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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

The author uses Minkowski sums to estimate the length of the perimeter of an ellipse.

The authors give two proofs, one geometric and one algebraic, to provide insight into why the sum of independent normal. random variables must be normal.

Hansheng Yang and Heng Yang used the arithmetic-geometric mean inequality to prove that the sequence \([1+1/n]^n\) is monotonic increasing converging to \(e\) whereas \([1+1/n]^{n+1}\) is monotonic decreasing converging to \(e\). The author provides a simpler proof using the same technique.

An old and forgotten method for determining whether a quartic polynomial over the rationals is reducible is revived.

A visual determination of the area of a right triangle is given using an inscribed circle.

The authors show that the locus of the focus of a parabola rolling on the \(x\)-axis is a catenary.