CTK Insights

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 [...]

A problem for the innocent minds There is a well known problem of finding two points of the same color in the plane all points of which have been colored either red or blue distance 1 unit apart. It is simple but not trivial. This said what about finding two points of different colors under [...]

The Bottleneck Principle The Bottleneck Principle is a problem-solving strategy according to which it may be useful to look into the circumstances in which the conditions of a problem at hand are either hardly or not at all satisfied. It is different from the Worst-Case Scenario in that the latter looks at the problem as [...]

In the Foreward to the new book by John McCormick, Chris Bishop wrote Computing is transforming our society in ways that are as profound as the changes wrought by physics and chemistry in the previous two centuries. Indeed, there is hardly an aspect of our lives that hasn't already been influenced, or even revolutionized, by [...]

Many book authors end their book Introduction expressing the hope that readers will enjoy reading the book as much as the author(s) enjoyed writing it. Persi Diaconis and Ron Graham do not. Nonetheless, their book - Magical Mathematics - oozes their enjoyment at writing it. The authors are master storytellers. Movingly, Martin Gardner wrote Foreword [...]

This puzzle comes from a wonderful Russian site, where its solution is presented as a sequence of animations. Is it possible to wrap the cube with a 3×3 piece of paper below it? Handling of the paper is subject to two conditions: The paper may be only cut or folded along the crease lines. The [...]

In a recent post, I have implied that Socrates new how to dissect a 2×1 rectangle into a square. There is actually no evidence that he did. However, he certainly knew how to produce a square half the area of a given one. How would he relate the two problems? A sangaku tablet has preserved [...]

Nowadays, finding the area of curvilinear shapes falls in the purview of calculus. But the problem of finding areas draw much interest in antiquity and preoccupied mathematicians ever since. One of the acknowledged results by Hippocrates of Chios (470-410 B.C.) is the Squaring of a Lune. The problem of squaring a shape refers to a [...]

A hyperbola has two axes of symmetry: one that crosses the hyperbola while the other does not. Two different 3D shapes are obtained when a hyperbola is made to rotate around its axes. Two sheet hyperboloid One sheet hyperboloid The equation of one is and that of the other is The one sheet hyperboloid has [...]

I just received a review copy of Fascinating Mathematical People by Donald Albers and Gerald Alexanderson (Princeton University Press, 2011). Right now I am into something else, but could not forego getting a quick first impression. Looks like I am going to enjoy reading the book. Here's something that caused me a healthy chuckle. I [...]