CTK Insights

Review of Mathematical Plums by Ross Honsberger. Mathematical Plums is the fourth book in the Dolciani Mathematical Expositions series

Calculus Proof of the Pythagorean Theorem. Begin with a right triangle drawn in the first quadrant. The legs are variables xand y and the hypotenuse is a fixed positive value c, where the verte xof the angle whose sides contain xand c is the origin

Creatures from a nearby dimension penetrate our reality and want to fill a large swimming pool with their lime-scented nutritional fluid. From Hose A pours a green slime that would, by itself, take 30 minutes to fill the pool. From Hose B surges a crimson slime that, by itself, would take 20 minutes to fill [...]

A circle is inscribed in triangle ABC. MN is the diameter perpendicular to the side AC. Let L be the intersection of BM with AC. Prove that AN = CL

Prove that the equation x^n + y^n = x^(n-1), n greater than 2 has infinitely many solutions in positive integers

In an acute triangle ABC, the median AM is longer than side AB. Prove that you can cut the triangle into three parts out of which you can construct a rhombus. From 2010 All-Russian Olympiad, grade 9

xx+ yy + zz = 59^n is solvable for all positive integers n

Helly's theorem, amended history, a proof in the plane, references to generalizations

Given s (s > 0) points in the plane such that every three of them are contained in a disk of radius 1. Prove that all s points are contained in a disk of radius 1