Graphical concepts in set theory
An Euler diagram (/ˈɔɪlər/, OY-lər) is a diagrammatic means of representing sets and their relationships. They are particularly useful for explaining complex hierarchies and overlapping definitions. They are similar to another set diagramming technique, Venn diagrams. Unlike Venn diagrams, which show all possible relations between different sets, the Euler diagram shows only relevant relationships. The first use of "Eulerian circles" is commonly attributed to Swiss mathematician Leonhard Euler (1707–1783). In the United States, both Venn and Euler diagrams were incorporated as part of instruction in set theory as part of the new math movement of the 1960s. Since then, they have also been adopted by other curriculum fields such as reading as well as organizations and businesses. Euler diagrams consist of simple closed shapes in a two-dimensional plane that each depict a set or category. How or whether these shapes overlap demonstrates the relationships between the sets. Each curve divides the plane into two regions or "zones": the interior, which symbolically represents the elements of the set, and the exterior, which represents all elements that are not members of the set. Curves that do not overlap represent disjoint sets, which have no elements in common. Two curves that overlap represent sets that intersect, that have common elements; the zone inside both curves represents the set of elements common to both sets (the intersection of the sets). A curve completely within the interior of another is a subset of it. Venn diagrams are a more restrictive form of Euler diagrams. A Venn diagram must contain all 2n logically possible zones of overlap between its n curves, representing all combinations of inclusion/exclusion of its constituent sets. Regions not part of the set are indicated by coloring them black, in contrast to Euler diagrams, where membership in the set is indicated by overlap as well as color. (Wikipedia).
Euler's formulas, Rodrigues' formula
In this video I proof various generalizations of Euler's formula, including Rodrigues' formula and explain their 3 dimensional readings. Here's the text used in this video: https://gist.github.com/Nikolaj-K/eaaa80861d902a0bbdd7827036c48af5
From playlist Algebra
Create Graph With Eulerian Tour - Intro to Algorithms
This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms
Graph Theory: Euler Paths and Euler Circuits
This lesson explains Euler paths and Euler circuits. Several examples are provided. Site: http://mathispower4u.com
From playlist Graph Theory
Introduction to Euler Paths and Euler Circuits
This video introduces Euler paths and Euler circuits. mathispower4u.com
From playlist Graph Theory (Discrete Math)
Proving Euler's Formula (2 of 4: Differentiating both sides)
More resources available at www.misterwootube.com
From playlist Introduction to Complex Numbers
I explore the Euler Characteristic, and prove that it is equal to 2 for any convex polyhedra. I also discuss some cases when it is not equal to 2. FaceBook: https://www.facebook.com/MathProfPierce Twitter: https://twitter.com/MathProfPierce TikTok: https://www.tiktok.com/@professorheather
From playlist Summer of Math Exposition Youtube Videos
This video given Euler's identity, reviews how to derive Euler's formula using known power series, and then verifies Euler's identity with Euler's formula http://mathispower4u.com
From playlist Mathematics General Interest
Euler Pronunciation: In Depth Analysis
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From playlist Fun and Amazing Math
Mandelbrot fractal zoom // featuring Euler bio
Mandelbrot fractal zoom // featuring Euler bio Come hang out and watch a fractal zoom through the Mandelbrot set. To celebrate Euler's contributions to mathematics, this video features a brief bio. of Leonhard Euler! ---------------------------------------------------------------------
From playlist Misc.
The hardest "What comes next?" (Euler's pentagonal formula)
Looks like I just cannot do short videos anymore. Another long one :) In fact, a new record in terms of the slideshow: 547 slides! This video is about one or my all-time favourite theorems in math(s): Euler's amazing pentagonal number theorem, it's unexpected connection to a prime numbe
From playlist Recent videos
This is a video that explains Euler Groups and incudes a coding demonstration for constructing the Cayley Table. The link to the JS Fiddle is: https://jsfiddle.net/colebabiuch/jpem1d73/10/
From playlist Summer of Math Exposition Youtube Videos
From geometry to topology: inverse theorems for distributed persistence - Paul Bendich
Workshop on Topology: Identifying Order in Complex Systems Topic: From geometry to topology: inverse theorems for distributed persistence Speaker: Paul Bendich Affiliation: Duke University Date: April 16, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Do KNOT watch this video! #SoME1
This video is an entry to the 3Blue1Brown, The Summer of Math Exposition, about proving the existence of prime knots and the interesting steps towards the result. Some images produced with SeifertView, Jarke J. van Wijk, Technische Universiteit Eindhoven. Download SeifertView at the link
From playlist Summer of Math Exposition Youtube Videos
Non-Orientable Knot Genus and the Jones Polynomial - Efstratia Kalfagianni
Efstratia Kalfagianni Michigan State University October 20, 2015 https://www.math.ias.edu/seminars/abstract?event=89714 The non-orientable genus (a.k.a crosscap number) of a knot is the smallest genus over all non-orientable surfaces spanned by the knot. In this talk, I’ll describe joint
From playlist Geometric Structures on 3-manifolds
7. Discrete Approximation of Continuous-Time Systems
MIT MIT 6.003 Signals and Systems, Fall 2011 View the complete course: http://ocw.mit.edu/6-003F11 Instructor: Dennis Freeman License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.003 Signals and Systems, Fall 2011
There's a Donut in the Wallpaper: Topology, Symmetry, and Conway's Magic Theorem
Made for the 3Blue1Brown Summer of Math Exploration
From playlist Summer of Math Exposition Youtube Videos
Finding tan 3θ and proving tan A + tan B + tan C = tan A tan B tan C in ΔABC using Complex Numbers
If you want to see how to do some of the problems mentioned at the end, put a request in the comments. To follow this video, you need to be familiar with trigonometry and remember some basics about complex numbers. If you're interested in Complex Analysis, consider Tristan Needham's Visu
From playlist Summer of Math Exposition Youtube Videos
Katharine Turner: Statistical Shape Analysis using the Persistent Homology Transform
The lecture was held within the framework of the Hausdorff Trimester Program : Applied and Computational Algebraic Topology
From playlist HIM Lectures: Special Program "Applied and Computational Algebraic Topology"
Learn how to apply Euler's Theorem to find the number of faces, edges, and vertices in a polyhedron in this free math video tutorial by Mario's Math Tutoring. We go through some examples in this video. 0:13 What is Euler's theorem 1:06 Example 1 we look at a rectangular prism 1:51 Example
From playlist Geometry