Geometric Animations

by bothmer

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0:12 Labs Septic bothmer 4,331 views 4 years ago 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...
0:11 Barth Sextic bothmer 1,630 views 4 years ago 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...
0:12 Togliatti Quintic bothmer 1,600 views 4 years ago 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-...
0:11 Clebsch Cubic bothmer 910 views 4 years ago 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...
0:48 The Barth Sextic bothmer 9,343 views 5 years ago 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...
0:19 A Catastrophe bothmer 34,816 views 5 years ago 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...
1:38 The Real Projective Plane bothmer 48,955 views 5 years ago 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 ...
0:19 Morsification bothmer 4,866 views 5 years ago 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...
0:38 The Alexander Sphere bothmer 98,824 views 5 years ago 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...
1:51 The fundamental Theorem of Algebra bothmer 22,615 views 5 years ago 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:...

About Geometric Animations

Together with Oliver Labs I uploaded an geometric animation together with a description of its mathematical content each day until Christmas 2006.

http://www.calendar.algebraicsurface.net/

by bothmer

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Nov 9, 2011

Date Joined

Oct 14, 2006

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