Geometric miscellany, from ancient to modern. On temporary hiatus; publishes occasionally. Curated by @Thalesdisciple.
Joined March 2013
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Geometry Fact retweeted
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/LivingProof…
Geometry Fact retweeted
If an infinite set of points in the plane determines only integer distances, then all the points lie on a straight line. -- Paul Erdös
Geometry Fact retweeted
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-…
Geometry Fact retweeted
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.
Geometry Fact retweeted
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.
Geometry Fact retweeted
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/20…
Geometry Fact retweeted
The geekiest calculator you'll see today: homotopy groups of spheres
johndcook.com/sphere_homotop…
Geometry Fact retweeted
You could describe the motion of a knight by saying it can move a distance of sqrt(5) in any direction.
Geometry Fact retweeted
"Crochet Topology" by Moira Chas, this month's Feature Column. Chas uses crochet to explore and understand map-coloring on surfaces bit.ly/2FzVIs8
Geometry Fact retweeted
Crocheting Adventures with Hyperbolic Planes: Tactile Mathematics, Art and Craft for all to Explore. Magnificent! crcpress.com/Crocheting-Adve…
Geometry Fact retweeted
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.h…
Geometry Fact retweeted
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! xitter.cf/TilingBot/status/98320…
Geometry Fact retweeted
When the connection between two supposedly disparate fields of mathematics was found, mathematicians couldn’t believe it. Now, that connection is at the heart of one of math’s most flourishing fields.
quantamagazine.org/mathemati…
Geometry Fact retweeted
Euclidean geometry has disk models too! I made these images of the {3,6} and {4,4} Euclidean tilings in a disk model where geodesics are circular arcs. Read more explanation by David Eppstein: 11011110.github.io/blog/2016…
Geometry Fact retweeted
ICYMI: The ancient Japanese art of kirigami, a cousin to origami, generates curved spaces from flat sheets of paper. After hundreds of hours of cutting and folding, mathematicians have recently uncovered the four rules behind the transformation.
buff.ly/2G4AN23
