Genus (InstanceTopic, 3)

From Hi.gher. Space

(Difference between revisions)

Latest revision as of 22:57, 11 February 2014

In 3D, the genus of a shape is equal to how many "holes" it has that fully pierce the shape. For example, a sphere has genus 0, and a torus has genus 1.

In higher dimensions, it gets more complicated: with each new dimension, a new type of hole is possible. So each of the different four-dimensional torii have a pair of numbers as their "genus".

This is closely related to homology groups.

@@ Line 1: / Line 1: @@
-The '''genus''' of an object is equal to how many "holes" it has that fully pierce the object.
+<[#ontology [kind topic] [cats Property]]>
+In 3D, the '''genus''' of a [[shape]] is equal to how many "holes" it has that fully pierce the shape. For example, a [[sphere]] has genus 0, and a [[torus]] has genus 1.
-[[Line (object)|Lines]] always have a genus of zero. If a hole was created it would be split in half.
+In higher dimensions, it gets more complicated: with each new dimension, a new type of hole is possible. So each of the different [[four-dimensional torii]] have a pair of numbers as their "genus".
-There are two types of holes that an object can have. ''Pockets'' are holes completely inside the object and cannot be seen by any outside viewer (unless the being viewing the object is in a higher dimension than the object itself). Ordinary ''holes'' are ones that can be seen from the outside, for example the hole in a [[torus]]. The only type of hole that can be placed inside a [[polygon]] is a pocket, as creating a normal hole would split the object in half.
+This is closely related to [[homology groups]].
-[[Category:Geometrical properties]]