Browse Classroom Capsules and Notes

You can filter the list below by selecting a subject category from the drop-down list below, for example by selecting 'One-Variable Calculus'. Then click the 'APPLY' button directly, or select a subcategory to further refine your results.

Displaying 861 - 870 of 1211

Filter by subject

Why Euclidean Area Measure Fails in the Noneuclidean Plane

The author discusses measuring areas of triangles in a non-Euclidean setting.

A Carpenter's Rule of Thumb

A discrepancy in a method popular with carpenters to check a rectangle for squareness is discussed.

Proof without Words: Viviani's Theorem

In an equilateral triangle, the sum of the distances from any interior point to the three sides is equal to the altitude of the triangle.

A Theorem of Frobenius and Its Applications

The Frobenius Theorem states that if \(d\) is a divisor of the order of a finite group \(G\), then the number of solutions of \(x^d = 1\) in \(G\) is a multiple of \(d\). The article includes...

Proof without Words: (0, 1) and [0, 1] Have the Same Cardinality

A 1-1 map is given of the half-open interval (0,1] onto the closed interval [0,1].

A "Base" Count of the Rationals

Another way of showing that the rationals are countable, relying on constructing a couple of simple functions, is presented.

Covering Systems of Congruences

The authors investigate how to partition the integers into three arithmetic progressions.

Proof without Words: Sums of Triangular Numbers

A well-known counting formula is presented visually.

Heads Up: No Teamwork Required

A variation of the Hat Problem is discussed.

On Tiling the n-Dimensional Cube

The authors investigate the problem of dissecting an n-cube into smaller n-cubes.