Differential geometry

Affine sphere

In mathematics, and especially differential geometry, an affine sphere is a hypersurface for which the affine normals all intersect in a single point. The term affine sphere is used because they play an analogous role in affine differential geometry to that of ordinary spheres in Euclidean differential geometry. An affine sphere is called improper if all of the affine normals are constant. In that case, the intersection point mentioned above lies on the hyperplane at infinity. Affine spheres have been the subject of much investigation, with many hundreds of research articles devoted to their study. (Wikipedia).

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This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the relation between affine and projective varieties, with some examples such as a cubic curve and the twisted cubic.

From playlist Algebraic geometry I: Varieties

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Find the volume of a sphere given the circumference

👉 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

👉 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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Finding the volume and the surface area 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

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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

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👉 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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This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers regular functions on affine and quasiprojective varieties.

From playlist Algebraic geometry I: Varieties

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This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It introduces projective space and describes the synthetic and analytic approaches to projective geometry

From playlist Algebraic geometry I: Varieties

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From playlist Ecole d'été 2014 - Analyse asymptotique en relativité générale

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From playlist Mathematics

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This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It describes the automorphisms of affine and projective space, and gives a brief discussion of the Jacobian conjecture.

From playlist Algebraic geometry I: Varieties

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From playlist Volume and Surface Area

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From playlist NUMSTRING 2022

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From playlist Workshop: High dimensional spatial random systems

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From playlist Mathematics

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From playlist Benson Farb: 29th Workshop in Geometric Topology

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From playlist 2019 - T2 - Reinventing rational points

Related pages

Paraboloid | Hyperplane at infinity | Differential geometry | Determinant | Affine differential geometry | Hypersurface | Quadric | Hessian matrix