Algebraic surfaces | Differential geometry

Cayley's ruled cubic surface

In differential geometry, Cayley's ruled cubic surface is the ruled cubic surface It contains a nodal line of self-intersection and two cuspital points at infinity. In projective coordinates it is . (Wikipedia).

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Tropical Geometry - Lecture 8 - Surfaces | Bernd Sturmfels

Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)

From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels

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Find the volume of a sphere given the circumference

πŸ‘‰ 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

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Archimedes Parabolic Area Formula for Cubics! | Algebraic Calculus One | Wild Egg

The very first and arguably most important calculation in Calculus was Archimedes' determination of the slice area of a parabola in terms of the area of a suitably inscribed triangle, involving the ratio 4/3. Remarkably, Archimedes' formula extends to the cubic case once we identify the ri

From playlist Old Algebraic Calculus Videos

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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

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Robert Lazarsfeld: Cayley-Bacharach theorems with excess vanishing

A classical result usually attributed to Cayley and Bacharach asserts that if two plane curves of degrees c and d meet in cd points, then any curve of degree (c + d - 3) passing through all but one of these points must also pass through the remaining one. In the late 1970s, Griffiths and H

From playlist Algebraic and Complex Geometry

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Sierpinski from Pascal

This is a recreation of a short clip from a long form video showing six different ways to construct the Sierpinski triangle: https://youtu.be/IZHiBJGcrqI In this short, we shade odd entries of the Halayuda/Pascal triangle to obtain the Sierpinski triangle. Can you explain why this works?

From playlist Fractals

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Finding the volume and the surface area of a sphere

πŸ‘‰ 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

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How do you find the surface area of a sphere

πŸ‘‰ 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

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Learn how to determine the volume of a sphere

πŸ‘‰ 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

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Cylindrical Surfaces

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

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The Cayley Expansion (feat. David Eisenbud) - Objectivity 174

David Eisenbud joins us at The Royal Society to look at the work of one of his all time favourite mathematicians. More links below ↓↓↓ Featuring David Eisenbud speaking with Brady and Keith Moore. Subscribe to Objectivity: http://bit.ly/Objectivity_Sub Check out David on Numberphile: h

From playlist David Eisenbud on Numberphile

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Integral points on Markoff-type cubic surfaces - Amit Ghosh

Special Seminar Topic: Integral points on Markoff-type cubic surfaces Speaker: Amit Ghosh Affiliation: Oklahoma State University Date: December 8, 2017 For more videos, please visit http://video.ias.edu

From playlist Mathematics

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Nonlinear algebra, Lecture 10: "Invariant Theory", by Bernd Sturmfels

This is the tenth lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences.

From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra

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Cubic surfaces and non-Euclidean geometry - William Goldman

Members’ Colloquium Topic: Cubic surfaces and non-Euclidean geometry Speaker: William Goldman Affiliation: University of Maryland; Member, School of Mathematics Date: January 24, 2022 The classification of geometric structures on manifolds naturally leads to actions of automorphism group

From playlist Mathematics

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Peter Sarnak: Integral points on Markoff type cubic surfaces [2016]

Integral points on Markoff type cubic surfaces Speaker: Peter Sarnak, Institute for Advanced Study, Princeton Date and Time: Tuesday, November 1, 2016 - 11:30am to 12:30pm Location: Fields Institute, Room 230 Abstract: Cubic surfaces in affine three space tend to have few integral poin

From playlist Mathematics

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Given the circumference how do you find the surface area of a hemisphere

πŸ‘‰ 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

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A Short Course in Algebra and Number Theory - 1. Groups

To supplement a course taught at The University of Queensland's School of Mathematics and Physics I present a very brief summary of algebra and number theory for those students who need to quickly refresh that material or fill in some gaps in their understanding. This is the first lectur

From playlist A Short Course in Algebra and Number Theory

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Matt Kerr

https://www.math.ias.edu/files/media/agenda.pdf More videos on http://video.ias.edu

From playlist Mathematics

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CurvesSurfaces3: De Casteljau Bezier Curves in Algebraic Calculus | N J Wildberger

We explain how to extend Archimedes' famous Parabolic Area Formula to the cubic situation. This formula was historically the first major calculation in Calculus, and gave an explicit and workable formula for the area of a slice of a parabola, cut off by a chord, in terms of the area of a p

From playlist MathSeminars

Related pages

Cubic surface | Differential geometry | Ruled surface