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.
Showing posts with label equilateral. Show all posts
Showing posts with label equilateral. Show all posts
Sunday, January 31, 2016
Wednesday, October 13, 2010
Varieties of triangles -- by Guillevic
My introduction to French poet Guillevic (1909-97) came from UK poet Tim Love who found three of his triangle poems translated into Italian. Jacqueline Lapidus translated them for me from French into English, after which I also found Guillevic's collection Geometries (Englished by Richard Sieburth, Ugly Duckling Presse, 2010) -- with its circles, ellipses, parallels, and so on. And so, beyond these three, there will be more to enjoy later.
Labels:
angle,
base,
equilateral,
Guillevic,
isosceles,
Jacqueline Lapidus,
scalene,
side,
Tim Love,
triangle
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