Pentagon: Difference between revisions
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{{for|the U.S. building|The Pentagon}} |
{{for|the U.S. building|The Pentagon}} |
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[[File:Regular polygon 5 annotated.svg|thumb|A regular pentagon]] |
[[File:Regular polygon 5 annotated.svg|thumb|A regular pentagon]] |
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A '''pentagon''' is a [[polygon]] with five edges. It is defined by five points, which are all on a [[Plane (mathematics)|plane]]. If all the edges have the same length and the [[Angle|angles]] at the corners are all [[Degree (angle)|108°]], the pentagon is called ''regular''. If the pentagon intersects itself, it is called a [[pentagram]]. |
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Pentagons also occur in [[nature]]: [[Fruit]]s of the [[Okra]] are pentangular. The [[flower]]s of [[Ipomoea]] are pentagular. In [[chemistry]], many [[Cyclic compound]]s are pentangles: [[Cyclopentane]] and [[Furan]] are examples for this. In architecture, many [[bastion]]s are pentangular: [[Bourtange]], in the [[Netherlands]] has been completely restored, and is a pentangle. The [[Citadel of Lille]], [[Nyenschantz]], near [[St. Petersburg]], or the [[Citadel of Pamplona]] are . The [[Villa Farnese]] is a [[palace]] in the form of a pentagon, so is the [[castle]] of [[Nowy Wiśnicz]]. The [[Pilgrimage Church of Saint John of Nepomuk]] near [[Žďár nad Sázavou]] also uses a pentangular design. |
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== Formulas == |
== Formulas == |
Latest revision as of 23:40, 16 May 2024
![](https://upload.wikimedia.org/wikipedia/commons/thumb/0/01/Regular_polygon_5_annotated.svg/220px-Regular_polygon_5_annotated.svg.png)
A pentagon is a polygon with five edges. It is defined by five points, which are all on a plane. If all the edges have the same length and the angles at the corners are all 108°, the pentagon is called regular. If the pentagon intersects itself, it is called a pentagram.
Pentagons also occur in nature: Fruits of the Okra are pentangular. The flowers of Ipomoea are pentagular. In chemistry, many Cyclic compounds are pentangles: Cyclopentane and Furan are examples for this. In architecture, many bastions are pentangular: Bourtange, in the Netherlands has been completely restored, and is a pentangle. The Citadel of Lille, Nyenschantz, near St. Petersburg, or the Citadel of Pamplona are . The Villa Farnese is a palace in the form of a pentagon, so is the castle of Nowy Wiśnicz. The Pilgrimage Church of Saint John of Nepomuk near Žďár nad Sázavou also uses a pentangular design.
Formulas[change | change source]
Note: these formulas only work for regular pentagons.
R is the radius of the circumcircle.
Examples of pentagons[change | change source]
Plants[change | change source]
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Pentagonal cross-section of okra.
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Morning glories, like many other flowers, have a pentagonal shape.
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Starfruit is another fruit with fivefold symmetry.
Animals[change | change source]
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A sea star. Many echinoderms have fivefold radial symmetry.
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An illustration of brittle stars, also echinoderms with a pentagonal shape.
Artificial[change | change source]
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The Pentagon, headquarters of the United States Department of Defense.
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Home plate of a baseball field
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Fort Bourtange,in the Netherlands