Differential geometry of surfaces | Complex surfaces | Geometric shapes | Differential geometry | Surfaces | Algebraic surfaces | Analytic geometry
In geometry, a surface S is ruled (also called a scroll) if through every point of S there is a straight line that lies on S. Examples include the plane, the lateral surface of a cylinder or cone, a conical surface with elliptical directrix, the right conoid, the helicoid, and the tangent developable of a smooth curve in space. A ruled surface can be described as the set of points swept by a moving straight line. For example, a cone is formed by keeping one point of a line fixed whilst moving another point along a circle. A surface is doubly ruled if through every one of its points there are two distinct lines that lie on the surface. The hyperbolic paraboloid and the hyperboloid of one sheet are doubly ruled surfaces. The plane is the only surface which contains at least three distinct lines through each of its points. The properties of being ruled or doubly ruled are preserved by projective maps, and therefore are concepts of projective geometry. In algebraic geometry, ruled surfaces are sometimes considered to be surfaces in affine or projective space over a field, but they are also sometimes considered as abstract algebraic surfaces without an embedding into affine or projective space, in which case "straight line" is understood to mean an affine or projective line. (Wikipedia).
Complex surfaces 4: Ruled surfaces
This talk gives an informal survey of ruled surfaces and their role in the Enriques classification. We give a few examples of ruled surfaces, summarize the basic invariants of surfaces, and sketch how one classifies the surfaces of Kodaira dimension minus infinity.
From playlist Algebraic geometry: extra topics
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
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
(New Version Available) Parameterized Surfaces
New Version: https://youtu.be/0kKBPbmzwm8 This video explains how to parameterized a equation of a surface. http://mathispower4u.wordpress.com/
From playlist Surface Integrals
This video explains how to parameterized a equation of a surface.
From playlist Surface Integrals
Parameterizing Surfaces and Computing Surface Normal Vectors
In this video we discuss parameterizing a surface. We use two approaches, a simple approach which models a surface using a level surface as well as a robust parameterization using two independent variables. We show how both formulations can be used to compute normal vectors to the surfac
From playlist Calculus
From playlist Drawing a sphere
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
Tensor Calculus Lecture 11a: Gauss' Theorema Egregium, Part 1
This course will eventually continue on Patreon at http://bit.ly/PavelPatreon Textbook: http://bit.ly/ITCYTNew Errata: http://bit.ly/ITAErrata McConnell's classic: http://bit.ly/MCTensors Table of Contents of http://bit.ly/ITCYTNew Rules of the Game Coordinate Systems and the Role of Te
From playlist Introduction to Tensor Calculus
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)
The Girl with the Hyperbolic Helicoid Tattoo - Numberphile
Sabetta Matsumoto explains her mathematical tattoo. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ Sabetta's Twitter: https://twitter.com/sabetta_ And her group's webpage at Georgia Tec
From playlist Women in Mathematics - Numberphile
The Polynomial Method and Applications From Finite Field Kakeya to Distinct Distances - Larry Guth
Larry Guth University of Toronto; Member, School of Mathematics April 22, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
Topological Constructs and Phases on Polarization Singularities by P. Senthilkumaran
DISCUSSION MEETING STRUCTURED LIGHT AND SPIN-ORBIT PHOTONICS ORGANIZERS: Bimalendu Deb (IACS Kolkata, India), Tarak Nath Dey (IIT Guwahati, India), Subhasish Dutta Gupta (UOH, TIFR Hyderabad, India) and Nirmalya Ghosh (IISER Kolkata, India) DATE: 29 November 2022 to 02 December 2022 VE
From playlist Structured Light and Spin-Orbit Photonics - Edited
Surface area of revolution - simpson's rule (KristaKingMath)
► My Applications of Integrals course: https://www.kristakingmath.com/applications-of-integrals-course Learn how to use Simpson's rule to find surface area of of a solid of revolution. ● ● ● GET EXTRA HELP ● ● ● If you could use some extra help with your math class, then check out Krist
From playlist Calculus II
The Holographic Universe Explained
PBS Member Stations rely on viewers like you. To support your local station, go to: http://to.pbs.org/DonateSPACE ↓ More info below ↓ We live in a universe with 3 dimensions of space and one of time. Up, down, left, right, forward, back, past, future. 3+1 dimensions. Or so our primitive P
From playlist Understanding the Holographic Universe
Tensor Calculus Lecture 14d: Non-hypersurfaces - Relationship Among Curvature Tensors 1
This course will eventually continue on Patreon at http://bit.ly/PavelPatreon Textbook: http://bit.ly/ITCYTNew Errata: http://bit.ly/ITAErrata McConnell's classic: http://bit.ly/MCTensors Table of Contents of http://bit.ly/ITCYTNew Rules of the Game Coordinate Systems and the Role of Te
From playlist Introduction to Tensor Calculus
The embedded Calabi-Yau problem for minimal surfaces of finite genus - Joaquin Perez
Workshop on Mean Curvature and Regularity Topic: The embedded Calabi-Yau problem for minimal surfaces of finite genus Speaker: Joaquin Perez Affiliation: UGR Date: November 8, 2018 For more video please visit http://video.ias.edu
From playlist Workshop on Mean Curvature and Regularity
Learn how to determine the volume of a sphere
👉 Learn how to find the volume and the surface area of a sphere. A sphere is a perfectly round 3-dimensional object. It is an object with the shape of a round ball. The distance from the center of a sphere to any point on its surface is called the radius of the sphere. A sphere has a unifo
From playlist Volume and Surface Area