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# Classroom Capsules and Notes

New The Mathematics of Planet Earth 2013 Collection is now available. These are articles published in the three journals of the MAA that are related to the Mathematics of Planet Earth 2013 theme.

Capsules By Courses. We are organizing the capsules into courses, when possible using the same topics as are used inSo far we have organized capsules for One-Variable Calculus, Multivariable Calculus, Ordinary Differential Equations, Number Theory, and Probability. The Number Theory collection of capsules does not correspond to a course in Course Communities, but has topics selected by the Editorial Board for Classroom Capsules and Notes.

Instructions

• Click on Browse Course Topics in the left-hand column of this page.
• Click on the course of interest. (Note that Sequences and Series is also part of One-Variable Calculus.)
• Click on the topic of interest and then on See Results. The capsules corresponding to that topic will be listed at the bottom of the page.

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.

## Polynomial Translation Groups

The topic of discussion is translations of polynomials about the Cartesian plane.

## Proof Without Words: A Reciprocal Pythagorean Theorem

The author proves visually that if $$a$$ and $$b$$ are the legs and h the altitude to the hypotenuse $$c$$ of a right triangle, then $$(1/a)^2 + (1/b)^2 = (1/h)^2$$.

## On a Perplexing Polynomial Puzzle

A polynomial with nonnegative integer coefficients can be determined by two specific values. The author generalizes this result by dropping the nonnegative condition.

## The Rental Car Problem

How to minimize the cost of filling up a rental car