Data types | Mathematical structures | Vectors (mathematics and physics)

In computer science, a 4D vector is a 4-component vector data type. Uses include homogeneous coordinates for 3-dimensional space in computer graphics, and red green blue alpha (RGBA) values for bitmap images with a color and alpha channel (as such they are widely used in computer graphics). They may also represent quaternions (useful for rotations) although the algebra they define is different. (Wikipedia).

What is the 4th Dimension REALLY? - 4D Golf Devlog #2

A more practical explanation for those interested in exploring 4D spaces. For those not already familiar with basic 4D concepts, here's some videos I can recommend: "Visualizing 4D Geometry" https://www.youtube.com/watch?v=4URVJ3D8e8k "The things you'll find in higher dimensions" https:/

From playlist 4D Golf

4th dimension 'n stuff -- Day 5

alright, 4th dimension visualized! -- Watch live at https://www.twitch.tv/simuleios

From playlist 4d visualization

4th dimension 'n stuff -- Day 1

alright, trying to visualize 4d. We'll see how this goes! -- Watch live at https://www.twitch.tv/simuleios

From playlist 4d visualization

Modification of "Spherical 4R mechanism 2a" and "Spherical 4R mechanism 2b". Because it is a combination of two spherical 4R joints, angles between line connecting two joint centers and the shaft axles must be set equal to each other in order to get constant velocity.

From playlist Mechanisms

4th dimension 'n stuff -- Day 4

alright, figured out some of this projection nonsense. Not all of it, but some of it... -- Watch live at https://www.twitch.tv/simuleios

From playlist 4d visualization

#some2 Articles about computer graphics: https://iquilezles.org/ Ray marching tutorials: https://www.youtube.com/c/TheArtofCodeIsCool In this video I am trying to construct a visualization of 4D shapes

From playlist Summer of Math Exposition 2 videos

4C Properties of the Transpose

The properties of the transpose of a matrix.

From playlist Linear Algebra

Calculus 3: Vector Calculus in 2D (1 of 39) Vector Notation

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain vector calculus in 2 dimensions. I will explain that vectors can represent physical quantities force, displacement, velocity, acceleration, torque, momentum, electric field, magnetic field, an

From playlist CALCULUS 3 CH 3 VECTOR CALCULUS

4B Transpose of a Matrix-YouTube sharing.mov

The transpose of a matrix.

From playlist Linear Algebra

Rotation from Mandelbrot to Julia and back. z = z^2 + c is initialized with a starting z_0 and c, and after a certain iteration scheme gives a color. z_0 and c are four values. So, every point in 4d space gets a color. The set of points in 4d space with which we want do that can be chosen

From playlist Fractal

Music In A 4D World - 4D Golf Devlog #4

For a multidimensional game like 4D Golf, we decided to build a soundtrack to give it the same dynamic feeling using some interesting techniques. Once again, the musical mastermind philmakesnoise, who created the Hyperbolica OST, is now bringing the 4D Golf soundtrack to life. #4dgolf Ch

From playlist 4D Golf

Coding Challenge #113: 4D Hypercube (aka "Tesseract")

In this coding challenge, I visualize a 4D Hypercube (aka "Tesseract") in Processing (Java). ๐ปChallenge: https://thecodingtrain.com/CodingChallenges/113-hypercube.html Links discussed in this challenge: ๐ Code: http://thecodingtrain.com/CodingChallenges/113-hypercube.html ๐ Matrix Multip

From playlist Coding Challenges

Geometry of Decoupled Fields - Ibrahima Bah

IAS Physics Group Meeting "Geometry of Decoupled Fields" Speaker: Ibrahima Bah Affiliation: Johns Hopkins University; Member, School of Natural Sciences, IAS Date: June 1, 2022 In this talk I will discuss aspects of decoupling fields that appear in the engineering of 4d SCFTs from compa

From playlist Physics Group Meeting

Live Stream #148.2: 4D Hypercube

Rendering a 4D Hypercube in Processing. 22:50 - Coding Challenge: 4D Hypercube ๐ 3D Projection on Wikipedia: : https://en.wikipedia.org/wiki/3D_projection ๐ Tesseract on Wikipedia: https://en.wikipedia.org/wiki/Tesseract ๐ฅ Understanding 4D -- The Tesseract: https://youtu.be/iGO12Z5Lw8s

From playlist Live Stream Archive

A mini-course on vertex operator algebras of N= 2 Superconformal... (Lecture 3) by Madalena Lemos

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)

Yimo Han - Assisting 4D-STEM data processing by machine learning and Bayesian optimization

Recorded 28 October 2022. Yimo Han of Rice University presents "Assisting 4D-STEM data processing by machine learning and Bayesian optimization" at IPAM's Mathematical Advances for Multi-Dimensional Microscopy Workshop. Abstract: From the highest-resolution electron ptychography to microme

From playlist 2022 Mathematical Advances for Multi-Dimensional Microscopy

Made for SoME2. I couldn't find this when i needed so I made video about it. Calculation for hypercross product: https://www.researchgate.net/publication/318543243_Vector_Cross_Product_in_4D_Euclidean_Space_A_Maple_worksheet Python code: def hypercross(u, v, t): s = [ (u[3] *

From playlist Summer of Math Exposition 2 videos

4D galaxy simulation [research]

Broadcasted live on Twitch -- Watch live at https://www.twitch.tv/leioslabs

From playlist research

4D Thinking for 3D Graphics #SoME2

This video was created by Maxwell Hunt and Alexander Kaminsky for the 2nd Summer of Math Exposition hosted by the channels 3Blue1Brown https://www.youtube.com/c/3blue1brown and Leios Labs https://www.youtube.com/c/LeiosOS. Essence of Linear Algebra Chapter 3: https://www.youtube.com/watch

From playlist Summer of Math Exposition 2 videos

What is a Four-Vector? Is a Spinor a Four-Vector? | Special Relativity

In special relativity, we are dealing a lot with four-vectors, but what exactly is a four-vector? A four-vector is an object with four entries, which get transformed and changed in a very special way after we change our frame of reference. More precisely, a four-vector transforms like a (1

From playlist Special Relativity, General Relativity