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Classroom Capsules and Notes

Note. We now return to our every-other-week schedule for featured articles, shown at the bottom of this page.

Capsules By Courses. We are organizing the capsules into courses, when possible using the same topics as are used in Course Communities. So far we have organized capsules for the following courses:

You may select topics within each course.


Featured Items

After a brief historical discussion of the aliquot parts of an integer the authors use elementary arguments to prove a theorem about the sums of its principal divisors.

The tiling of a sphere by spherical triangles is discussed.

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 a proof and applications of the 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.

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

Certain subsets of the ring of integers mod n with hidden group structure are discussed.