The Geometry of the Octonions

How to construct an Octahedron

How the greeks constructed the 2nd platonic solid: the regular octahedron Source: Euclids Elements Book 13, Proposition 14. In geometry, an octahedron is a polyhedron with eight faces, twelve edges, and six vertices. The term is most commonly used to refer to the regular octahedron, a Plat

From playlist Platonic Solids

Quaternions EXPLAINED Briefly

This is a video I have been wanting to make for some time, in which I discuss what the quaternions are, as mathematical objects, and how we do calculations with them. In particular, we will see how the fundamental equation of the quaternions i^2=j^2=k^2=ijk=-1 easily generates the rule for

From playlist Quaternions

What's an Octagon? Geometry Terms and Definitions

An introduction to the octagon, a fundamental geometric shape. Geometer: Louise McCartney Artwork: Kelly Vivanco Director: Michael Harrison Written & Produced by Kimberly Hatch Harrison and Michael Harrison ♦♦♦♦♦♦♦♦♦♦ Ways to support our channel: ► Join our Patreon : https://www.patre

From playlist Socratica: The Geometry Glossary Series

6 2 4 Slide1 3 1Oct2021

From playlist Linear Algebra Ch 6

Cohl Furey on the Octonions and Particle Physics

Cohl Furey explains what octonions are and what they might have to do with particle physics. Read the full article: https://www.quantamagazine.org/the-octonion-math-that-could-underpin-physics-20180720/ Video by Susannah Ireland for Quanta Magazine https://www.quantamagazine.org/ Facebook

From playlist Inside the Mind of a Scientist

Using a set of points determine if the figure is a parallelogram using the midpoint formula

👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr

From playlist Quadrilaterals on a Coordinate Plane

Alberto Elduque: Triality

Duality in projective geometry is a well-known phenomenon in any dimension. On the other hand, geometric triality deals with points and spaces of two different kinds in a sevendimensional projective space. It goes back to Study (1913) and Cartan (1925), and was soon realizedthat this pheno

From playlist Algebra

Étienne Ghys: A guided tour of the seventh dimension

Abstract: One of the most amazing discoveries of John Milnor is an exotic sphere in dimension 7. For the layman, a sphere of dimension 7 may not only look exotic but even esoteric... It took a long time for mathematicians to gradually accept the existence of geometries in dimensions higher

From playlist Abel Lectures

From Hamilton’s Quaternions to Graves & Cayley’s Octonions – Louis Kauffman

We describe geometric and topological approaches to Hamilton's Quaternions and to the Octonions of Graves and Cayley.

From playlist G4G12 Videos

How do we find the area of a octagon (side lengths are not correct)

👉 Learn how to find the area and perimeter of polygons. A polygon is a closed shape with 3 or more sides. The area of a shape is the measure of the portion enclosed by the shape while the perimeter of a shape is the measure of the outline enclosing the shape. To find the area of a polygon

From playlist Area and Perimeter

Could These Numbers Unravel New Dimensions in Space?

These multidimensional number systems are helping us explain the laws of nature. Here’s how. Can Hawking’s Black Hole Paradox Be Solved With Fuzzballs? - https://youtu.be/esPa1tVSjew Read More: The Peculiar Math That Could Underlie The Laws of Nature https://www.quantamagazine.org/the-

From playlist Elements | Season 4 | Seeker

Cohl Furey on the Octonions and Particle Physics (lower volume)

Cohl Furey explains what octonions are and what they might have to do with particle physics. Read the full article: https://www.quantamagazine.org/the-octonion-math-that-could-underpin-physics-20180720 Video by Susannah Ireland for Quanta Magazine https://www.quantamagazine.org/ Facebook:

From playlist Inside the Mind of a Scientist

What are the names of different types of polygons based on the number of sides

👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1

From playlist Classify Polygons

Dominique HULIN - Harmonic coarse embeddings

The Schoen conjecture, recently proved by V. Markovic, states that any quasi-isometric map from the hyperbolic plane to itself is within bounded distance from a unique harmonic map. We generalize this result to coarse embeddings between two Hadamard manifolds with pinched curvature. This

From playlist Riemannian Geometry Past, Present and Future: an homage to Marcel Berger

Beauty and Truth in Mathematics; a Tribute to Albert Einstein and Hermann Weyl - Sir Michael Atiyah

Sir Michael Atiyah Institute for Advanced Study November 8, 2010 For more videos, visit http://video.ias.edu

From playlist Mathematics

Determine if a set of points is a parallelogram using the distance formula

👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr

From playlist Quadrilaterals on a Coordinate Plane

Caustics of Lagrangian homotopy spheres with stably trivial Gauss map - Daniel Alvarez-Gavela

Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Topic: Caustics of Lagrangian homotopy spheres with stably trivial Gauss map Speaker: Daniel Alvarez-Gavela Date: May 14, 2021 For more video please visit https://www.ias.edu/video

From playlist Mathematics

Lie Groups and Lie Algebras: Lesson 2 - Quaternions

This video is about Lie Groups and Lie Algebras: Lesson 2 - Quaternions We study the algebraic nature of quaternions and cover the ideas of an algebra and a field. Later we will discover how quaternions fit into the description of the classical Lie Groups. NOTE: An astute viewer noted th

From playlist Lie Groups and Lie Algebras

What are four types of polygons

👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1

From playlist Classify Polygons