Geometry Fact

Geometric miscellany, from ancient to modern. On temporary hiatus; publishes occasionally. Curated by @Thalesdisciple.

[Geometry Fact @GeometryFact]

“Geometry is unique and eternal, and it shines in the mind of God.” —Johannes Kepler, Conversation with Galileo’s Sidereal Messenger

[Kjetil Golid @kGolid]

Proofs of Nothing 🖍📐

[American Mathematical Society @amermathsoc]

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. https://t.co/wzOY7u6ndP

[Algebra Etc. @AlgebraFact]

If an infinite set of points in the plane determines only integer distances, then all the points lie on a straight line. -- Paul Erdös

[Quanta Magazine @QuantaMagazine]

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.
https://t.co/eGRgL0iN7m

[Robert Fathauer @RobFathauerArt]

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.

[Robert Fathauer @RobFathauerArt]

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.

[James Propp @JimPropp]

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! https://t.co/IWGQbYXyA2

[Analysis Fact @AnalysisFact]

'Old Macdonald had a form; e_i /\ e_i = 0.' -- Mike Stay

[Topology Fact @TopologyFact]

The geekiest calculator you'll see today: homotopy groups of spheres
https://t.co/NtwsBDlMPX

[Algebra Etc. @AlgebraFact]

You could describe the motion of a knight by saying it can move a distance of sqrt(5) in any direction.

[Topology Fact @TopologyFact]

Desargues' Theorem https://t.co/zufDUoVIiA

[Matt Enlow @CmonMattTHINK]

The Koch Star. Fractal Dimension = log-base-phi of 2 ≈ 1.44

[American Mathematical Society @amermathsoc]

"Crochet Topology" by Moira Chas, this month's Feature Column. Chas uses crochet to explore and understand map-coloring on surfaces https://t.co/x4Rh3pOsR3

[Steven Strogatz @stevenstrogatz]

Crocheting Adventures with Hyperbolic Planes: Tactile Mathematics, Art and Craft for all to Explore. Magnificent! https://t.co/CwMGNlTDck

[Geometry Fact @GeometryFact]

“For Example: On Occasion of the Fiftieth Anniversary of Grünbaum’s Convex Polytopes” Examples, images, and problems from polytope theory. https://t.co/OjNtQv4JE5 [pdf, 6 pages]

[Geometry Fact @GeometryFact]

“Circle packings, conformal maps, and quasiconformal maps” from Terence Tao’s course notes on complex analysis https://t.co/sJAul8xFJT

[Geometry Fact @GeometryFact]

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: https://t.co/n8pbjUI4o8 https://t.co/HyWCXfbzUb

[Mathematics Papers @MathPaper]

The chromatic number of the plane is at least 5. https://t.co/tLtpfjd5zS

[Greg Egan @gregeganSF]

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:
https://t.co/A3487G20PQ

[Geometry Fact @GeometryFact]

Handouts for a summer workshop led in 1991 by John Conway, Peter Doyle, Jane Gilman, and Bill Thurston. https://t.co/rWzgB7bWKG

[Mathematics Papers @MathPaper]

Geometry and the Imagination in Minneapolis. https://t.co/0QJWpUI0YS

[Roice @roice713]

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! https://t.co/MVCMhXIVfq