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- Ptolemy's_theorem abstract "In Euclidean geometry, Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices lie on a common circle). The theorem is named after the Greek astronomer and mathematician Ptolemy (Claudius Ptolemaeus). Ptolemy used the theorem as an aid to creating his table of chords, a trigonometric table that he applied to astronomy.If the quadrilateral is given with its four vertices A, B, C, and D in order, then the theorem states that: where the vertical lines denote the lengths of the line segments between the named vertices.This relation may be verbally expressed as follows: If a quadrilateral is inscribable in a circle then the product of the measures of its diagonals is equal to the sum of the products of the measures of the pairs of opposite sides.Moreover, the converse of Ptolemy's theorem is also true:In a quadrilateral, if the sum of the products of its two pairs of opposite sides is equal to the product of its diagonals, then the quadrilateral can be inscribed in a circle.↑".
- Ptolemy's_theorem thumbnail Ptolemy_Theorem.svg?width=300.
- Ptolemy's_theorem wikiPageExternalLink 1543droc.book.
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- Ptolemy's_theorem wikiPageExternalLink PtolemysTheorem.
- Ptolemy's_theorem wikiPageExternalLink gjarcmg.geometry-math-journal.ro.
- Ptolemy's_theorem wikiPageExternalLink PtolemyInequality.html.
- Ptolemy's_theorem wikiPageExternalLink PtolemysTheorem.html.
- Ptolemy's_theorem wikiPageExternalLink index.html.
- Ptolemy's_theorem wikiPageExternalLink index.html.
- Ptolemy's_theorem wikiPageExternalLink ptolemy.shtml.
- Ptolemy's_theorem wikiPageExternalLink sine_cosine.shtml.
- Ptolemy's_theorem wikiPageExternalLink derivation-proof-ptolemy-s-theorem-cyclic-quadrilateral.
- Ptolemy's_theorem wikiPageExternalLink kmath099.htm.
- Ptolemy's_theorem wikiPageID "1521971".
- Ptolemy's_theorem wikiPageRevisionID "599381691".
- Ptolemy's_theorem hasPhotoCollection Ptolemy's_theorem.
- Ptolemy's_theorem subject Category:Articles_containing_proofs.
- Ptolemy's_theorem subject Category:Euclidean_plane_geometry.
- Ptolemy's_theorem subject Category:Ptolemy.
- Ptolemy's_theorem subject Category:Quadrilaterals.
- Ptolemy's_theorem subject Category:Theorems_in_geometry.
- Ptolemy's_theorem type Abstraction100002137.
- Ptolemy's_theorem type Communication100033020.
- Ptolemy's_theorem type Message106598915.
- Ptolemy's_theorem type Proposition106750804.
- Ptolemy's_theorem type Statement106722453.
- Ptolemy's_theorem type Theorem106752293.
- Ptolemy's_theorem type TheoremsInGeometry.
- Ptolemy's_theorem comment "In Euclidean geometry, Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices lie on a common circle). The theorem is named after the Greek astronomer and mathematician Ptolemy (Claudius Ptolemaeus).".
- Ptolemy's_theorem label "Ptolemy's theorem".
- Ptolemy's_theorem label "Satz von Ptolemäus".
- Ptolemy's_theorem label "Stelling van Ptolemaeus".
- Ptolemy's_theorem label "Teorema de Ptolomeo".
- Ptolemy's_theorem label "Teorema de Ptolomeu".
- Ptolemy's_theorem label "Teorema di Tolomeo".
- Ptolemy's_theorem label "Théorème de Ptolémée".
- Ptolemy's_theorem label "Twierdzenie Ptolemeusza".
- Ptolemy's_theorem label "Неравенство Птолемея".
- Ptolemy's_theorem label "مبرهنة بطليموس".
- Ptolemy's_theorem label "トレミーの定理".
- Ptolemy's_theorem label "托勒密定理".
- Ptolemy's_theorem sameAs Satz_von_Ptolemäus.
- Ptolemy's_theorem sameAs Teorema_de_Ptolomeo.
- Ptolemy's_theorem sameAs Théorème_de_Ptolémée.
- Ptolemy's_theorem sameAs Teorema_di_Tolomeo.
- Ptolemy's_theorem sameAs トレミーの定理.
- Ptolemy's_theorem sameAs 프톨레마이오스_정리.
- Ptolemy's_theorem sameAs Stelling_van_Ptolemaeus.
- Ptolemy's_theorem sameAs Twierdzenie_Ptolemeusza.
- Ptolemy's_theorem sameAs Teorema_de_Ptolomeu.
- Ptolemy's_theorem sameAs m.057r6r.
- Ptolemy's_theorem sameAs Q459547.
- Ptolemy's_theorem sameAs Q459547.
- Ptolemy's_theorem sameAs Ptolemy's_theorem.
- Ptolemy's_theorem wasDerivedFrom Ptolemy's_theorem?oldid=599381691.
- Ptolemy's_theorem depiction Ptolemy_Theorem.svg.
- Ptolemy's_theorem isPrimaryTopicOf Ptolemy's_theorem.
