Self-dual tilings | Honeycombs (geometry)
In hyperbolic geometry, the order-5 dodecahedral honeycomb is one of four compact regular space-filling tessellations (or honeycombs) in hyperbolic 3-space. With Schläfli symbol {5,3,5}, it has five dodecahedral cells around each edge, and each vertex is surrounded by twenty dodecahedra. Its vertex figure is an icosahedron. A geometric honeycomb is a space-filling of polyhedral or higher-dimensional cells, so that there are no gaps. It is an example of the more general mathematical tiling or tessellation in any number of dimensions. Honeycombs are usually constructed in ordinary Euclidean ("flat") space, like the convex uniform honeycombs. They may also be constructed in non-Euclidean spaces, such as hyperbolic uniform honeycombs. Any finite uniform polytope can be projected to its circumsphere to form a uniform honeycomb in spherical space. (Wikipedia).
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
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
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
A fold-up, slice-and-dice dodecahedron and its complement. With a 3D printer, you can make your own using the files here: http://georgehart.com/rp/T-O-M/t-o-m.html
From playlist Odds and Ends
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
Henry Segerman - 3D Shadows: Casting Light on the Fourth Dimension - 02/11/17
Henry Segerman "3D Shadows: Casting Light on the Fourth Dimension" February 11, 2017 Wesier Hall Ann Arbor, Michigan
From playlist 3D printing
The remarkable Platonic solids II: symmetry | Universal Hyperbolic Geometry 48 | NJ Wildberger
We look at the symmetries of the Platonic solids, starting here with rigid motions, which are essentially rotations about fixed axes. We use the normalization of angle whereby one full turn has the value one, and also connect the number of rigid motions with the number of directed edges.
From playlist Universal Hyperbolic Geometry
Bridges 2014 talk: The quaternion group as a symmetry group
This is a talk I gave at the Bridges conference on mathematics and the arts (http://bridgesmathart.org/), on 18th August 2014, about my paper with Vi Hart with the same title. The slides are available at https://www.math.okstate.edu/~segerman/talks/quaternion_group_as_a_symmetry_group.pdf
From playlist 3D printing
Abstract Algebra: Find all subgroups in S5, the symmetric group on 5 letters, that are isomorphic to D12, the dihedral group with 12 elements.
From playlist Abstract Algebra
This shows a 3d print of a puzzle I produced using shapeways.com. This is joint work with Saul Schleimer. This is available at http://shpws.me/lmxi. A larger version of the puzzle is available at http://shpws.me/lmxi.
From playlist 3D printing
Day 14 ceramic crystal structures
0:00 reading quiz 5:25 HCP structure and close-packing 10:27 theoretical density calculation 15:00 difference between observed and theoretical densities 18:16 ceramic crystal structures and using rc/ra ratio to determine coordination 23:26 rock salt (NaCl) structure 29:28 cesium chloride (
From playlist Introduction to Materials Science and Engineering Fall 2017
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
To Build Viruses: A Markov Chain Monte Carlo Algorithm for Stimulating Viral Assembly Kinetics
For the latest information, please visit: http://www.wolfram.com Speaker: Nicholas Brunk Wolfram developers and colleagues discussed the latest in innovative technologies for cloud computing, interactive deployment, mobile devices, and more.
From playlist Wolfram Technology Conference 2015
This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/q0PF.
From playlist 3D printing
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
5. Honeycombs: Out-of-plane Behavior
MIT 3.054 Cellular Solids: Structure, Properties and Applications, Spring 2015 View the complete course: http://ocw.mit.edu/3-054S15 Instructor: Lorna Gibson Modeling mechanical behavior of honeycombs and out-of-plane properties are discussed. License: Creative Commons BY-NC-SA More info
From playlist MIT 3.054 Cellular Solids: Structure, Properties and Applications, Spring 2015
MIT 3.054 Cellular Solids: Structure, Properties and Applications, Spring 2015 View the complete course: http://ocw.mit.edu/3-054S15 Instructor: Lorna Gibson Professor Gibson takes questions from students in order to review concepts that will be covered on the midterm exam. License: Crea
From playlist MIT 3.054 Cellular Solids: Structure, Properties and Applications, Spring 2015
Group theory 13: Dihedral groups
This lecture is part of an online mathematics course on group theory. It covers some basic properties of dihedral groups.
From playlist Group theory
Large deviations for random hives and the spectrum of the sum of two random.. by Hariharan Narayanan
PROGRAM COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS: Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE & TIME: 27 June 2022 to 08 July 2022 VENUE: Madhava Lecture Hall and Online Algebraic geometry is t
From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)