Euclidean geometry | Hyperbolic geometry | Non-associative algebra
A gyrovector space is a mathematical concept proposed by Abraham A. Ungar for studying hyperbolic geometry in analogy to the way vector spaces are used in Euclidean geometry. Ungar introduced the concept of gyrovectors that have addition based on gyrogroups instead of vectors which have addition based on groups. Ungar developed his concept as a tool for the formulation of special relativity as an alternative to the use of Lorentz transformations to represent compositions of velocities (also called boosts – "boosts" are aspects of relative velocities, and should not be conflated with "translations"). This is achieved by introducing "gyro operators"; two 3d velocity vectors are used to construct an operator, which acts on another 3d velocity. (Wikipedia).
Rendering Hyperbolic Spaces - Hyperbolica Devlog #3
This is the 3rd devlog for Hyperbolica where I talk about how I build and render hyperbolic worlds. If you haven't seen the first 2 videos in the series, make sure you watch them first or else this may be confusing. Devlog #1: https://www.youtube.com/watch?v=zQo_S3yNa2w Devlog #2: https:
From playlist Hyperbolica
Find the volume of a sphere given the circumference
👉 Learn how to find the volume and the surface area of a sphere. A sphere is a perfectly round 3-dimensional object. It is an object with the shape of a round ball. The distance from the center of a sphere to any point on its surface is called the radius of the sphere. A sphere has a unifo
From playlist Volume and Surface Area
In this video we'll build something cool with Gyroids. A Gyroid is a minimal surface: a surface that minimizes its area for a given boundary. Minimal surfaces appear in nature as well, soap bubbles for minimal surfaces for example. The cool thing about Gyroids is that their distance functi
From playlist Shader Coding
Finding the volume and the surface area of a sphere
👉 Learn how to find the volume and the surface area of a sphere. A sphere is a perfectly round 3-dimensional object. It is an object with the shape of a round ball. The distance from the center of a sphere to any point on its surface is called the radius of the sphere. A sphere has a unifo
From playlist Volume and Surface Area
Learn how to determine the volume of a sphere
👉 Learn how to find the volume and the surface area of a sphere. A sphere is a perfectly round 3-dimensional object. It is an object with the shape of a round ball. The distance from the center of a sphere to any point on its surface is called the radius of the sphere. A sphere has a unifo
From playlist Volume and Surface Area
Given the circumference how do you find the surface area of a hemisphere
👉 Learn how to find the volume and the surface area of a sphere. A sphere is a perfectly round 3-dimensional object. It is an object with the shape of a round ball. The distance from the center of a sphere to any point on its surface is called the radius of the sphere. A sphere has a unifo
From playlist Volume and Surface Area
How do you find the volume of a sphere
👉 Learn how to find the volume and the surface area of a sphere. A sphere is a perfectly round 3-dimensional object. It is an object with the shape of a round ball. The distance from the center of a sphere to any point on its surface is called the radius of the sphere. A sphere has a unifo
From playlist Volume and Surface Area
How do you find the volume of a hemisphere
👉 Learn how to find the volume and the surface area of a sphere. A sphere is a perfectly round 3-dimensional object. It is an object with the shape of a round ball. The distance from the center of a sphere to any point on its surface is called the radius of the sphere. A sphere has a unifo
From playlist Volume and Surface Area
How do you find the surface area of a sphere
👉 Learn how to find the volume and the surface area of a sphere. A sphere is a perfectly round 3-dimensional object. It is an object with the shape of a round ball. The distance from the center of a sphere to any point on its surface is called the radius of the sphere. A sphere has a unifo
From playlist Volume and Surface Area
Quickly fill in the unit circle by understanding reference angles and quadrants
👉 Learn about the unit circle. A unit circle is a circle which radius is 1 and is centered at the origin in the cartesian coordinate system. To construct the unit circle we take note of the points where the unit circle intersects the x- and the y- axis. The points of intersection are (1, 0
From playlist Trigonometric Functions and The Unit Circle
CGSR Seminar Series | War in Space: Strategy, Spacepower, Geopolitics
Speaker Biography Bleddyn Bowen primary research interests concern modern warfare, politics, and security in outer space, as well as classical strategic theory. Dr. Bowen provides research-led teaching in his 3rd year specialist module PL3144 Politics and War in Outer Space. He is the au
From playlist Center for Global Security Research
10. The Four Fundamental Subspaces
MIT 18.06 Linear Algebra, Spring 2005 Instructor: Gilbert Strang View the complete course: http://ocw.mit.edu/18-06S05 YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8 10. The Four Fundamental Subspaces License: Creative Commons BY-NC-SA More information at http
From playlist MIT 18.06 Linear Algebra, Spring 2005
[Lesson 11] QED Prerequisites - Tensor Product Spaces
We take a detour from the Angular Momentum Mind Map to cover the important topic of Tensor Product spaces in the Dirac Formalism. In quantum mechanics, the notion of tensors is hidden under the hood of the formalism and this lesson opens that hood. The goal is to make us confident that we
From playlist QED- Prerequisite Topics
Nicolò Zava (3/17/23): Every stable invariant of finite metric spaces produces false positives
In computational topology and geometry, the Gromov-Hausdorff distance between metric spaces provides a theoretical framework to tackle the problem of shape recognition and comparison. However, the direct computation of the Gromov-Hausdorff distance between finite metric spaces is known to
From playlist Vietoris-Rips Seminar
CGSR Seminar Series | U.S. National Security Space Strategy: The Cold War to the Present
Talk Abstract At the present time, U.S. government officials are faced with the increasingly complex task of protecting critical national security space infrastructure in a rapidly evolving threat environment. When placed in a historical context, we find that anxiety about space security
From playlist Center for Global Security Research
Vice President Pence Calls for Human Missions to Moon, Mars at National Space Council
Vice President Mike Pence called for returning U.S. astronauts to the Moon and eventual missions to Mars during the first meeting of the National Space Council, held on October 5 at the Smithsonian National Air and Space Museum’s Steven F. Udvar-Hazy Center, outside Washington. Chaired by
From playlist Return to the Moon Playlist
Sanjay Mishra: Preservation of Properties during Topological Equivalence of Function Space
Sanjay Mishra, Lovely Professional University Title: Preservation of Properties during Topological Equivalence of Function Space The study of convergence of sequence of functions is the most important and active area of research in theoretical mathematics that solve several problems of app
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
Marvels of Space-Time | Episode 705 | Closer To Truth
Einstein showed that space and time are essentially the same thing-a single entity, space-time. But space and time seem so radically different. How could space and time be literally the same thing? Featuring interviews with Max Tegmark, J. Gott, Juan Maldacena, Fotini Markopoulou, and Joh
From playlist Closer To Truth | Season 7
How to determine the perimeter of a quadrilateral using distance formula of four points
👉 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
CS224W: Machine Learning with Graphs | 2021 | Lecture 19.2 - Hyperbolic Graph Embeddings
For more information about Stanford’s Artificial Intelligence professional and graduate programs, visit: https://stanford.io/3Brc7vN Jure Leskovec Computer Science, PhD In previous lectures, we focused on graph representation learning in Euclidean embedding spaces. In this lecture, we in
From playlist Stanford CS224W: Machine Learning with Graphs