Editing 2721: Euler Diagrams
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[[File:Euler Diagrams title text.png|300px|thumb|right|The title text as a Venn (and, simultaneously, an Euler) diagram]] | [[File:Euler Diagrams title text.png|300px|thumb|right|The title text as a Venn (and, simultaneously, an Euler) diagram]] | ||
| − | {{w|John Venn}} was not the first to invent the idea of drawing regions whose overlap shows the intersection of | + | {{w|John Venn}} was not the first to invent the idea of drawing regions whose overlap shows the intersection of sets—that was popularized by Euler (although he may not have been the first to do it) and was known as {{w|Euler Diagram}}s. Venn's innovation, roughly 100 years later, was to consistently draw ALL intersections of sets, even those intersections that had no members. In a Venn diagram, all 'circles' must overlap with all other circles, even if there are no items in the overlap. This is easy enough for 2 and 3 sets, but as the number of sets increases, the diagrams can get rather complicated, as previously shown in [[2122: Size Venn Diagram]]. [https://www.newscientist.com/article/dn22159-logic-blooms-with-new-11-set-venn-diagram/ These] [https://raw.githubusercontent.com/wiki/tctianchi/pyvenn/venn6.png three] [https://en.wikipedia.org/wiki/Template:Supranational_European_Bodies links] demonstrate the issue, in which sets can start looking very non-circular. An Euler diagram is required to depict only the non-empty combinations/sets, and therefore does not have this constraint. The diagram in the comic does not have any overlap between the left and right sections so, while it is an Euler diagram, it is not a Venn diagram. |
The title text is an example of a "written" Venn diagram, with Leonhard Euler creating "{{w|Contributions of Leonhard Euler to mathematics|most of math}}", both of them having created overlapping circle diagrams, and John Venn creating a {{w|cricket}} {{w|bowling (cricket)|bowling}} machine. In his Wikipedia article it is stated that ''He built rare machines. A certain machine was meant to bowl cricket balls.'' See the title text drawn as a diagram in the inserted picture. | The title text is an example of a "written" Venn diagram, with Leonhard Euler creating "{{w|Contributions of Leonhard Euler to mathematics|most of math}}", both of them having created overlapping circle diagrams, and John Venn creating a {{w|cricket}} {{w|bowling (cricket)|bowling}} machine. In his Wikipedia article it is stated that ''He built rare machines. A certain machine was meant to bowl cricket balls.'' See the title text drawn as a diagram in the inserted picture. | ||
