In mathematics, Pappus's hexagon theorem (attributed to Pappus of Alexandria) states that given one set of collinear points A , B , C , {\displaystyle...

Pappus's theorem may refer to: Pappus's area theorem Pappus's centroid theorem Pappus's hexagon theorem This disambiguation page lists mathematics articles...

cases when opposite sides are parallel. This theorem is a generalization of Pappus's (hexagon) theorem, which is the special case of a degenerate conic...

known for his Synagoge (Συναγωγή) or Collection (c. 340), and for Pappus's hexagon theorem in projective geometry. Almost nothing is known about his life...

coordinate system must be a division ring (skewfield). Pappus's hexagon theorem states that, if a hexagon AbCaBc is drawn in such a way that vertices a, b and...

tribe Mirini Pappus of Alexandria, Greek mathematician Pappus's hexagon theorem, often just called 'Pappus's theorem', a theorem named for Pappus of Alexandria...

of a hexagon lie on a line L, then the six vertices of the hexagon lie on a conic C; the conic may be degenerate, as in Pappus's hexagon theorem. The...

be defined over a (commutative) field. Equivalently Pappus's hexagon theorem and Desargues's theorem are supposed to be true. A large part of the results...

sides of a hexagon lie on a line, then the six vertices of the hexagon lie on a conic, which may be degenerate as in Pappus's hexagon theorem. By Monge's...

through each point. This configuration is named after Pappus of Alexandria. Pappus's hexagon theorem states that every two triples of collinear points ABC...

Brianchon's theorem its principal diagonals are concurrent (as in the above image). Concurrent lines arise in the dual of Pappus's hexagon theorem. For each...

cubic passing through 8 of the points. A second application is Pappus's hexagon theorem, similar to the above, but the six points are on two lines instead...

The honeycomb theorem, formerly the honeycomb conjecture, states that a regular hexagonal grid or honeycomb has the least total perimeter of any subdivision...

(geometry) Pappus's hexagon theorem (geometry) Pascal's theorem (conics) Pasch's theorem (order theory) Pitot theorem (plane geometry) Pivot theorem (circles)...

lines CA' and C'A are parallel. (This is the affine version of Pappus's hexagon theorem). The full axiom system proposed has point, line, and line containing...

field – except that the commutativity of multiplication requires Pappus's hexagon theorem. As a result, the points of each line are in one-to-one correspondence...

both mathematics with Jacobus Golius, who confronted him with Pappus's hexagon theorem, and astronomy with Martin Hortensius. In October 1630, he had...

perspective in three ways. This is one of the equivalent forms of Pappus's (hexagon) theorem. When this happens, the nine associated points (six triangle vertices...

similar application to open the gates to the city. Pappus's hexagon theorem Pappus's centroid theorem Ptolemy's world map — It included 8,000 locations...

k-vector spaces. In these spaces, the Pappus hexagon theorem holds. Conversely, if the Pappus hexagon theorem is included in the axioms of a plane geometry...

theorem of projective geometry Projective transformation Möbius transformation Cross-ratio Duality Homogeneous coordinates Pappus's hexagon theorem Incidence...

satisfies the intersection theorem if and only if the division ring D satisfies the rational identity. Pappus's hexagon theorem holds in a desarguesian projective...

be defined over a (commutative) field. Equivalently Pappus's hexagon theorem and Desargues's theorem are supposed to be true. A large part of the results...

with the three roots of the resolvent cubic. Pappus's hexagon theorem is the special case of Pascal's theorem, when a conic degenerates to two lines. In...

Many classical theorems of algebraic geometry have counterparts in tropical geometry, including: Pappus's hexagon theorem. Bézout's theorem. The degree-genus...

with three parallel families, which has as its dual the hexagonal tiling, and the bisected hexagonal tiling is an infinite simplicial line arrangement with...

porismatibus, begins with the definitions for theorem, problem, datum, porism, and locus. Simon wrote that Pappus's definition is too general, and that he substituted...

field k. Axioms 4a and 4b are equivalent to Desargues' theorem. When Pappus's hexagon theorem holds in the affine geometry, k is commutative and hence...

geometry, where he is known for proving that Desargues' theorem is a consequence of Pappus's hexagon theorem, and differential geometry where he is known for...

Pappus 1.   Pappus of Alexandria. 2.  The Pappus configuration is the configuration of 9 lines and 9 points that occurs in Pappus's hexagon theorem....