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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

Solving Pell Equations using Fibonacci-like sequences

The area under the segment of a parabola is found via the volume of a pyramid.

In plane geometry, if a similarity is not an isometry, it is either a dilative rotation or a dilative reflection. A new proof is given based on Apollonius circles.

The author presents a geometric proof of Machin's formula, which expresses \(\frac {\pi}{4}\) as the difference of two inverse tangent functions.

Inspired by the Pascal triangle, three young "rascals" from three different countries devise a number triangle based on a diamond recurrence formula.

Coefficients are obtained for the Maclaurin series for arctan \(x\) using l'Hôpital's rule.