Difference between revisions of "Kummer Quartic"
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A Kummer surface has sixteen double points, the maximum possible for a surface of degree four in three-dimensional space. For the default case <math>aa</math> = 1.3, all these double points are real and they appear in the visualization as the vertices of five tetrahedra. | A Kummer surface has sixteen double points, the maximum possible for a surface of degree four in three-dimensional space. For the default case <math>aa</math> = 1.3, all these double points are real and they appear in the visualization as the vertices of five tetrahedra. | ||
− | |s1a= | + | |s1a=Yes |
|s1b=No | |s1b=No | ||
|s1c=No | |s1c=No | ||
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|s4a=No | |s4a=No | ||
|s4b=No | |s4b=No | ||
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|s4d=No | |s4d=No | ||
|s5a=No | |s5a=No | ||
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|Field2=Geometry | |Field2=Geometry | ||
|FieldLinks=:* [http://xahlee.org/surface/kummer/_jv_kummer.html Rotate a Kummer Quartic] | |FieldLinks=:* [http://xahlee.org/surface/kummer/_jv_kummer.html Rotate a Kummer Quartic] | ||
+ | :* [http://mathworld.wolfram.com/KummerSurface.html Kummer Surfaces - Wolfram Mathworld] | ||
}} | }} |
Revision as of 11:57, 23 July 2008
Kummer Quartic |
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Kummer Quartic
- A Kummer surface is any one of a one parameter family of algebraic surfaces defined by a specific polynomial equation of degree four.
Contents
A More Mathematical Explanation
- Note: understanding of this explanation requires: *Linear Algebra *Differential Geometry
The polynomial equation of degree four that describes a Kummer surfaces is:
'"`UNIQ--math-00000000-Q [...]The polynomial equation of degree four that describes a Kummer surfaces is: , where:
- is any real number,
- ,
- ,
- ,
- ,
- and .
The family was described originally by Ernst Eduard Kummer in 1864.
A Kummer surface has sixteen double points, the maximum possible for a surface of degree four in three-dimensional space. For the default case = 1.3, all these double points are real and they appear in the visualization as the vertices of five tetrahedra.
Teaching Materials (1)
Teaching Materials (1)
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