Geometric Animations
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Labs Septic
bothmer
4,294 views
A classical question in algebraic geometry is how many cone-singularities a surface of a given degree can have. For degree 7 surfaces this problem is still unsolved. The mo...
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Barth Sextic
bothmer
1,614 views
A classical question in algebraic geometry is how many cone-singularities a surface of a given degree can have. In 1996 Barth found the beautyful degree 6 surfaces shown in...
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Togliatti Quintic
bothmer
1,585 views
A classical question in algebraic geometry is how many cone-singularities a surface of a given degree can have. In 1940 Togliatti proved that for degree 5 surfaces 31 cone-...
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Clebsch Cubic
bothmer
888 views
A classical question in algebraic geometry is how many cone-singularities a surface of a given degree can have. For degree 3 surface this problem was solved in 1863 and 186...
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The Barth Sextic
bothmer
9,172 views
At least since Kummer's work (1860s) on 16-nodal quartics algebraic geometers ask the question how many isolated singularities a surface of degree d in projective 3-space c...
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A Catastrophe
bothmer
34,690 views
Here we show the p,q-plane (red) together with the zeros of the polynomial
x^3 + px + q (yellow) and its discriminant 4x^3+27y^2=0 (black on red). The white line shows th...
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The Real Projective Plane
bothmer
47,713 views
The projective plane is the space of lines through the origin in 3-space. In the projective plane, we have the remarkable fact that any two distinct lines meet in a unique ...
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Morsification
bothmer
4,835 views
This is a visualisation of the morsification F(x,y,z) = (x^3-x)+(y^3-y)+(z^3-z) of the funktion x^3+y^3+z^3. The morsefunction has 8 critical values at levels -3, -1, +1 an...
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The Alexander Sphere
bothmer
98,284 views
A path that is homoemorphic to a circle devides a compactified plane into two pieces (inside and outside). Arthur Schönflies proved in 1906 that in this situation the insid...
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The fundamental Theorem of Algebra
bothmer
22,163 views
This video illustrates a proof of the Fundamental Theorem of Algebra: "Every polynomial degree at least 1 with complex coefficients has a least one complex zero".
Proof:...
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