A sonnet for Napoleon's Theorem

     In geometry, Napoleon's theorem (often attributed to Napoleon Bonaparte, 1769–1821) states that if equilateral triangles are constructed on the sides of any triangle, either all outward or all inward, the centers of those equilateral triangles themselves are the vertices of an equilateral triangle.  In a 2015 lecture at the  University of Maryland,  mathematician Douglas Hofstadter (perhaps best known for Godel, Escher, Bach: an Eternal Golden Braid -- Basic Books, 1970) presented Napoleon’s theorem by means of a sonnet.  Perhaps you will want to have pencil and paper available to draw as you read:

Napoleon's Theorem     by Douglas Hofstadter

Equilateral triangles three we’ll erect
Facing out on the sides of our friend ABC.
We’ll link up their centers, and when we inspect
These segments, we find tripartite symmetry.

Sum of moments

Here is a 3x3 square poem -- inspired by a recently-found margin-note I made in Differential and Integral Calculus (by Ross R Middlemiss) when it was my text for an introductory calculus course at Westminster College all those years ago:

          The sum of

          the moments

          is zero.

While the pages of text near the note go on with discussions and diagrams of slices and sums and limits -- they introduce the centroid, the moment of inertia, and the radius of gyration, and are importantly informative -- it is the margin-note that has today delighted me.  I wonder if the girl who wrote it saw it as I do today. I like the mystery.