Analytic geometry | Differential geometry of surfaces | Surfaces | Differential geometry
In differential geometry a translation surface is a surface that is generated by translations: * For two space curves with a common point , the curve is shifted such that point is moving on . By this procedure curve generates a surface: the translation surface. If both curves are contained in a common plane, the translation surface is planar (part of a plane). This case is generally ignored. Simple examples: 1. * Right circular cylinder: is a circle (or another cross section) and is a line. 2. * The elliptic paraboloid can be generated by and (both curves are parabolas). 3. * The hyperbolic paraboloid can be generated by (parabola) and (downwards open parabola). Translation surfaces are popular in descriptive geometry and architecture, because they can be modelled easily. In differential geometry minimal surfaces are represented by translation surfaces or as midchord surfaces (s. below). The translation surfaces as defined here should not be confused with the translation surfaces in complex geometry. (Wikipedia).
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
An introduction to surfaces | Differential Geometry 21 | NJ Wildberger
We introduce surfaces, which are the main objects of interest in differential geometry. After a brief introduction, we mention the key notion of orientability, and then discuss the division in the subject between algebraic surfaces and parametrized surfaces. It is very important to have a
From playlist Differential Geometry
Geometric and algebraic aspects of space curves | Differential Geometry 20 | NJ Wildberger
A space curve has associated to it various interesting lines and planes at each point on it. The tangent vector determines a line, normal to that is the normal plane, while the span of adjacent normals (or equivalently the velocity and acceleration) is the osculating plane. In this lectur
From playlist Differential Geometry
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
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!
Examples of curvatures of surfaces | Differential Geometry 30 | NJ Wildberger
We review the formulas for the curvature of a surface we derived/discussed in the last lecture, and then give explicit examples of how these formulas work out in special cases. The formulas were given in several roughly equivalent forms, applying to different situations. The first applied
From playlist Differential Geometry
Classical curves | Differential Geometry 1 | NJ Wildberger
The first lecture of a beginner's course on Differential Geometry! Given by Prof N J Wildberger of the School of Mathematics and Statistics at UNSW. Differential geometry is the application of calculus and analytic geometry to the study of curves and surfaces, and has numerous applications
From playlist Differential Geometry
CS 468: Differential Geometry for Computer Science
From playlist Stanford: Differential Geometry for Computer Science (CosmoLearning Computer Science)
C. Judge - Systoles in translation surfaces
I will discuss joint work with Hugo Parlier concerning the shortest noncontractible loops—’systoles’—in a translation surface. In particular, we provide estimates (some sharp) on the number of systoles (up to homotopy) in the strata H(2g-2) and the stratum H(1,1). We also determine the ma
From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications
Lecture 1: Overview (Discrete Differential Geometry)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg
From playlist Discrete Differential Geometry - CMU 15-458/858
Lecture 13: Smooth Surfaces II (Discrete Differential Geometry)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg
From playlist Discrete Differential Geometry - CMU 15-458/858
Lecture 10: Smooth Curves (Discrete Differential Geometry)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg
From playlist Discrete Differential Geometry - CMU 15-458/858
Lecture 14: Discrete Surfaces (Discrete Differential Geometry)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg
From playlist Discrete Differential Geometry - CMU 15-458/858
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)
C. Leininger - Teichmüller spaces and pseudo-Anosov homeomorphism (Part 3)
I will start by describing the Teichmuller space of a surface of finite type from the perspective of both hyperbolic and complex structures and the action of the mapping class group on it. Then I will describe Thurston's compactification of Teichmuller space, and state his classification
From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications
The SL (2, R) action on spaces of differentials (Lecture 01) by Jayadev Athreya
DISCUSSION MEETING SURFACE GROUP REPRESENTATIONS AND PROJECTIVE STRUCTURES ORGANIZERS: Krishnendu Gongopadhyay, Subhojoy Gupta, Francois Labourie, Mahan Mj and Pranab Sardar DATE: 10 December 2018 to 21 December 2018 VENUE: Ramanujan Lecture Hall, ICTS Bangalore The study of spaces o
From playlist Surface group representations and Projective Structures (2018)
Alex Wright - Minicourse - Lecture 3
Alex Wright Dynamics, geometry, and the moduli space of Riemann surfaces We will discuss the GL(2,R) action on the Hodge bundle over the moduli space of Riemann surfaces. This is a very friendly action, because it can be explained using the usual action of GL(2,R) on polygons in the plane
From playlist Maryland Analysis and Geometry Atelier
Holomorphic Curves in Compact Quotients of SL(2,C) by Sorin Dumitrescu
DISCUSSION MEETING TOPICS IN HODGE THEORY (HYBRID) ORGANIZERS: Indranil Biswas (TIFR, Mumbai, India) and Mahan Mj (TIFR, Mumbai, India) DATE: 20 February 2023 to 25 February 2023 VENUE: Ramanujan Lecture Hall and Online This is a followup discussion meeting on complex and algebraic ge
From playlist Topics in Hodge Theory - 2023
More general surfaces | Differential Geometry 22 | NJ Wildberger
This video follows on from DiffGeom21: An Introduction to surfaces, starting with ruled surfaces. These were studied by Euler, and Monge gave examples of how such surfaces arose from the study of curves, namely as polar developables. A developable surface is a particularly important and us
From playlist Differential Geometry
Large Genus Asymptotics in Flat Surfaces and Hyperbolic Geodesics - Amol Aggarwal
Mathematical Physics Seminar Topic: Large Genus Asymptotics in Flat Surfaces and Hyperbolic Geodesics Speaker: Amol Aggarwal Affiliation: Visiting Professor, School of Mathematics Date: March 30, 2022 In this talk we will describe the behaviors of flat surfaces and geodesics on hyperboli
From playlist Mathematics