Canonical structures inside the Platonic solids III | Universal Hyperbolic Geometry 51
The dodecahedron is surely one of the truly great mathematical objects---revered by the ancient Greeks, Kepler, and many mathematicians since. Its symmetries are particularly rich, and in this video we look at how to see the five-fold and six-fold symmetries of this object via internal str
From playlist Universal Hyperbolic Geometry
These sculptures are joint work with Roice Nelson. They are available from shapeways.com at http://shpws.me/oNgi, http://shpws.me/oqOx and http://shpws.me/orB8.
From playlist 3D printing
Geometry: Ch 4 - Geometric Figures (8 of 18) The Regular Pentagon
Visit http://ilectureonline.com for more math and science lectures! In this video I will find the 3 angles of the regular pentagon and its parameter and area. Next video in this series can be seen at: https://youtu.be/3G_jjW1d280
From playlist GEOMETRY 4 - GEOMETRIC FIGURES
Interior Angle Sums of Polygons
Review the pattern developed when we look at the interior angle sums of different polygons.
From playlist Geometry
How to Construct a Dodecahedron
How the greeks constructed the Dodecahedron. Euclids Elements Book 13, Proposition 17. In geometry, a dodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagons as faces, which is a Platonic solid. A regular dode
From playlist Platonic Solids
The classification of Platonic solids I | Universal Hyperbolic Geometry 53 | NJ Wildberger
Euclid showed in the last Book XIII of the Elements that there were exactly 5 Platonic solids. Here we go through the argument, but using some modern innovations of notation: in particular instead of talking about angles that sum to 360 degrees around the circle, or perhaps 2 pi radians, w
From playlist Universal Hyperbolic Geometry
Reaching for Infinity Through Honeycombs – Roice Nelson
Pick any three integers larger than 2. We describe how to understand and draw a picture of a corresponding kaleidoscopic {p,q,r} honeycomb, up to and including {∞,∞,∞}.
From playlist G4G12 Videos
Bridges 2018 talk - Visualizing hyperbolic honeycombs
This is a talk I gave at the Bridges conference on mathematics and the arts (http://bridgesmathart.org/), on 27th July 2018, about my JMA paper with Roice Nelson: https://www.tandfonline.com/doi/abs/10.1080/17513472.2016.1263789 Many high resolution images at hyperbolichoneycombs.org Ray-m
From playlist Talks
Interior and Exterior Angles of a Polygon
http://mathispower4u.wordpress.com/
From playlist Geometry Basics
The Mystery of the Fibonacci Cycle
A video about the mysterious pattern found in the final digits of Fibonacci numbers. It turns out, if you write out the full sequence of Fibonacci numbers, the pattern of final digits repeats every 60 numbers. What’s up with that? Watch this video and you’ll find out! (My apologies to any
From playlist Summer of Math Exposition Youtube Videos
This is lecture 8 of an online mathematics course on group theory. It discusses extensions of groups and uses them to classify the five groups of order 8.
From playlist Group theory
Why do honeybees love hexagons? - Zack Patterson and Andy Peterson
View full lesson: http://ed.ted.com/lessons/why-do-honeybees-love-hexagons-zack-patterson-and-andy-peterson Honeybees are some of nature's finest mathematicians. Not only can they calculate angles and comprehend the roundness of the earth, these smart insects build and live in one of the
From playlist A Bug's Life
Math Mornings at Yale: Asher Auel - Wallpaper, Platonic Solids, and Symmetry
The Platonic solids-the tetrahedron, cube, octahedron, dodecahedron, and icosahedron-are some of the most beautiful and symmetric geometrical objects in 3-dimensional space. Their mysteries started to be unraveled by the ancient Greeks and still fascinate us today. In 1872, the German geom
From playlist Math Mornings at Yale
A space-filling polyhedron, based on the Weaire-Phelan foam
The Weaire-Phelan foam is a relaxation of a packing of irregular dodecahedra and tetrakaidecahedra. Dissect the dodecahedra into pentagon-based pyramids by adding a vertex at the center, then glue their bases to the surrounding tetrakaidecahedra. Amazingly the faces line up and the result
From playlist Geometry
Amazon Honeycode | Build An Application Without Coding | AWS Training | Edureka | AWS Rewind - 4
🔥Edureka AWS Certification Training: https://www.edureka.co/aws-certification-training This "Amazon Honeycode Tutorial" video by Edureka will help you understand what exactly is Amazon Honeycode and how you can create an application using honeycode without any programming. 🔹Checkout Edur
From playlist AWS Tutorial Videos
Fiona Burnell - Lattice Topological Phases - IPAM at UCLA
Recorded 01 September 2021. Fiona Burnell of University of Minnesota, Twin Cities, presents "Lattice Topological Phases" at IPAM's Graduate Summer School: Mathematics of Topological Phases of Matter. Learn more online at: http://www.ipam.ucla.edu/programs/summer-schools/graduate-summer-sc
From playlist Graduate Summer School 2021: Mathematics of Topological Phases of Matter
Amina Buhler - The Magic of Polytopes-Mandalas - CoM July 2021
Polytopes are 3-Dimensional shadows from higher dimensional polyhedra (4-Dimensional & above). These 3-D shadows, when rotated suddenly out of chaos, line-up & reveal, cast mandala patterns into 2-D of 2,3, & 5-fold symmetry. While constructing a stainless steel 120-cell (4-D dodecahed
From playlist Celebration of Mind 2021
A fun number pattern built from the number 987654321
From playlist Number Patterns
James Propp - Conjectural Enumerations of Trimer Covers of Finite Subgraphs of the Triangular (...)
The work of Conway and Lagarias applying combinatorial group theory to packing problems suggests what we might mean by “domain-wall boundary conditions” for the trimer model on the infinite triangular lattice in which the permitted trimers are triangle trimers and three-in-a-line trimers.
From playlist Combinatorics and Arithmetic for Physics: special days