Geometry Fact
@GeometryFact
Geometric miscellany, from ancient to modern. On temporary hiatus; publishes occasionally. Curated by @Thalesdisciple.
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“Geometry is unique and eternal, and it shines in the mind of God.” —Johannes Kepler, Conversation with Galileo’s Sidereal Messenger
The AMS, jointly with the MAA, is pleased to offer their book, Living Proof: Stories of Resilience Along the Mathematical Journey, as a free PDF download. ams.org/about-us/Livin…
If an infinite set of points in the plane determines only integer distances, then all the points lie on a straight line. -- Paul Erdös
A several-hundred-page doctoral dissertation from 40 years ago that went largely unnoticed is now fueling a renaissance in studying the geometry of soap films. quantamagazine.org/math-duo-maps-…
quantamagazine.org
Math Duo Maps the Infinite Terrain of Minimal Surfaces | Quanta Magazine
A pair of mathematicians has built on an obscure, 30-year-old mathematical theory to show that soap-filmlike minimal surfaces appear abundantly in a wide range of shapes.
Book illustration: the 21 types of vertices that can be formed by regular polygons. Those in a generate the regular tessellations, b semi-regular, c tessellations with more than one type of vertex. There are no tilings of regular polygons that contain the vertices in area d.
I’m writing a book on tessellations, which means making lots of figures. These illustrate the Laves tessellations, along with the Archimedeans to which they're dual. They’re also known as the Catalan tessellations in analogy to the Catalan solids, dual to the Archimedean solids.
My latest Mathematical Enchantment explains the ins and outs of magic portals between worlds. If you find one that's knotted, be careful how you enter it: your choice could determine which alternate world you end up in! mathenchant.wordpress.com/2018/08/16/kno…
'Old Macdonald had a form; e_i /\ e_i = 0.' -- Mike Stay
The geekiest calculator you'll see today: homotopy groups of spheres johndcook.com/sphere_homotop…
You could describe the motion of a knight by saying it can move a distance of sqrt(5) in any direction.
The Koch Star. Fractal Dimension = log-base-phi of 2 ≈ 1.44
"Crochet Topology" by Moira Chas, this month's Feature Column. Chas uses crochet to explore and understand map-coloring on surfaces bit.ly/2FzVIs8
Crocheting Adventures with Hyperbolic Planes: Tactile Mathematics, Art and Craft for all to Explore. Magnificent! crcpress.com/Crocheting-Adv…
“For Example: On Occasion of the Fiftieth Anniversary of Grünbaum’s Convex Polytopes” Examples, images, and problems from polytope theory. ams.org/journals/notic… [pdf, 6 pages]
“Circle packings, conformal maps, and quasiconformal maps” from Terence Tao’s course notes on complex analysis terrytao.wordpress.com/2018/04/12/246…
Progress on the Hadwiger–Nelson problem, to determine the minimum number of colors required to color every point of the plane in such a way that any 2 points at distance 1 have different colors: en.wikipedia.org/wiki/Hadwiger%…
The chromatic number of the plane is at least 5. arxiv.org/abs/1804.02385
A generic 2D slice through the centre of an icosahedron is an irregular decagon. A generic 3D slice through the centre of a 4D 600-cell is an irregular polyhedron with 218 faces (152 triangles, 66 quadrangles). Slice all the regular 4D polytopes here: gregegan.net/APPLETS/27/27.…
Handouts for a summer workshop led in 1991 by John Conway, Peter Doyle, Jane Gilman, and Bill Thurston.
Geometry and the Imagination in Minneapolis. arxiv.org/abs/1804.03055
I wrote a twitter bot that generates 2-dimensional tilings with randomized parameters. It will auto-tweet once a day, though it may occasionally be more chatty when I'm having fun extending it. I hope you enjoy!
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