learn a new topic. I got this memory flash when reading an article in Mathematics Teacher: Our teachers misled us, but we [...]

You have to see it to believe it.

[mathjax] A decimal integer has the form A divisibility criterion is a procedure, in some sense simpler than straight division, that allows us to determine whether or not number is divisible by another number . For example, is divisible by if and only if the sum of digits is divisible by . For example, is [...]