# 7-orthoplex

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

Example of Fourier's Trick

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.

3.6.4

OpenStax Calculus Volume 1

From playlist OpenStax Calculus Volume 1 (By Objectives)

Orthogonal and Orthonormal Sets of Vectors

This video defines orthogonal and orthonormal sets of vectors.

From playlist Orthogonal and Orthonormal Sets of Vectors

X4 ORTHOCENTER

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

Lesson 9 revisit

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

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