CTK Insights

Today's activity is based on a problem by Vyacheslav Proizvolov offered at the 1985 All-Union Soviet Math Olympiad. What do you need? Strictly speaking, that activity needs nothing beyond a piece of paper and a pencil. However, it may be convenient to have numbers, say, 1 through 20, written on small paper pieces: What is [...]

The setup Draw 6 dots more or less evenly distributed over a circle: The activity Join the dots by lines of two colors, say, red and blue. Join all pairs of dots. See how many lines of the two colors emanate from each dot. What's to observe At every dot there are at least three [...]

Breaking chocolate bars is one of my most favorite activities. Assume you have a chocolate bar consisting, as usual, of a number of squares arranged in a rectangular pattern. Your task is to split the bar into small squares (always breaking along the lines between the squares) with a minimum number of breaks. How many [...]

An engaging activity has been described by Martin Gardner in his Mathematical Games column in Scientific American, v 201, No 6, Dec 1959 and later included in one of his collections, New Mathematical Diversions. Rather recently, an upgraded variant has emerged as the Japanese ladders game. Amazingly, neither Gardner has mentioned the Japanese sources in [...]

Mathematics is certainly not (only) about counting, graphing and solving equations. I do not believe that every child can reach beyond those. I do not believe that a child who does not show an inclination to dig deeper into math mysteries lacks in intellect or creativity. I do think that it is worth trying to [...]

To an average student (and, perhaps, an average teacher used to teaching from a textbook) it may come as a surprise that there are numerous problems with multiple known solutions. "How come?" - may wonder the average student, "Who would want the drudge of solving a problem whose solution is already known?" Why, it's a [...]

I have recently come across an article by Atara Shriki of the Technion - Israeli Institute of Technology - where she extended an engaging property of the graph of y = x³ introduced by R. Honsberger. At an arbitrary point P on the graph of y = x³ draw the tangent line and mark its [...]

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 [...]

Euclid did not know yet that the same constant (π) appears in the formula for the circumference and the area of a circle. Archimedes did, athough his method of approximating either by exausting the circle with regular polygons does not make this quite obvious. In the 16th century, Leonardo da Vinci, and in the 17th [...]