In geometry, a 7-orthoplex, or 7-cross polytope, is a regular 7-polytope with 14 vertices, 84 edges, 280 triangle faces, 560 tetrahedron cells, 672 5-cells 4-faces, 448 5-faces, and 128 6-faces. It has two constructed forms, the first being regular with Schläfli symbol {35,4}, and the second with alternately labeled (checkerboarded) facets, with Schläfli symbol {3,3,3,3,31,1} or Coxeter symbol 411. It is a part of an infinite family of polytopes, called cross-polytopes or orthoplexes. The dual polytope is the 7-hypercube, or hepteract. (Wikipedia).
Orthocenters exist! | Universal Hyperbolic Geometry 10 | NJ Wildberger
In classical hyperbolic geometry, orthocenters of triangles do not in general exist. Here in universal hyperbolic geometry, they do. This is a crucial building block for triangle geometry in this subject. The dual of an orthocenter is called an ortholine---also not seen in classical hyperb
From playlist Universal Hyperbolic Geometry
Orthogonality and Orthonormality
We know that the word orthogonal is kind of like the word perpendicular. It implies that two vectors have an angle of ninety degrees or half pi radians between them. But this term means much more than this, as we can have orthogonal matrices, or entire subspaces that are orthogonal to one
From playlist Mathematics (All Of It)
Linear Algebra - Lecture 39 - Orthonormal Sets
In this lecture, we discuss orthonormal sets of vectors. We investigate matrices with orthonormal columns. We also define an orthogonal matrix.
From playlist Linear Algebra Lectures
Seminar on Applied Geometry and Algebra (SIAM SAGA): Dustin Mixon
Title: Packing Points in Projective Spaces Speaker: Dustin Mixon Date: Tuesday, March 8, 2022 at 11:00am Eastern Abstract: Given a compact metric space, it is natural to ask how to arrange a given number of points so that the minimum distance is maximized. For example, the setting of the
From playlist Seminar on Applied Geometry and Algebra (SIAM SAGA)
Linear Algebra: Orthonormal Basis
Learn the basics of Linear Algebra with this series from the Worldwide Center of Mathematics. Find more math tutoring and lecture videos on our channel or at http://centerofmath.org/ More on unit vectors: https://www.youtube.com/watch?v=C6EYJVBYXIo
From playlist Basics: Linear Algebra
Linear Algebra: Given an orthonormal basis of R^n, we present a quick method for finding coefficients of linear combination in terms of the basis. We also give an analogue of Parseval's Identity, which relates these coefficients to the squared length of the vector.
From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics
Orthogonal and Orthonormal Sets of Vectors
This video defines orthogonal and orthonormal sets of vectors.
From playlist Orthogonal and Orthonormal Sets of Vectors
The orthocenter (X4) is the meet of the altitudes of a triangle. It's not obvious that these meet! ************************ Here are the Wild Egg Maths Playlists (some available only to Members!) Algebraic Calculus One (for the Open Learning Course) : https://www.youtube.com/playlist?lis
From playlist Triangle Geometry
finding the orthocenter - coordinate geometry
In this video, I show how to find the coordinates of the orthocenter. I go through a step by step process of writing the equation of the 3 altitudes of a triangle. Then using algebra to find the point of intersection of the 3 altitudes. The concepts of linear equations and perpendicular li
From playlist Geometry
This Problem Stumped Vietnamese Students - Solution To Viral Puzzler
This problem was asked to students in Vietnam. Can you figure it out? Place the numbers 1 to 9, using each number once, to make a valid equation. In this video I explain how you can solve this problem logically. UPDATE: I've posted all 136 solutions, at the end of this description, found
From playlist Viral Math Memes
Definite Integral with Absolute Value |2x - 7| from 0 to 7/2
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definite Integral with Absolute Value |2x - 7| from 0 to 7/2
From playlist Calculus
Algebra - Ch. 35: Systems of of Linear Eq. in 3 Variables (21 of 25) Word Prob. Ex 2: Inverse Matrix
Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will solve the following Word Problem Ex. 2 using the INVERSE MATRIX: Find 3 numbers, such that, the difference of the 1st and 2nd
From playlist ALGEBRA CH 35 SYSTEMS OF 3 EQUATIONS
EngageNY Grade 3 Module 3 Lesson 6
EngageNY/Eureka Math Grade 3 Module 3 Lesson 6 For more videos, please visit http://bit.ly/engageportal
From playlist EngageNY Grade 3 Module 3
Inverse Matrix Using Gauss-Jordan / Row Reduction , Example 2
Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Inverse Matrix Using Gauss-Jordan / Row Reduction , Example 2. Here I look at a quick example of finding the inverse of a 3 x 3 matrix using Gauss - Jordan / r
From playlist All Videos - Part 1
An application of linear equations. This is an optional lesson.
From playlist Eureka Math Grade 8 Module 4
Least squares examples | Alternate coordinate systems (bases) | Linear Algebra | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/orthogonal-projections/v/linear-algebra-least-squares-examples An example using the least squares solution to an unsolvable system
From playlist Alternate coordinate systems (bases) | Linear Algebra | Khan Academy
Dividing fractions with common denominators
You've probably seen the trick about dividing fractions with common denominators. But WHY does this work? Duane Habecker: https://about.me/duanehabecker Twitter: @dhabecker
From playlist Fraction Operations
Why must every year have a Friday the 13th? SoME Entry. An introduction to Modular Arithmetic.
In this video, the concept of Modular Arithmetic is gently introduced. Then it is used to prove an interesting fact: that every year must have at least one Friday the 13th! I hope this video gives you both chills and thrills.
From playlist Summer of Math Exposition Youtube Videos
Orthogonal + orthonormal vectors
What are orthogonal and orthonormal vectors? Find out here! Free ebook https://bookboon.com/en/introduction-to-vectors-ebook (updated link) Test your understanding via a short quiz http://goo.gl/forms/EqfOfx0Z9N
From playlist Introduction to Vectors