Several British objects of constant width. Image: Evelyn Lamb.
Almost immediately after getting off the plane at Heathrow, I got some breakfast and some change in the form of metal shapes of constant width. That’s right, all British coins are shapes of constant width. This isn’t remarkable because circles have constant width, and [...]
Posts tagged geometry
British Objects of Constant Width
Several British objects of constant width. Image: Evelyn Lamb.
Almost immediately after getting off the plane at Heathrow, I got some breakfast and some change in the form of metal shapes of constant width. That’s right, all British coins are shapes of constant width. This isn’t remarkable because circles have constant width, and [...]
What’s the Deal with EuclidR...
An illustration from Oliver Byrne’s 1847 edition of Euclid’s Elements. Euclid’s fourth postulate states that all the right angles in this diagram are congruent. Image: Public domain, via Wikimedia Commons.
Why the heck do we need a postulate that says that all right angles are equal to one another? You probably remember lear [...]
The Math Wars, Lewis Carroll Style
Lewis Carroll in 1863, photographed by Oscar Gustave Rejlander. Image: Public domain, via Wikimedia Commons.
Carroll’s book was a salvo in the “math wars” of the day, the subject of which was how best to teach geometry. Euclid was the standard textbook in private schools that taught mathematics, but many people found it wanting. To them, it w [...]
Chasing the Parallel Postulate
If you’d like to see these again, you’d better accept the parallel postulate. Image: Webber, via Wikimedia Commons.
Euclidean geometry, codified around 300 BCE by Euclid of Alexandria in one of the most influential textbooks in history, is based on 23 definitions, 5 postulates, and 5 axioms, or “common notions.” But as [...]
Hyperbolic Quotes about Hyperbolic Ge...
“The treatise itself, therefore, contains only twenty-four pages—the most extraordinary two dozen pages in the whole history of thought!”
This Hungarian postage stamp does not depict János Bolyai. No portraits of him survive. For more information about the “real face of János Bolyai,” click the picture to read Tamás Dé [...]
How Much Pi Do You Need?
NASA scientists keep the space station operational with only 15 or 16 significant digits of pi, and the fundamental constants of the universe only require 32. Yet in 2006 Akira Haraguchi of Japan recited 100,000 digits of pi from memory in 16 ½ hours, stopping for five minutes every hour to replenish his strength with onigiri rice balls. And [...]
A Tasty Geometric Morsel Every Day
#426 Tectonic Activity. Image copyright Tilman Zitzmann. Used with permission.
It’s fun to look through the Geometry Daily archives and notice similarities between designs published around the same time. Tilman seems to have had a hexagon phase in the 320’s, and you can definitely see the designs getting more complex but also more [...]
Platonic Solids, Symmetry, and the Fo...
The icosidodecahedron, a solid “halfway through” the transition from the dodecahedron to its dual, the icosahedron. Image: Tomruen, via Wikipedia. Created using Robert Webb’s Great Stella software.
On his blog Azimuth, John Baez has been posting a series called “Symmetry and the Fourth Dimension.” He writes: R [...]
Strumming the Lute of Pythagoras
Columbia College Chicago instructor Ann Hanson and two of her students generously shared artwork they made using the geometric figure the “Lute of Pythagoras.”
A drawing by Joseph Koch incorporates the Lute of Pythagoras into a portrait of Pythagoras himself. Image copyright Joseph Koch. Used with permission.
The ancient mathemati [...]
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