Editing 2625: Field Topology
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{{w|Baseball}}, {{w|tetherball}} and {{w|soccer}} are played on fields which are continuous in three-dimensional space. This means it is possible to traverse any path around or over any of the structures defining the field, while there are no obstructions which can be traversed through in a loop around them. The goals on a soccer field presumably do not create holes because the goalposts and crossbar are connected to the field by the net; Randall apparently considers these to form continuous surfaces which do not allow loops through them. | {{w|Baseball}}, {{w|tetherball}} and {{w|soccer}} are played on fields which are continuous in three-dimensional space. This means it is possible to traverse any path around or over any of the structures defining the field, while there are no obstructions which can be traversed through in a loop around them. The goals on a soccer field presumably do not create holes because the goalposts and crossbar are connected to the field by the net; Randall apparently considers these to form continuous surfaces which do not allow loops through them. | ||
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+ | [[File:Double torus illustration.png|thumb|150px|A genus two surface]] | ||
{{w|Volleyball}} and {{w|badminton}} are played using a net suspended from poles, and the {{w|high jump}} has a bar that contestants jump over. The structure formed by the net or bar and the supporting poles can be considered to be a "hole" through the playing field, as a path over and under the net/bar forming a loop cannot be contracted to a single point, so their playing fields in the comic all have one "hole". | {{w|Volleyball}} and {{w|badminton}} are played using a net suspended from poles, and the {{w|high jump}} has a bar that contestants jump over. The structure formed by the net or bar and the supporting poles can be considered to be a "hole" through the playing field, as a path over and under the net/bar forming a loop cannot be contracted to a single point, so their playing fields in the comic all have one "hole". | ||
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A basketball court has two hoops. {{w|Parallel bars}} can be thought of as two archways. Both have opportunities to pass through either (or both) structures, and so the material of the structures define a hole in the topological abstract of the playing 'space'. Since we are told that these sports fields belong to the Topology Department - and are not necessarily generalized to all sports fields - we might assume that their "football" field is either for {{w|Rugby_sevens|rugby}} or for American football using H-shaped {{w|Goal (sports)|uprights}}. | A basketball court has two hoops. {{w|Parallel bars}} can be thought of as two archways. Both have opportunities to pass through either (or both) structures, and so the material of the structures define a hole in the topological abstract of the playing 'space'. Since we are told that these sports fields belong to the Topology Department - and are not necessarily generalized to all sports fields - we might assume that their "football" field is either for {{w|Rugby_sevens|rugby}} or for American football using H-shaped {{w|Goal (sports)|uprights}}. |