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. | ||
− | | | + | |other=Differential Geometry, Algebra |
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|AuthorName=3DXM Consortium | |AuthorName=3DXM Consortium | ||
|AuthorDesc=The 3DXM Consortium is the group in charge of the 3D-XplorMath software development project and the related Virtual Mathematics Museum website project. The Consortium is an international volunteer group of mathematicians. | |AuthorDesc=The 3DXM Consortium is the group in charge of the 3D-XplorMath software development project and the related Virtual Mathematics Museum website project. The Consortium is an international volunteer group of mathematicians. | ||
|SiteName=Virtual Math Museum | |SiteName=Virtual Math Museum | ||
|SiteURL=http://virtualmathmuseum.org/ | |SiteURL=http://virtualmathmuseum.org/ | ||
+ | |TeachingMaterials=:* A teaching material test. [[Kummer Quartic Teaching]] | ||
|Field=Algebra | |Field=Algebra | ||
|Field2=Geometry | |Field2=Geometry | ||
+ | |FieldLinks=:* [http://xahlee.org/surface/kummer/_jv_kummer.html Rotate a Kummer Quartic] | ||
+ | :* [http://mathworld.wolfram.com/KummerSurface.html Kummer Surfaces - Wolfram Mathworld] | ||
}} | }} | ||
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+ | <accesscontrol>Math-Images-Staff</accesscontrol> |
Latest revision as of 15:09, 15 January 2010
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: *Differential Geometry, Algebra
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)
Want to add your own teaching materials or lesson plans? Add teaching materials.About the Creator of this Image
The 3DXM Consortium is the group in charge of the 3D-XplorMath software development project and the related Virtual Mathematics Museum website project. The Consortium is an international volunteer group of mathematicians.
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<accesscontrol>Math-Images-Staff</accesscontrol>