In mathematics, a surface is a mathematical model of the common concept of a surface. It is a generalization of a plane, but, unlike a plane, it may be curved; this is analogous to a curve generalizing a straight line. There are several more precise definitions, depending on the context and the mathematical tools that are used for the study. The simplest mathematical surfaces are planes and spheres in the Euclidean 3-space. The exact definition of a surface may depend on the context. Typically, in algebraic geometry, a surface may cross itself (and may have other singularities), while, in topology and differential geometry, it may not. A surface is a topological space of dimension two; this means that a moving point on a surface may move in two directions (it has two degrees of freedom). In other words, around almost every point, there is a coordinate patch on which a two-dimensional coordinate system is defined. For example, the surface of the Earth resembles (ideally) a two-dimensional sphere, and latitude and longitude provide two-dimensional coordinates on it (except at the poles and along the 180th meridian). (Wikipedia).
MATH331: Riemann Surfaces - part 1
We define what a Riemann Surface is. We show that PP^1 is a Riemann surface an then interpret our crazy looking conditions from a previous video about "holomorphicity at infinity" as coming from the definition of a Riemann Surface.
From playlist The Riemann Sphere
Surface area of revolution of functions
Free ebook http://tinyurl.com/EngMathYT A lecture on how to calculate the surface area of graphs that are revolved around an axis. Plenty of exampls are discussed and solved. Such ideas are seen in university, college and high school mathematics.
From playlist A second course in university calculus.
From playlist Surface integrals
Rotate Curve: Find Surface Area of Resulting Solid
Free ebook http://bookboon.com/en/learn-calculus-2-on-your-mobile-device-ebook Rotate a curve about the x-axis. How do we calculate the surface area of the resulting solid? We can use calculus - find out here! A surface of revolution is a surface in Euclidean space created by rotating a
From playlist Learn Calculus 2 on Your Mobile Device / Learn Math on Your Phone!
Math 032 Multivariable Calculus 24 112414: Integrals of Functions on Parametrized Surfaces
Surface area of a parametrized surface; integral of a function on a parametrized surface
From playlist Course 4: Multivariable Calculus (Fall 2014)
In the first mini-lecture, we ask the question: what is surface anatomy? We learn how anatomy is the study of the structure of our bodies, including osteology, histology, gross anatomy, imaging, embryology and indeed surface anatomy. As you might imagine, surface anatomy studies the extern
From playlist Biology
This video defines a cylindrical surface and explains how to graph a cylindrical surface. http://mathispower4u.yolasite.com/
From playlist Quadric, Surfaces, Cylindrical Coordinates and Spherical Coordinates
Surface integrals are kind of like higher-dimensional line integrals, it's just that instead of integrating over a curve C, we are integrating over a surface S. This can be tricky, but it has lots of applications, so let's learn how to do these things! Script by Howard Whittle Watch the
From playlist Mathematics (All Of It)
This Object has Infinite Surface Area, but Finite Volume
Watch over 2,400 documentaries for free for 30 days AND get a free Nebula account by signing up at https://curiositystream.com/upandatom and using the code "upandatom". Once you sign up you'll get an email about Nebula. If you don't get one, contact the curiosity stream support team and th
From playlist Math
The Discrete Charm of Geometry by Alexander Bobenko
Kaapi with Kuriosity The Discrete Charm of Geometry Speaker: Alexander Bobenko (Technical University of Berlin) When: 4pm to 6pm Sunday, 22 July 2018 Where: J. N. Planetarium, Sri T. Chowdaiah Road, High Grounds, Bangalore Discrete geometric structures (points, lines, triangles, recta
From playlist Kaapi With Kuriosity (A Monthly Public Lecture Series)
The Mathematics of Clothing Design - Etienne Ghys
Public lecture
From playlist Mathematics Research Center
Small deformations of biomembranes
Charlie Elliott University of Warwick, UK
From playlist 2018 Modeling and Simulation of Interface Dynamics in Fluids/Solids and Their Applications
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
The Poincaré Conjecture (special lecture) John W. Morgan [ICM 2006]
slides for this talk: https://www.mathunion.org/fileadmin/IMU/Videos/ICM2006/tars/morgan2006.pdf The Poincaré Conjecture (special lecture) John W. Morgan Columbia University, USA https://www.mathunion.org/icm/icm-videos/icm-2006-videos-madrid-spain/icm-madrid-videos-24082006
From playlist Mathematics
Mathematics as Metaphor - Curtis McMullen (Harvard University)
Public lecture
From playlist Mathematics Research Center
Colloqui della Classe di Scienze: Corinna Ulcigrai, Slow Chaos - 2 febbraio 2022
Corinna Ulcigrai, University of Zurich - Switzerland. How can we understand chaotic behavior mathematically? A well popularized feature of chaotic systems is the butterfly effect: a small variation of initial conditions may lead to a drastically different future evolution, a mechanism at
From playlist Colloqui della Classe di Scienze
Knotty Problems - Marc Lackenby
Knots are a familiar part of everyday life, for example tying your tie or doing up your shoe laces. They play a role in numerous physical and biological phenomena, such as the untangling of DNA when it replicates. However, knot theory is also a well-developed branch of pure mathematics.
From playlist Oxford Mathematics Public Lectures
CS 468: Differential Geometry for Computer Science
From playlist Stanford: Differential Geometry for Computer Science (CosmoLearning Computer Science)
A brief history of geometry II: The European epoch | Sociology and Pure Mathematics | N J Wildberger
Let's have a quick overview of some of the developments in the European story of geometry -- at least up to the 19th century. We'll discuss Cartesian geometry, Projective geometry, Descriptive geometry, Algebraic geometry and Differential geometry. This is meant for people from outside m
From playlist Sociology and Pure Mathematics