Composition algebras | Octonions
In mathematics, the octonions are a normed division algebra over the real numbers, a kind of hypercomplex number system. The octonions are usually represented by the capital letter O, using boldface O or blackboard bold . Octonions have eight dimensions; twice the number of dimensions of the quaternions, of which they are an extension. They are noncommutative and nonassociative, but satisfy a weaker form of associativity; namely, they are alternative. They are also power associative. Octonions are not as well known as the quaternions and complex numbers, which are much more widely studied and used. Octonions are related to exceptional structures in mathematics, among them the exceptional Lie groups. Octonions have applications in fields such as string theory, special relativity and quantum logic. Applying the Cayley–Dickson construction to the octonions produces the sedenions. (Wikipedia).
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
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
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
‘Octobot’ is the world’s first soft-bodied robot
Flexible machine goes where no robot has gone before. Learn more: http://www.sciencemag.org/news/2016/08/octobot-world-s-first-soft-bodied-robot
From playlist Robots, AI, and human-machine interfaces
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
From playlist Linear Algebra Ch 6
Octahedron in Geogebra Step by step tutorial here: https://youtu.be/LmCs6dzZreA In case you wanna to pay me a drink: https://www.paypal.me/admirsuljicic/
From playlist Geogebra [Tutoriali]
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
Octahedron in Geogebra [Tutorial]
Octahedron in Geogebra [Tutorial] In case you wanna to pay me a drink: https://www.paypal.me/admirsuljicic/
From playlist Geogebra [Tutoriali]
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
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
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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.
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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
Algebraic Topology - 12.2 - Fiber Bundles
From playlist Algebraic Topology
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
History of Science and Technology Q&A (May 4, 2022)
Stephen Wolfram hosts a live and unscripted Ask Me Anything about the history of science and technology for all ages. Find the playlist of Q&A's here: https://wolfr.am/youtube-sw-qa Originally livestreamed at: https://twitch.tv/stephen_wolfram If you missed the original livestream of
From playlist Stephen Wolfram Ask Me Anything About Science & Technology
From playlist Linear Algebra Ch 6