# 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

##### When Cauchy and Hölder Met Minkowski: A Tour through Well-Known Inequalities

The author states a "Master Theorem" from which, exploiting concavity, he deduces several classical inequalities.

##### The Class of Heron Triangles

The author shows that every Heron triangle is similar to one with sides $r + 1/r$, $s + 1/s$, and $r - 1/r + s -1/s$ for rational numbers $r$ and $s$ greater than one.

##### The Lost Cousin of the Fundamental Theorem of Algebra

A Fundamental-like Theorem of Algebra for exponential functions is discussed and proved.

##### Fitting One Right Triangle in Another

The authors answer the question in the title of the paper. This result constitutes part of the output of an undergraduate summer research project by the second author under the supervision of the first author.

##### Proof without Words: The Law of Cosines

The author proves visually the law of cosines.

##### Suspension Bridge Profiles

The author describes the shape of an overhead cable suspended from a horizontal deck with non-uniform lineal mass.