A coincidence in geometry:
Take a regular dodecahedron (yellow) and a regular octagon (blue), both with edge length 1. When they are concentric, some of the octagon's vertices seem to coincide with the centres of the dodecahedron's edges (see black circle).
But actually the dodecahedron's midradius is (3+√5)/4 or ~1.309, while the octagon's circumradius is just 1/√(2−√2) or ~1.307.

#geometry

“A New Way to Look at Möbius Strips”

Nothing new in terms of results, even the ones that I knew as a kid, but a nice visualization that clarifies why things work out the way that they do.

https://www.youtube.com/watch?v=izIKV98Awnw

#Numberphile #geometry #math

Advent of Tilings - Day 16.2

The gluing rules and unfolded tiles.

t₂²
(f₁f₂)⁸
(f₁t₁t₁)³

#math #geometry #3d #combinatorics #tiling #AdventOfTilings

Advent of Tilings - Day 16.1

Light enough for the mid-tree branches. Another best effort immersion of an intricate finite surface tiling of genus 169 that is made up of 1344 tiles.

#math #geometry #3d #combinatorics #tiling #AdventOfTilings

🎁📐 @stecks demonstrates the logical approach to wrapping oddly shaped #presents. Her mathematical techniques work for cylinders, triangular prisms, and even squidgy-shaped #gifts through careful measuring and thoughtful folding.

👉 Learn more: https://thekidshouldseethis.com/post/mathematical-present-wrapping-with-katie-steckles?utm_source=mastodon&utm_medium=social&utm_campaign=new_content&utm_content=mathematical_wrapping

#diy #holidays #howto #math #maths #geometry #stem #tksst #video

#APLQuest 2014-01: Write a function that takes the length of the legs of a triangle as its left argument, and the length of the hypotenuse as its right argument, and returns 1 if the triangle is a right triangle, 0 otherwise (see https://apl.quest/2014/1/ to test your solution and view ours).

#APL #PythagoreanTheorem #Geometry

Here's a "cheat sheet" for geometry. If you come across a number you don't recognise, e.g. 0.866025404, you can look up the number and see its exact value may be √(3)/2. If so, it's either the height of a triangle, inradius of a hexagon, circumradius of a cube or midradius of a cuboctahedron. (All the polygons and polyhedra are assumed to be regular and have edges of length 1.)
https://qalle.neocities.org/geometrymagic

#geometry

Schwarz's Lemma from a Differential Geometric Viewpoint (Iisc Lecture Notes) by Kang-Tae Kim (PDF)
Author: Kang-Tae Kim
File Type: PDF
Download at https://sci-books.com/schwarzs-lemma-from-a-differential-geometric-viewpoint-iisc-lecture-notes-9814324787/
#Geometry, #Kang-TaeKim

Advent of Tilings - Day 15.2

The unfolded hexagonal tile in the Poincaré plane with zoom in.

Gluing rules are
t₂²
(f₁f₂f₁f₂f₁t₁)²

#math #geometry #3d #combinatorics #tiling #AdventOfTilings

Advent of Tilings - Day 15.1

The growth of this genus 49 bauble made up of 384 tiles runs through several wonderfully twisted starry constellations before it finally closes up.

Below the growth steps starting from the initial hexagon to the final best effort immersion.

#math #geometry #3d #combinatorics #tiling #AdventOfTilings

AlmostMatched

Video: https://www.youtube.com/watch?v=26e3_wmg06I

Blogpost: https://blog.illestpreacha.com/wcccalmost

#pixelation #glitchy #Livecoding #animation #WCCC #WCCChallenge #Almost #sounddesign

For this week's Creative Code challenge by @sableraph : “Almost”, AlmostMatched coded in #HydraVideoSynth & #SonicPi with the sketch being layered in a near Symmetrical way.

#poem

Almost
Nearly & Barely
On the Symmetrical Coast
Attempted to be on the even Post
Nearly & Barely
Almost

#creativecoding #coding
#newmedia #scifi #flowstate
#geometricart #geometry

Advent of Tilings - Day 14

A Genus 31 surface tiling needing 240 tiles to form, shown again grown ring by ring around the central tile.

The growth of the group elements
1 + 9 + 30 + 51 + 71 + 51 + 24 + 3 ‎ = 240

The looping relators (gluing rules)
t₂⁶
(f₁t₁)²
(t₂⁻¹t₁)³

#math #geometry #3d #combinatorics #tiling #AdventOfTilings

@mf_magazine
LOL I've always done boxes that way - isn't it obvious?
#geometry #wrapping

DotsPlacementOverload

Video: https://youtu.be/_dZcOf8OJzk

Coded #Tixyland

#creativecoding
#geometry
#dots
#livecoding

A Second Course in Mathematical Analysis (Cambridge Mathematical Library) by J. C. Burkill (PDF)
Author: J. C. Burkill
File Type: PDF
Download at https://sci-books.com/a-second-course-in-mathematical-analysis-cambridge-mathematical-library-0521523435/
#Geometry, #J.C.Burkill