Browse Classroom Capsules and Notes

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Minimum Integral Drawings of the Platonic Graphs

The authors discuss drawing Platonic solids.

Proof without Words: Sum of Products of Consecutive Integers

A geometric demonstration of an identity for the sum of products of consecutive integers.

Proof without Words: The Sum of a Positive Number and Its Reciprocal Is at Least Two (four proofs)

Four geometric demonstrations of an inequality: the sum of a positive number and its reciprocal is at least \(2\)

On Length and Curvature

The author uses the concept of curvature to prove that one curve is longer than another over [0, 1].

How Much Search Is Enough?

This article demonstrates how to use statistical inferences to solve a real life problem, e.g., finding the lowest price for a certain product.

Proof without Words: A Monotone Sequence Bounded by \(e\)

A geometric construction of a monotone sequence bounded above by \(e\).

Coin Flipping, Dynamical Systems, and the Fibonacci Numbers

This article links two seemingly unrelated problems, one in probability and the other in dynamical systems, and shows they are actually one involving Fibonacci numbers.

A Fibonacci-Like Sequence of Composite Numbers

The author finds a pair of positive integers that generates a generalized Fibonacci sequence containing no prime numbers.

A River-Crossing Problem in Cross-Cultural Perspective

The author compares an African version with the Western version of the famous river-crossing puzzle, and concludes that many mathematical ideas are of panhuman nature.

On the Rational Solutions of \( x^y = y^x \)

The author provides a new way of finding all rational solutions of \( x^y = y^x \) as well as a historical survey of this problem.