In geometry, exterior dimension is a type of dimension that can be used to characterize the scaling behavior of "fat fractals".A fat fractal is defined to be a subset of Euclidean space such that, for every point of the set and every sufficiently small number ,the ball of radius centered at contains both a nonzero Lebesgue measure of points belonging to the fractal, and a nonzero Lebesgue measure of points that do not belong to the fractal. For such a set, the Hausdorff dimension is the same as that of the ambient space. The Hausdorff dimension of a set can be computed by "fattening" (taking its Minkowski sum with a ball of radius ), and examining how the volume of the resulting fattened set scales with , in the limit as tends to zero. The exterior dimension is computed in the same way but looking at the volume of the difference set obtained by subtracting the original set from the fattened set. In the paper introducing exterior dimension, it was claimed that it would be applicable to networks of blood vessels. However, inconsistent behavior of these vessels in different parts of the body, the relatively low number of levels of branching, and the slow convergence of methods based on exterior dimension cast into doubt the practical applicability of this parameter. (Wikipedia).
definition and proof that exterior angles add to 180
From playlist Common Core Standards - 8th Grade
How to find the measure of one exterior angle given the number of sides ex 1
👉 Learn how to find the measure of the exterior angle of a regular polygon. The exterior angle of a polygon is the angle between a side of the polygon and an outward extension of the adjacent side. The sum of the exterior angles of a polygon is 360 degrees. A regular polygon is a polygon w
From playlist One Exterior Angle of a Polygon
How to determine the measure of one exterior angle given the number of sides ex 3
👉 Learn how to find the measure of the exterior angle of a regular polygon. The exterior angle of a polygon is the angle between a side of the polygon and an outward extension of the adjacent side. The sum of the exterior angles of a polygon is 360 degrees. A regular polygon is a polygon w
From playlist One Exterior Angle of a Polygon
Determine the measure of each exterior angle of a regular octagon
👉 Learn how to find the measure of the exterior angle of a regular polygon. The exterior angle of a polygon is the angle between a side of the polygon and an outward extension of the adjacent side. The sum of the exterior angles of a polygon is 360 degrees. A regular polygon is a polygon w
From playlist One Exterior Angle of a Polygon
How to determine the measure of each exterior angles for a regular hexagon
👉 Learn how to find the measure of the exterior angle of a regular polygon. The exterior angle of a polygon is the angle between a side of the polygon and an outward extension of the adjacent side. The sum of the exterior angles of a polygon is 360 degrees. A regular polygon is a polygon w
From playlist One Exterior Angle of a Polygon
Exterior Angles of Polygons: Revisited
Link: https://www.geogebra.org/m/xDrd5X3w
From playlist Geometry: Dynamic Interactives!
Where does the exterior angle theorem come from
👉 Learn about the interior and the exterior angles of a polygon. A polygon is a plane shape bounded by a finite chain of straight lines. The interior angle of a polygon is the angle between two sides of the polygon. The sum of the interior angles of a regular polygon is given by the formul
From playlist Interior and Exterior Angles of Polygons
"Interior and exterior angles of regular and irregular polygons."
From playlist Shape: Angles
What is a Tensor? Lesson 26: P-vectors and P-forms Recap
What is a Tensor? Lesson 26: P-vectors and P-forms Recap I'm struggling with this complex topic. I don't like any of the other lessons on p-forms so I am going to keep trying till I get it right. This little "recap" re-does a few topics and introduces the idea of p-vectors.
From playlist What is a Tensor?
How to find the measure of one exterior angle of a regular polygon
👉 Learn about the interior and the exterior angles of a polygon. A polygon is a plane shape bounded by a finite chain of straight lines. The interior angle of a polygon is the angle between two sides of the polygon. The sum of the interior angles of a regular polygon is given by the formul
From playlist Interior and Exterior Angles of Polygons
What is a Tensor? Lesson 23: Operations on p-forms. The Exterior Algebra.
What is a Tensor? Lesson 23: Operations on p-forms. The Exterior Algebra.
From playlist What is a Tensor?
Lie Groups and Lie Algebras: Lesson 3 - Classical Groups Part I
Lie Groups and Lie Algebras: Lesson 3 - Classical Groups Part I We introduce the idea of the classical matrix groups and their associated carrier spaces. Please consider supporting this channel via Patreon: https://www.patreon.com/XYLYXYLYX
From playlist Lie Groups and Lie Algebras
Schemes 48: The canonical sheaf
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. In this lecture we define the canonical sheaf, giev a survey of some applications (Riemann-Roch theorem, Serre duality, canonical embeddings, Kodaira dimensio
From playlist Algebraic geometry II: Schemes
Maxwell's Equations via Differential Forms Part 2
In this lesson we review the Hodge star operator and the concept of the Hodge dual of a vector. We present and demonstrate a specific formula that calculates the Hodge dual of any k-form. The purpose of this is to set ourselves up to cast Maxwell's Equations in the language of differential
From playlist QED- Prerequisite Topics
Martin Taylor - The nonlinear stability of the Schwarzschild family of black holes - IPAM at UCLA
Recorded 26 October 2021. Martin Taylor of the Imperial College London presents "The nonlinear stability of the Schwarzschild family of black holes" at IPAM's Workshop II: Mathematical and Numerical Aspects of Gravitation. Abstract: I will present a theorem on the full finite codimension n
From playlist Workshop: Mathematical and Numerical Aspects of Gravitation
What is a Tensor? Lesson 35: Elementary Hodge Dual Calculations
What is a Tensor? Lesson 35: Elementary Hodge Dual Calculations
From playlist What is a Tensor?
Webs in type C - Benjamin Elias
Workshop on Representation Theory and Geometry Topic: Webs in type C Speaker: Benjamin Elias Affiliation: University of Oregon; von Neumann Fellow, School of Mathematics Date: March 31, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
LC001.04 - Exterior algebra as a Hilbert space
Introduces the natural Hilbert space structure on the exterior algebra, and relates the wedge product and contraction operators to creation and annihilation operators in quantum mechanics. This video is a recording made in a virtual world (https://www.roblox.com/games/6461013759/metauni-R
From playlist Metauni
Solving for an inteior angle given one interior angle and exterior angle in two ways ex 8
👉 Learn how to solve for an unknown variable in the exterior angle of a polygon. The exterior angle of a polygon is the angle between a side of the polygon and an outward extension of the adjacent side. The sum of the exterior angles of a polygon is 360 degrees. Given the expressions for
From playlist Polygons
What is a Tensor? Lesson 22: Invitation to p-forms
What is a Tensor? Lesson 22: Invitation to p-forms We introduce the idea of forms with a literal presentation: forms are antisymmetric tensors.
From playlist What is a Tensor?