Wilson's theorem and Euler characteristic: Difference between pages

Latest revision as of 23:47, 4 October 2016

The Euler characteristic of a shape is a number that describes a topological space, so that anything in the space will have the same number. It is calculated by taking the number of points in the shape, the number of lines in the shape, and the number of faces of the shape. Then, you find the Euler characteristic with this formula:

[math]\displaystyle{ \chi=V-E+F \,\! }[/math]

V is the point count, E the line count, and F the amount of faces. For most common shapes, the Euler Characteristic is 2.

Name	Image	Vertices (Points) V	Edges (Lines) E	Faces F	Euler characteristic: V − E + F
Tetrahedron	File:Tetrahedron.png	4	6	4	2
Hexahedron or cube	File:Hexahedron.png	8	12	6	2
Octahedron	File:Octahedron.png	6	12	8	2
Dodecahedron	File:Dodecahedron.png	20	30	12	2
Icosahedron	File:Icosahedron.png	12	30	20	2

Template:Math-stub

@@ Line 1: / Line 1: @@
-'''Wilson's theorem''' is a theorem of [[number theory]]. Let ''n'' be any [[natural number]]. Wilson's theorem says that ''n'' is a [[prime number]] if and only if:
+The '''Euler characteristic''' of a [[shape]] is a [[number]] that describes a [[topological space]], so that anything in the space will have the same number.
-:<math>(n-1)!\ \equiv\ -1 \pmod n</math>
+It is calculated by taking the number of [[Point (geometry)|points]] in the shape, the number of [[line]]s in the shape, and the number of [[wikt:face|faces]] of the shape. Then, you find the Euler characteristic with this formula:
-This means that if ''n'' is a prime number, the equation is correct. Also, if the equation is correct, then ''n'' is a prime number. The equation says that the [[factorial]] of ''(n - 1)'' is one less than a multiple of ''n''.
-{{Math-stub}}
+:<math>\chi=V-E+F \,\!</math>
+V is the point count, E the line count, and F the amount of faces. For most common shapes, the Euler Characteristic is 2.
-[[Category:Number theory]]
+{| class="wikitable"
+|-
+!Name
+!Image
+!Vertices (Points)<BR>''V''
+!Edges (Lines)<BR>''E''
+!Faces <BR>''F''
+!Euler characteristic:<BR>''V'' &minus; ''E'' + ''F''
+|- align=center
+|[[Tetrahedron]]
+|[[File:tetrahedron.png|50px]]
+|4
+|6
+|4
+|'''2'''
+|- align=center
+|[[Hexahedron]] or [[cube (geometry)|cube]]
+|[[File:hexahedron.png|50px]]
+|8
+|12
+|6
+|'''2'''
+|- align=center
+|[[Octahedron]]
+|[[File:octahedron.png|50px]]
+|6
+|12
+|8
+|'''2'''
+|- align=center
+|[[Dodecahedron]]
+|[[File:dodecahedron.png|50px]]
+|20
+|30
+|12
+|'''2'''
+|- align=center
+|[[Icosahedron]]
+|[[File:icosahedron.png|50px]]
+|12
+|30
+|20
+|'''2'''
+|}
+[[Category:Mathematics]]
+{{math-stub}}

Wilson's theorem and Euler characteristic: Difference between pages

Latest revision as of 23:47, 4 October 2016

Navigation menu

Search