Dimension | Multi-dimensional geometry
In mathematics, a sequence of n real numbers can be understood as a location in n-dimensional space. When n = 8, the set of all such locations is called 8-dimensional space. Often such spaces are studied as vector spaces, without any notion of distance. Eight-dimensional Euclidean space is eight-dimensional space equipped with the Euclidean metric. More generally the term may refer to an eight-dimensional vector space over any field, such as an eight-dimensional complex vector space, which has 16 real dimensions. It may also refer to an eight-dimensional manifold such as an 8-sphere, or a variety of other geometric constructions. (Wikipedia).
Do physicists describe the world in 4D?
Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https://twitter.com/worldscienceu
From playlist Science Unplugged: Physics
From playlist Dimensions Russian / Pусский
From playlist Dimensions Deutsch
Extra Dimensions - Sixty Symbols
We take a look at the mysterious world of extra dimensions. More at http://www.sixtysymbols.com/ Featuring Ed Copeland.
From playlist Ed Copeland - Sixty Symbols
From playlist Dimensions Arabe/Arabic / العربية
In this short, we show how to think about the four dimensional and five dimensional hypercube. Even though we don't have these dimensions to visualize, we can give an idea of these objects in three dimensional space by the analogy learned from building lines, squares and cubes from smaller
From playlist MathShorts
From playlist Dimensions Arabe/Arabic / العربية
From playlist Dimensions Arabe/Arabic / العربية
Chapter 5 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Henry Adams (8/30/21): Vietoris-Rips complexes of hypercube graphs
Questions about Vietoris-Rips complexes of hypercube graphs arise naturally from problems in genetic recombination, and also from Kunneth formulas for persistent homology with the sum metric. We describe the homotopy types of Vietoris-Rips complexes of hypercube graphs at small scale param
From playlist Beyond TDA - Persistent functions and its applications in data sciences, 2021
Tropical Geometry - Lecture 8 - Surfaces | Bernd Sturmfels
Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)
From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels
Overview of gauge theory and submanifold geometry on G_2 manifolds - Simon Donaldson [2014]
Name: Simon Donaldson Event: Program: G2 manifolds Event URL: view webpage Title: Overview of gauge theory and submanifold geometry on G_2 manifolds, I Date: 2014-08-19 @3:30 PM
From playlist Mathematics
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
Code AUTOENCODERS w/ Python + KERAS Layers (Colab, TensorFlow2, Autumn 2022)
An elegant way to code AUTOENCODERS with KERAS layers in TensorFlow2 on COLAB w/ Python. Autoencoders are applied for dimensionality reduction, where PCA fails for non-linearity. A coding Example on COLAB shows the way forward to code your own AUTOENCODER for your low-dimensional latent sp
From playlist Stable Diffusion / Latent Diffusion models for Text-to-Image AI
2014 Hari Shankar Memorial lecture: "How to make sculptures of 4-dimensional things"
The Hari Shankar Memorial Lecture is an annual public lecture held at the University of Northern Iowa. Slides: https://www.math.okstate.edu/~segerman/talks/how_to_make_sculptures_of_4d_things.pdf
From playlist 3D printing
An introduction to persistent homology
Title: An introduction to persistent homology Venue: Webinar for DELTA (Descriptors of Energy Landscape by Topological Analysis Abstract: This talk is an introduction to applied and computational topology, in particular as related to the study of energy landscapes arising in chemistry. W
From playlist Tutorials
Henry Segerman shows us shadows (and dust) from the fourth dimension! More links & stuff in full description below ↓↓↓ Dr Segerman is an assistant professor in the Department of Mathematics at Oklahoma State University. More Numberphile with him: http://bit.ly/Segerman_Videos Polytopes i
From playlist Henry Segerman on Numberphile
From playlist Dimensions Arabe/Arabic / العربية
Tropical Geometry - Lecture 6 - Structure Theorem | Bernd Sturmfels
Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)
From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels