Split-octonion

Split Complex Numbers in Matrix Form

In this video, we'll find the matrix representation for the split complex numbers, which are those numbers similar to the complex numbers but with an imaginary unit, j, which squares to 1 instead of -1. We will also review Euler's formula for the split complex numbers and how this relates

From playlist Math

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

The Complex Numbers You Haven't Heard Of

In this video, I introduce the split-complex numbers, which are similar to the complex numbers except we now have an object, called "j", which squares to +1. As you will see, multiplying split-complex numbers with j^2=1 in mind will generate motion following hyperbolas, similar to how comp

From playlist Math

Trigonometry 7 The Cosine of the Sum and Difference of Two Angles

A geometric proof of the cosine of the sum and difference of two angles identity.

From playlist Trigonometry

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

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

Trigonometry 10 The Sum of Sines

The sum of the sine of two angles.

From playlist Trigonometry

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 is a split function?: Dr Chris Tisdell Live Stream

Split functions follow one rule and the swtich to another rule, depending on where you are on a x-axis. I define what a split function is (also called a picewise defined function) and discuss and example. In mathematics, functions are an important tool for understanding how things depend

From playlist Calculus for Beginners

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

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

Trigonometry 5 The Cosine Relationship

A geometrical explanation of the law of cosines.

From playlist Trigonometry

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

Commutative algebra 39 (Stably free modules)

This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We discuss the relation between stably free and free modules. We first give an example of a stably free module that is not fre

From playlist Commutative algebra

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

Trigonometry 9 The Sum of Cosines.mov

The sum of the cosine of two angles.

From playlist Trigonometry

L07 split plot

From playlist STAT 503

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

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