Pascal's theorem
In projective geometry, Pascal's theorem (also known as the hexagrammum mysticum theorem) states that if six arbitrary points are chosen on a conic (which may be an ellipse, parabola or hyperbola in an appropriate affine plane) and joined by line segments in any order to form a hexagon, then the three pairs of opposite sides of the hexagon (extended if necessary) meet at three points which lie on a straight line, called the Pascal line of the hexagon. It is named after Blaise Pascal.
- Abstraction100002137
- Attribute100024264
- Communication100033020
- ConicSection113872975
- Figure113862780
- Message106598915
- PlaneFigure113863186
- Proposition106750804
- Shape100027807
- Statement106722453
- Theorem106752293
- WikicatConicSections
- WikicatMathematicalTheorems
- WikicatTheorems
- WikicatTheoremsInGeometry
- WikicatTheoremsInProjectiveGeometry
- Comment
- enIn projective geometry, Pascal's theorem (also known as the hexagrammum mysticum theorem) states that if six arbitrary points are chosen on a conic (which may be an ellipse, parabola or hyperbola in an appropriate affine plane) and joined by line segments in any order to form a hexagon, then the three pairs of opposite sides of the hexagon (extended if necessary) meet at three points which lie on a straight line, called the Pascal line of the hexagon. It is named after Blaise Pascal.
- Depiction
- First
- enA.S.
- enP.S.
- Has abstract
- enIn projective geometry, Pascal's theorem (also known as the hexagrammum mysticum theorem) states that if six arbitrary points are chosen on a conic (which may be an ellipse, parabola or hyperbola in an appropriate affine plane) and joined by line segments in any order to form a hexagon, then the three pairs of opposite sides of the hexagon (extended if necessary) meet at three points which lie on a straight line, called the Pascal line of the hexagon. It is named after Blaise Pascal. The theorem is also valid in the Euclidean plane, but the statement needs to be adjusted to deal with the special 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 of two lines with three points on each line.
- Is primary topic of
- Pascal's theorem
- Label
- enPascal's theorem
- Last
- enModenov
- enParkhomenko
- Link from a Wikipage to an external page
- books.google.com/books%3Fid=awAfO7Ff_z0C&q=smith+source+book
- www.mathematik.tu-darmstadt.de/~ehartmann/circlegeom.pdf
- citeseerx.ist.psu.edu/viewdoc/download%3Fdoi=10.1.1.665.5892&rep=rep1&type=pdf
- digitale-sammlungen.gwlb.de/index.php%3Fid=6&no_cache=1&tx_dlf%5Bid%5D=548&tx_dlf%5Bpage%5D=19&cHash=7c32039131e4b3387740fbc6c9fd1cb8
- archive.today/20121129152851/http:/www.math.uregina.ca/~fisher/Norma/paper.html
- www.cut-the-knot.org/Curriculum/Geometry/Pascal.shtml
- www.cut-the-knot.org/Curriculum/Geometry/PascalLines.shtml
- archive.org/details/penguindictionar0000well
- www.ias.ac.in/mathsci/vol120/nov2010/pm-10-00024.PDF
- Link from a Wikipage to another Wikipage
- Affine plane
- American Mathematical Monthly
- August Ferdinand Möbius
- Bézout's theorem
- Blaise Pascal
- Braikenridge–Maclaurin construction
- Braikenridge–Maclaurin theorem
- Brianchon's theorem
- Broadside (printing)
- Bulletin of the London Mathematical Society
- Category:Articles containing proofs
- Category:Blaise Pascal
- Category:Conic sections
- Category:Euclidean plane geometry
- Category:Theorems about polygons
- Category:Theorems in projective geometry
- Cayley–Bacharach theorem
- Colin Maclaurin
- Conic section
- Cut-the-knot
- Dandelin spheres
- Degenerate conic
- Desargues's theorem
- Desargues' theorem
- Edge (geometry)
- Ellipse
- Euclidean plane
- Extended side
- File:Pascal'sTheoremLetteredColored.PNG
- File:Pascal-3456.png
- File:Pascaltheoremgenericwithlabels.svg
- File:THPascal.svg
- Five points determine a conic
- Gergonne triangle
- Germinal Pierre Dandelin
- Hexagon
- Hyperbola
- Isogonal conjugate
- Law of sines
- Line at infinity
- Mathematical Association of America
- Menelaus' theorem
- Pappus's hexagon theorem
- Parabola
- Polar reciprocation
- Pole and polar
- Projective configuration
- Projective dual
- Projective geometry
- Projective plane
- Similarity (geometry)
- Synthetic geometry
- The Mathematical Intelligencer
- Thomas Kirkman
- Unicursal hexagram
- William Braikenridge
- SameAs
- 53gW6
- m.033w0s
- Pascal's theorem
- Pascalin lause
- Pascal-tétel
- Q899002
- Satz von Pascal
- Stelling van Pascal
- Teorema de Pascal
- Teorema de Pascal
- Teorema de Pascal
- Teorema de Pascal
- Teorema di Pascal
- Theorema Pascalium
- Théorème de Pascal
- Twierdzenie Pascala
- Định lý Pascal
- Теорема Паскаля
- Теорема Паскаля
- Պասկալի թեորեմ
- משפט פסקל
- شش ضلعی عرفانی
- شەشلای عیرفانی
- مبرهنة باسكال
- パスカルの定理
- 帕斯卡定理
- 파스칼의 정리
- Subject
- Category:Articles containing proofs
- Category:Blaise Pascal
- Category:Conic sections
- Category:Euclidean plane geometry
- Category:Theorems about polygons
- Category:Theorems in projective geometry
- Thumbnail
- Title
- enPascal theorem
- WasDerivedFrom
- Pascal's theorem?oldid=1118194566&ns=0
- WikiPageLength
- 17699
- Wikipage page ID
- 699966
- Wikipage revision ID
- 1118194566
- WikiPageUsesTemplate
- Template:=
- Template:Blaise Pascal
- Template:Citation
- Template:Cite web
- Template:Commons category
- Template:Eom
- Template:Harv
- Template:Harvtxt
- Template:Math
- Template:Reflist
- Template:Short description
