# CTK Insights

• ## Pages

26 Nov

### 3² + 4² = 5²

Tweet3² + 4² = 5² is the first and the simplest member in an infinite sequence if the Pythagorean triples. It is also the first and the simplest member in an infinite sequence of identities of the sums of successive squares, the next ones being 10² + 11² + 12² = 13² + 14², 21² […]

11 Nov

### G.K. Chesterton's Wisdom

TweetJerry Becker who runs a very useful list server occasionally broadcasts collections of sayings to read, enjoy and benefit from. In the latest (SAYINGS XXVIII) the first piece of wisdom was credited to G. K. Chesterton, an English writer of more than 100 years ago. The oxymoronic quote "The thing I hate about an argument […]

10 Nov

### The Size is in the Eyes of the Beholder

TweetHere is an engaging problem for all ages: Six points are given in the space such that the pairwise distances between them are all distinct. Consider the triangles with vertices at these points. Prove that the longest side of one of these triangles is at the same time the shortest side of another (See, http://www.cut-the-knot.org/proofs/ShortestIsLongest.shtml)

04 Nov

### Archimedes' Law of the Lever

TweetTwo material points are in equilibrium if their distances from the fulcrum are inversely proportional to their weights. This is known as the Law of the Lever. The law serves as an engaging exercise for finding the greatest common divisor of two integers. Its proof by Archimedes is a captivating example - accessible in middle […]

03 Nov

### Drug Use and Abuse

TweetThis is a caption of a quiz my 6 grader son has recently taken. What can I say? Seeing this quiz I feel cheated. Do we really pay the taxes so that the kids in grade 6 learn the difference between inhalants and stimulants? Quite candidly, by sound of it, I could surmise the meaning […]