How to Construct an Icosahedron
How the greeks constructed the icosahedron. Source: Euclids Elements Book 13, Proposition 16. In geometry, a regular icosahedron is a convex polyhedron with 20 faces, 30 edges and 12 vertices. It is one of the five Platonic solids, and the one with the most faces. https://www.etsy.com/lis
From playlist Platonic Solids
Seminar: Five-fold symmetry, Schiffler points and the twisted icosahedron
This is a seminar talk given at UNSW in the School of Mathematics and Statistics. It discusses joint work with Dr. Nguyen Le of San Francisco State University on a combination of projective geometry and triangle geometry, figuring five fold symmetry, dihedral orderings, a lovely distance r
From playlist MathSeminars
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
👉 Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
👉 Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
👉 Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
What is an equilateral triangle
👉 Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
What is a perpendicular bisector
👉 Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
Lecture 19: Refolding & Smooth Folding
MIT 6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra, Fall 2012 View the complete course: http://ocw.mit.edu/6-849F12 Instructor: Erik Demaine This lecture begins with a problem involving unfolding and refolding. Examples of smooth foldings and unfoldings are given, follow
From playlist MIT 6.849 Geometric Folding Algorithms, Fall 2012
👉 Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
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
AlgTop8: Polyhedra and Euler's formula
We investigate the five Platonic solids: tetrahedron, cube, octohedron, icosahedron and dodecahedron. Euler's formula relates the number of vertices, edges and faces. We give a proof using a triangulation argument and the flow down a sphere. This is the eighth lecture in this beginner's
From playlist Algebraic Topology: a beginner's course - N J Wildberger
Group theory 27: The icosahedral group
This lecture is part of an online math course on group theory. The lecture is about a few examples of groups, in particular the icosahedral group. In it we see that the icosahedral group is the only simple group of order 60, and show that all larger alternating groups are simple.
From playlist Group theory
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
LMS Popular Lecture Series 2008, Know your Enemy, Dr Reidun Twarock
LMS Popular Lecture Series 2008, Know your enemy - viruses under the mathematical microscope, Dr Reidun Twarock
From playlist LMS Popular Lectures 2007 - present
Topics in Combinatorics lecture 1.5 --- averaging and double counting
This is the first video where the course gets down to some actual mathematics. It is quite basic, but introduces ideas that will be used in several places in more sophisticated arguments later on. 0:00 The average of a random variable lies between its minimum and its maximum. 7:10 Double
From playlist Topics in Combinatorics (Cambridge Part III course)
Gauge Equivariant Convolutional Networks and the Icosahedral CNN
Ever wanted to do a convolution on a Klein Bottle? This paper defines CNNs over manifolds such that they are independent of which coordinate frame you choose. Amazingly, this then results in an efficient practical method to achieve state-of-the-art in several tasks! https://arxiv.org/abs/
From playlist Deep Learning Architectures
Richard Esterle - Icosohedrons Almost 13 - G4G13 Apr 2018
Insights from my models and puzzles into the Icosahedron and sphere packing through the years. The Tetraball Puzzle and ICOSA 4 coloring.
From playlist G4G13 Videos
AlgTop9: Applications of Euler's formula and graphs
We use Euler's formula to show that there are at most 5 Platonic, or regular, solids. We discuss other types of polyhedra, including deltahedra (made of equilateral triangles) and Schafli's generalizations to higher dimensions. In particular in 4 dimensions there is the 120-cell, the 600-c
From playlist Algebraic Topology: a beginner's course - N J Wildberger
👉 Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
