About: Bottema's theorem

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Bottema's theorem is a theorem in plane geometry by the Dutch mathematician (Groningen, 1901–1992). The theorem can be stated as follows: in any given triangle , construct squares on any two adjacent sides, for example and . The midpoint of the line segment that connects the vertices of the squares opposite the common vertex, , of the two sides of the triangle is independent of the location of . The theorem is true when the squares are constructed in one of the following ways: If the squares are replaced by regular polygons of the same type, then a generalized Bottema theorem is obtained:

Attributes	Values
rdf:type	Thing
rdfs:label	Bottema's theorem (en) Stelling van Bottema (nl)
rdfs:comment	De stelling van Bottema is een stelling uit de euclidische meetkunde vernoemd naar Oene Bottema. Bottema beschreef de stelling in de vorm van een verhaal over een verloren schat in een van zijn "Verscheidenheden" in het Nieuw Tijdschrift voor Wiskunde in 1959. Hij is echter niet de eerste auteur van de stelling. (nl) Bottema's theorem is a theorem in plane geometry by the Dutch mathematician (Groningen, 1901–1992). The theorem can be stated as follows: in any given triangle , construct squares on any two adjacent sides, for example and . The midpoint of the line segment that connects the vertices of the squares opposite the common vertex, , of the two sides of the triangle is independent of the location of . The theorem is true when the squares are constructed in one of the following ways: If the squares are replaced by regular polygons of the same type, then a generalized Bottema theorem is obtained: (en)
foaf:depiction
dcterms:subject	Theorems about triangles
Wikipage page ID	63906911 (xsd:integer)
Wikipage revision ID	1117394380 (xsd:integer)
Link from a Wikipage to another Wikipage	Midpoint Line segment Theorem Theorems about triangles Groningen Triangle Vertex (geometry) Napoleon's theorem Van Aubel's theorem Plane geometry dbr:Oene_Bottema
Link from a Wikipage to an external page	https://demonstrations.wolfram.com/BottemasTheorem/ https://www.cut-the-knot.org/Curriculum/Geometry/Bottema.shtml https://www.geogebra.org/classic/bnwynrkx https://www.geogebra.org/classic/bteup6qh.shtml
sameAs	Bottema's theorem Bottema's theorem Bottema's theorem Bottema's theorem
dbp:wikiPageUsesTemplate	dbt:Authority_control dbt:Reflist dbt:Short_description dbt:Elementary-geometry-stub
thumbnail	wiki-commons:Special:FilePath/Bottema's_theorem.png?width=300
has abstract	Bottema's theorem is a theorem in plane geometry by the Dutch mathematician (Groningen, 1901–1992). The theorem can be stated as follows: in any given triangle , construct squares on any two adjacent sides, for example and . The midpoint of the line segment that connects the vertices of the squares opposite the common vertex, , of the two sides of the triangle is independent of the location of . The theorem is true when the squares are constructed in one of the following ways: * Looking at the figure, starting from the lower left vertex, , follow the triangle vertices clockwise and construct the squares to the left of the sides of the triangle. * Follow the triangle in the same way and construct the squares to the right of the sides of the triangle. If the squares are replaced by regular polygons of the same type, then a generalized Bottema theorem is obtained: In any given triangle construct two regular polygons on two sides and .Take the points and on the circumcircles of the polygons, which are diametrically opposed of the common vertex . Then, the midpoint of the line segment is independent of the location of . * Van Aubel's theorem * Napoleon's theorem (en) De stelling van Bottema is een stelling uit de euclidische meetkunde vernoemd naar Oene Bottema. Bottema beschreef de stelling in de vorm van een verhaal over een verloren schat in een van zijn "Verscheidenheden" in het Nieuw Tijdschrift voor Wiskunde in 1959. Hij is echter niet de eerste auteur van de stelling. (nl)
prov:wasDerivedFrom	wikipedia-en:Bottema's_theorem?oldid=1117394380&ns=0
page length (characters) of wiki page	3676 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Bottema's_theorem
is Link from a Wikipage to another Wikipage of	Van Aubel's theorem
is foaf:primaryTopic of	wikipedia-en:Bottema's_theorem

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