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In mathematics, genus (plural genera) has a few different, but closely related, meanings: ==Topology== ===Orientable surface=== The genus of a connected, orientable surface is an integer representing the maximum number of cuttings along non-intersecting closed simple curves without rendering the resultant manifold disconnected.〔Munkres, James R. Topology. Vol. 2. Upper Saddle River: Prentice Hall, 2000.〕 It is equal to the number of handles on it. Alternatively, it can be defined in terms of the Euler characteristic ''χ'', via the relationship ''χ'' = 2 − 2''g'' for closed surfaces, where ''g'' is the genus. For surfaces with ''b'' boundary components, the equation reads ''χ'' = 2 − 2''g'' − ''b''. For instance: * The sphere ''S''''2'' and a disc both have genus zero. * A torus has genus one, as does the surface of a coffee mug with a handle. This is the source of the joke that "a topologist is someone who can't tell his donut from his coffee mug." An explicit construction of surfaces of genus ''g'' is given in the article on the fundamental polygon. File:Sphere filled blue.svg|genus 0 File:Torus illustration.png|genus 1 File:Double torus illustration.png|genus 2 File:Triple torus illustration.png|genus 3 In simpler terms, the value of an orientable surface's genus is equal to the number of "holes" it has.〔http://mathworld.wolfram.com/Genus.html〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Genus (mathematics)」の詳細全文を読む スポンサード リンク
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