In differential geometry Dupin's theorem, named after the French mathematician Charles Dupin, is the statement: * The intersection curve of any pair of surfaces of different pencils of a threefold orthogonal system is a curvature line. A threefold orthogonal system of surfaces consists of three pencils of surfaces such that any pair of surfaces out of different pencils intersect orthogonally. The most simple example of a threefold orthogonal system consists of the coordinate planes and their parallels. But this example is of no interest, because a plane has no curvature lines. A simple example with at least one pencil of curved surfaces: 1) all right circular cylinders with the z-axis as axis, 2) all planes, which contain the z-axis, 3) all horizontal planes (see diagram). A curvature line is a curve on a surface, which has at any point the direction of a principal curvature (maximal or minimal curvature). The set of curvature lines of a right circular cylinder consists of the set of circles (maximal curvature) and the lines (minimal curvature). A plane has no curvature lines, because any normal curvature is zero. Hence, only the curvature lines of the cylinder are of interest: A horizontal plane intersects a cylinder at a circle and a vertical plane has lines with the cylinder in common. The idea of threefold orthogonal systems can be seen as a generalization of orthogonal trajectories. Special examples are systems of confocal conic sections. (Wikipedia).
Proving Law of Cosines - Trigonometry
This video goes through a proof of the Law of Cosines. The Cartesian x-y plane is utilized to prove the Law of Cosines. To understand this proof, the viewer should be familiar with the definition of the trigonometric functions, the Pythagorean Theorem, and the Pythagorean Identity. Stude
From playlist Trigonometry (old videos)
Proof of Lemma and Lagrange's Theorem
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof of Lemma and Lagrange's Theorem. This video starts by proving that any two right cosets have the same cardinality. Then we prove Lagrange's Theorem which says that if H is a subgroup of a finite group G then the order of H div
From playlist Abstract Algebra
Colloque d'histoire des sciences "Gaston Darboux (1842 - 1917)" - Barnabé Croizat - 17/11/17
En partenariat avec le séminaire d’histoire des mathématiques de l’IHP Ovales, cyclides et surfaces orthogonales : les premières amours géométriques de Darboux Barnabé Croizat, Laboratoire Paul Painlevé, Université Lille 1 & CNRS À l’occasion du centenaire de la mort de Gaston Darboux, l
From playlist Colloque d'histoire des sciences "Gaston Darboux (1842 - 1917)" - 17/11/2017
Trigonometry 7 The Cosine of the Sum and Difference of Two Angles
A geometric proof of the cosine of the sum and difference of two angles identity.
From playlist Trigonometry
PreCalculus - Trigonometry: The Law of Cosines (11 of 15) The Law of Cosines Proved
Visit http://ilectureonline.com for more math and science lectures! In this video I will prove The Law of Cosines.
From playlist Michel van Biezen: Pre-Calculus 6-9 - Trigonometry Review
Meusnier, Monge and Dupin III | Differential Geometry 33 | NJ Wildberger
We look at some of the work of Charles Dupin, a French naval engineer and student of Monge. He made some lovely discoveries about triply orthogonal surfaces and lines of curvatures, for example confocal families of ellipses and hyperbolas. He studied conjugate directions on surfaces (going
From playlist Differential Geometry
Featuring Professor Elisabeth Werner. Part 2 is on our Numberphile2 channel: https://youtu.be/HXqzs5Q0G0A More links & stuff in full description below ↓↓↓ Filmed at MSRI. Professor Werner is based at the Department of Mathematics at Case Western Reserve University. Numberphile is support
From playlist Women in Mathematics - Numberphile
Divisibility Proof with the Sorcerer: a|b and a|c implies a|(b + c)
Divisibility Proof with the Sorcerer: a|b and a|c implies a|(b + c)
From playlist Number Theory
Trigonometry 5 The Cosine Relationship
A geometrical explanation of the law of cosines.
From playlist Trigonometry
Discrete Math - 4.1.1 Divisibility
The definition and properties of divisibility with proofs of several properties. Formulas for quotient and remainder, leading into modular arithmetic. Textbook: Rosen, Discrete Mathematics and Its Applications, 7e Playlist: https://www.youtube.com/playlist?list=PLl-gb0E4MII28GykmtuBXNU
From playlist Discrete Math I (Entire Course)
Introduction to additive combinatorics lecture 1.8 --- Plünnecke's theorem
In this video I present a proof of Plünnecke's theorem due to George Petridis, which also uses some arguments of Imre Ruzsa. Plünnecke's theorem is a very useful tool in additive combinatorics, which implies that if A is a set of integers such that |A+A| is at most C|A|, then for any pair
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
Meusnier, Monge and Dupin II | Differential Geometry 32 | NJ Wildberger
Here we continue our study of the works of three important French differential geometers. Today we discuss G. Monge, who is sometimes called the father of the subject. He was the inventor of descriptive geometry (which he developed for military applications), and various theorems in Euclid
From playlist Differential Geometry
Chapter 8 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Meusnier, Monge and Dupin I | Differential Geometry 31 | NJ Wildberger
This is the first of three videos that discuss the mathematical lives and works of three influential French differential geometers. We begin with J. Meusnier, who was a soldier, engineer and mathematician. He investigated lines of curvature and discovered a famous result that shows how to
From playlist Differential Geometry
Paraboloids and associated quadratic forms | Differential Geometry 23 | NJ Wildberger
Paraboloids are going to play a special role in our understanding of curvature. The idea is that we are going to locally approximate a surface S near a point by a normal paraboloid---one that shares the same tangent plane, but has an axis which is perpendicular to that tangent plane. It w
From playlist Differential Geometry
Machine learning on Google Cloud Platform - Amy Unruh (Google)
Amy Unruh offers a quick overview of machine learning on Google Cloud Platform and demonstrates a couple of the Google Cloud ML APIs. She then briefly highlights a few OSS TensorFlow models and explains how to use transfer learning to fine-tune them with your own data. Subscribe to O'Reil
From playlist O'Reilly Artificial Intelligence Conference 2017 - New York, New York
Why should you read Edgar Allan Poe? - Scott Peeples
Check out our Patreon page: https://www.patreon.com/teded View full lesson: https://ed.ted.com/lessons/why-should-you-read-edgar-allan-poe-scott-peeples The prisoner strapped under a descending pendulum blade. A raven who refuses to leave the narrator’s chamber. A beating heart buried un
From playlist New TED-Ed Originals
We finally get to Lagrange's theorem for finite groups. If this is the first video you see, rather start at https://www.youtube.com/watch?v=F7OgJi6o9po&t=6s In this video I show you how the set that makes up a group can be partitioned by a subgroup and its cosets. I also take a look at
From playlist Abstract algebra
What is Hive, and why should developers working in the Hadoop ecosystem care?
From playlist Programming Podcast
Number Theory | Linear Diophantine Equations
We explore the solvability of the linear Diophantine equation ax+by=c
From playlist Divisibility and the Euclidean Algorithm