In the branch of mathematics known as topology, the topologist's sine curve or Warsaw sine curve is a topological space with several interesting properties that make it an important textbook example. It can be defined as the graph of the function sin(1/x) on the half-open interval (0, 1], together with the origin, under the topology induced from the Euclidean plane: (Wikipedia).
Here is one of the most important curves in mathematics. It is an example of a set that is connected, but not path-connected, and is very prominent in topology and analysis. Topology Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmA13vj9xkHGGBXRMV32EKVI Subscribe to my channel
From playlist Topology
arguing with a math PhD friend be like (unscripted, unedited)
I asked a math Ph.D. @Dr Peyam to explain the topologist sine circle (topologist sine curve) from the book "Real Analysis" by Charles Pugh. It is the set of all (x,y) so that x=0 and the absolute value of y are less than or equal to 1 or y=sin(1/x) for x belongs to (0,1]. This is a very i
From playlist Binge-able math for fun videos (2022)
Trigonometry 6 The Sine of the Sum and the Difference of Two Angles
A description of the sine function of the sum and difference of two angles.
From playlist Trigonometry
Metric Spaces - Lectures 17 & 18: Oxford Mathematics 2nd Year Student Lecture
For the first time we are making a full Oxford Mathematics Undergraduate lecture course available. Ben Green's 2nd Year Metric Spaces course is the first half of the Metric Spaces and Complex Analysis course. This is the 9th of 11 videos. The course is about the notion of distance. You ma
From playlist Oxford Mathematics Student Lectures - Metric Spaces
What are the derivatives of inverse trig functions? - Week 6 - Lecture 8 - Mooculus
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From playlist Ohio State: Jim Fowler's Calculus One Lectures | CosmoLearning Mathematics
Sine of a Sum I (visual proof; trigonometry)
This is a short, animated visual proof of the sum formula for the sine function using the Side-Angle-Side triangle area formula. This theorem relates the sine of a sum to the sum of products of sines and cosines. #mathshorts #mathvideo #math #trigonometry #sine #sinofsum #triangle #manim
From playlist Trigonometry
What is General Relativity? Lesson 8: Intro to the metric connection and the induced metric.
This lesson is an introduction to the concept of the metric connection followed by a long exercise in classical differential geometry. It is a long lesson because I complete a full example: the derivation of the metric of the "glome" induced by the Euclidean metric of 4-dimensional space.
From playlist What is General Relativity?
"Illustrating Geometry" exhibition: Artist's talk by Saul Schleimer: "Minimal and Seifert Surfaces"
Slides: http://homepages.warwick.ac.uk/~masgar/Talks/minimal_and_seifert_surfaces.pdf This video is also available at the Simons Center website, at http://scgp.stonybrook.edu/archives/11540 Thanks to Josh Klein for filming and editing.
From playlist 3D printing
The Sine Function: f(x) = sin(x)
In this video we discuss the sine function. We look at it's graph, it's relationship with the unit circle and we compute some trig function values of sine at the quadrantal angles using this relationship. We also look at how it is bounded above and below and talk about how this gives us a
From playlist Trigonometry Problems
Determining the equation of a trigonometric function
Determining the amplitude and period of sine and cosine functions.
From playlist Trigonometry
The mathematical work of Vladimir Voevodsky - Dan Grayson
Vladimir Voevodsky Memorial Conference Topic: The mathematical work of Vladimir Voevodsky Speaker: Dan Grayson Affiliation: University of Illinois, Urbana-Champaign Date: September 11, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
Topology, Winding Numbers and Signed Area | Algebraic Calculus One | Wild Egg
Topology arises from a key property of the continuum as modelled by the rational numbers: that we have distinguished positive numbers (x greater than or equal to 0) which are closed under addition and multiplication. This is the starting point of notions of inside and outside. When we mov
From playlist Algebraic Calculus One from Wild Egg
Lagrangian Cobordisms and Enriched Knot Diagrams - Ipsita Datta
Joint IAS/Princeton University Symplectic Geometry Seminar Topic: Lagrangian Cobordisms and Enriched Knot Diagrams Speaker: Ipsita Datta Affiliation: Member, School of Mathematics Date: November 08, 2021 We present some obstructions to the existence of Lagrangian cobordisms in ℝ4. The ob
From playlist Mathematics
Using the Sine Rule to Find Angles (1 of 3: Basic Example)
More resources available at www.misterwootube.com
From playlist Trigonometry
Homeomorphisms and Homotopy Equivalences [Henry Adams]
We give a brief introduction to homeomorphisms, homotopy equivalences, and the difference between them. These notions describe when two shapes are described to be "the same" to a topologist. his tutorial was contributed as part of the WinCompTop+AATRN Tutorial-a-thon in Spring 2021: https
From playlist Tutorial-a-thon 2021 Spring
Evaluating for sine using the half angle formula
👉 Learn how to evaluate the Sine of an angle using the half-angle formula. The half-angle formula for Sine is helpful when you need to determine the exact value of function given an angle but cannot use a calculator or the angle is not on the unit circle. To evaluate all we need to do is
From playlist Half Angle Formulas
How to Fill a Klein Bottle - Numberphile
In a 3D world, it's possible to fill 4D Klein Bottles - featuring Cliff Stoll. More Cliff videos: http://bit.ly/Cliff_Videos More links & stuff in full description below ↓↓↓ More Klein Bottle videos: http://bit.ly/KleinBottles You can buy a bottle from Cliff: https://www.kleinbottle.com
From playlist Klein Bottles on Numberphile