skip to main content

Mathematics (thesaurus)

Content language

Home / Explore / Browse / Vocabularies / Mathematics (thesaurus)

geometry > geometric drawing > triangle center > Jacobi's theorem

... > geometric figure > point > center > triangle center > Jacobi's theorem

... > Euclidean geometry > point > center > triangle center > Jacobi's theorem

Preferred term

Jacobi's theorem

Definition(s)

In plane geometry, a Jacobi point is a point in the Euclidean plane determined by a triangle $△ ABC$ and a triple of angles $α, β, γ$ . This information is sufficient to determine three points $X, Y, Z$ such that ${\\displaystyle {\egin{aligned}\\angle ZAB&=\\angle YAC&=\\alpha ,\\\\\\angle XBC&=\\angle ZBA&=\eta ,\\\\\\angle YCA&=\\angle XCB&=\\gamma .\\end{aligned}}}$ Then, by a theorem of Karl Friedrich Andreas Jacobi, the lines $AX, BY, CZ$ are concurrent, at a point $N$ called the Jacobi point.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Jacobi%27s_theorem_(geometry))

Broader concept(s)

triangle center

Related concept(s)

triangle

Synonym(s)

Jacobi point

In other languages

théorème de Jacobi

French
point de Jacobi
théorème de Fermat-Toricelli généralisé
théorème isogonal

URI

http://data.loterre.fr/ark:/67375/PSR-D1LDBSDF-L

Download this concept:

RDF/XML TURTLE JSON-LD Created 8/11/23, last modified 8/11/23