Six-dimensional space is any space that has six dimensions, six degrees of freedom, and that needs six pieces of data, or coordinates, to specify a location in this space. There are an infinite number of these, but those of most interest are simpler ones that model some aspect of the environment. Of particular interest is six-dimensional Euclidean space, in which 6-polytopes and the 5-sphere are constructed. Six-dimensional elliptical space and hyperbolic spaces are also studied, with constant positive and negative curvature. Formally, six-dimensional Euclidean space, ℝ6, is generated by considering all real 6-tuples as 6-vectors in this space. As such it has the properties of all Euclidean spaces, so it is linear, has a metric and a full set of vector operations. In particular the dot product between two 6-vectors is readily defined and can be used to calculate the metric. 6 × 6 matrices can be used to describe transformations such as rotations that keep the origin fixed. More generally, any space that can be described locally with six coordinates, not necessarily Euclidean ones, is six-dimensional. One example is the surface of the 6-sphere, S6. This is the set of all points in seven-dimensional space (Euclidean) ℝ7 that are a fixed distance from the origin. This constraint reduces the number of coordinates needed to describe a point on the 6-sphere by one, so it has six dimensions. Such non-Euclidean spaces are far more common than Euclidean spaces, and in six dimensions they have far more applications. (Wikipedia).
Do physicists describe the world in 4D?
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From playlist Science Unplugged: Physics
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 Deutsch
From playlist Dimensions Russian / Pусский
Ex: Find the Distance Between Two Points In Space
This video provides an example of how to find the distance between two points in 3D. Site: http://mathispower4u.com
From playlist Vectors in Space (3D)
Dimensions (1 of 3: The Traditional Definition - Directions)
More resources available at www.misterwootube.com
From playlist Exploring Mathematics: Fractals
Chapter 5 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Drawing the 4th, 5th, 6th, and 7th dimension
How to draw 4, 5, 6, and 7 dimensional objects.
From playlist Physics
Chapter 6 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Sergei Gukov - Fivebranes and 4-manifolds
Sergei GUKOV (Caltech, Pasadena, USA)
From playlist Algèbre, Géométrie et Physique : une conférence en l'honneur
Seok Kim - 6 dimensional superconformal field theories (1)
PROGRAM: THE 8TH ASIAN WINTER SCHOOL ON STRINGS, PARTICLES AND COSMOLOGY DATES: Thursday 09 Jan, 2014 - Saturday 18 Jan, 2014 VENUE: Blue Lily Hotel, Puri PROGRAM LINK: http://www.icts.res.in/program/asian8 The 8th Asian Winter School on Strings, Particles and Cosmology is part of a seri
From playlist The 8th Asian Winter School on Strings, Particles and Cosmology
Applied topology 6: Homology Abstract: We give a visual introduction to homology groups. Roughly speaking, i-dimensional homology "counts the number of i-dimensional holes" in a space. This video accompanies the class "Topological Data Analysis" at Colorado State University: https://www.
From playlist Applied Topology - Henry Adams - 2021
Knot Categorification From Mirror Symmetry (Lecture- 3) by Mina Aganagic
PROGRAM QUANTUM FIELDS, GEOMETRY AND REPRESENTATION THEORY 2021 (ONLINE) ORGANIZERS: Aswin Balasubramanian (Rutgers University, USA), Indranil Biswas (TIFR, india), Jacques Distler (The University of Texas at Austin, USA), Chris Elliott (University of Massachusetts, USA) and Pranav Pan
From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)
Panorama of Mathematics: Andrew Neitzke
Panorama of Mathematics To celebrate the tenth year of successful progression of our cluster of excellence we organized the conference "Panorama of Mathematics" from October 21-23, 2015. It outlined new trends, results, and challenges in mathematical sciences. Andrew Neitzke: "Some new g
From playlist Panorama of Mathematics
Tropical Geometry - Lecture 5 - Fundamental 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
SVM Kernels : Data Science Concepts
A backdoor into higher dimensions. SVM Dual Video: https://www.youtube.com/watch?v=6-ntMIaJpm0 My Patreon : https://www.patreon.com/user?u=49277905
From playlist Data Science Concepts
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
What is (a) Space? From Zero to Geo 1.5
What is space? In this video, we learn about the many different things that we might call "space". We come up with both a geometric and an algebraic definition, and the discussion also leads us to the important concept of subspaces. Sorry for how long this video took to make! I mention
From playlist From Zero to Geo
Perfect Shapes in Higher Dimensions - Numberphile
Carlo Sequin talks through platonic solids and regular polytopes in higher dimensions. More links & stuff in full description below ↓↓↓ Extra footage (Hypernom): https://youtu.be/unC0Y3kv0Yk More videos with with Carlo: http://bit.ly/carlo_videos Edit and animation by Pete McPartlan Pete
From playlist Carlo Séquin on Numberphile