_____________________________

References in EQF/EPG

[1] Brianchon C. J., Poncelet J.-V.,Recherche sur la détermination d'une hyperbole équilatère au moyende quatre conditions données,

Annales Mathématiques de 1821

* Page 512 about Euler Circles.

[2a] Jean-Louis Ayme, La droite de Gauss et la droite de Steiner, available at

http://perso.orange.fr/jl.ayme vol. 4 La droite de Gauss et la droite de Steiner.

[2b] Jean-Louis Ayme, Le point de Kantor-Hervey, available at

http://perso.orange.fr/jl.ayme vol. 6 Le point de Kantor-Hervey.

[2c] Jean-Louis Ayme, Le Point- d’Euler-Poncelet d‘un Quadrilatère, available at

http://perso.orange.fr/jl.ayme vol. 8 Le point d’Euler-Poncelet d’un quadrilatère.

* Page 11 Synthetical proof midcircles are concurrent

[2d] Jean-Louis Ayme, ''LA CHAÎNE INACHEVÉE DE WILLIAM KINGDON CLIFFORD” , available at

http://jl.ayme.pagesperso-orange.fr/Docs/Etude%204.pdf

[3] Jean-Louis Ayme: “Méthodes et techniques en géométrie: A propos de la droite de Newton”.

[4] Jean Pierre Ehrmann - Steiner’s Theorems on the Complete Quadrilateral, Forum Geometricorum 4 (2004) 35-52,

available at: http://forumgeom.fau.edu/FG2004volume4/index.html

Note: Since 2024 the official site of Forum Geometricorum was closed.
Copies can now be found at:
2001-2009 https://mathematicalolympiads.wordpress.com/wp-content/uploads/2012/08/forum-geometricorum-all-volumes.pdf

2001-2019 https://garciacapitan.blogspot.com/2020/12/links-related-to-triangle-geometry.html

[5] Alexei Myakishev - On Two Remarkable Lines related to a Quadrilateral, Forum Geometricorum 6 (2006) 289-295

available at: http://forumgeom.fau.edu/FG2006volume6/index.html

See note at [4].

[6] Alain Levelut – A note on the Hervey Point of a complete Quadrilateral, Forum Geometricorum 11 (2011) 1-7

available at: http://forumgeom.fau.edu/FG2011volume11/FG2011index.html

See note at [4].

[7] Heinrich Dörrie: "100 great problems of Elementary Mathematics"

* Page 213 about “A hyperbola from four points”.

* Page 231 about “The most nearly Circular Ellipse Circumscribing a Quadrilateral”

* Page 265 about “Desargues’ Involution Theorem”.

[8] Dick Klingens, Vlakke Meetkunde, available at

http://www.pandd.demon.nl/

* Stelling van Poncelet-Brianchon

* Euler Cirkels (mentioning of Euler point)

* Aubel, Stelling van Van,

* Tien niet zo bekende eigenschappen van (koorden)vierhoeken

[9] Alexander Bogomolny – Cut The Knot! – The complete Quadrilateral

* Morley Point: http://www.cut-the-knot.org/ctk/CompleteQuadrilateral.shtml#Morley

* Isogonal Center: http://www.cut-the-knot.org/Curriculum/Geometry/PerpBisectQuadri.shtml#explanation

* Miquel Point and similarity: http://www.cut-the-knot.org/Curriculum/Geometry/SpiralSim.shtml

[10] Francisco Javier García Capitán, Baricentricas.

Description and Notebook on barycentric algebraic formulas, available at

http://garciacapitan.epizy.com/baricentricas/

[11] Hyacinthos, Internet forum for discussion on Triangle Geometry.

1. This former Yahoo-forum was closed at December 2019.

The archive is available at: www.hyacinthos.epizy.com

You can go to a specific message with number nnnn by typing: www.hyacinthos.epizy.com/message.php?msg=nnnn

You can go to a specific topic with number tttt by typing: www.hyacinthos.epizy.com/message.php?topic=tttt

2. A file with all messages can be downloaded at this page:

http://garciacapitan.blogspot.com/2020/12/links-related-to-triangle-geometry.html

There also was a Yahoo-forum named Anopolis. This forum also was closed December 2019.
Unfortunately there is no more online program for viewing messages. However many of the Anopolis-messages also were placed in Hyacinthos, but not all of them.

[12] C. Kimberling, Encyclopedia of Triangle Centers, available at

http://faculty.evansville.edu/ck6/encyclopedia/ETC.html.

[13] Weisstein, Eric W., MathWorld--A Wolfram Web Resource , available at

http://mathworld.wolfram.com

* Anallagmatic Curve

* Anticenter

* Bimedian

* Circular points at infinity

* (Complete) Quadrangle

* (Complete) Quadrilateral

* Crossdifference

* Cyclocevian Conjugate

* Euler Triangle

* Gauss-Bodenmiller Theorem

* First/Second/Third Morley Triangle

* Harmonic Conjugate

* Isoconjugation

* Isotomic Transversal

* Miquel's Pentagram Theorem

* Nine-point Circle
* Orthologic Triangles

* Orthopole

* Petr-Neumann-Douglas Theorem

* Pivotal Isocubic

* Pivotal Isogonal cubic

* Polar

* Trilinear Pole

* Trilinear Polar

* Van Aubel's Theorem

* Wittenbauer's Parallelogram

[14] Philippe Chevanne, Mad Maths, Recreational mathematic collection, available at

* Construction of a parabola:http://mathafou.free.fr/themes_en/parabole2.html

* Problem equidistance lines: http://mathafou.free.fr/pbg_en/pb127.html

* Problem inscribed and circumscribed squares: http://mathafou.free.fr/pbg_en/pb122.html

[15] Eckart Schmidt

[15a] 05-4 Ein weiterer merkwürdiger Viereckspunkt:

http://eckartschmidt.de/ZPunkt.pdf (QA-P3)

[15b] 05-6 Geometrie auf der ZirkularKurve:

http://eckartschmidt.de/Zirkul..pdf (Cubic QA-Cu1)

[15c] 07-1 Das Steiner Dreieck von vier Punkten:

http://eckartschmidt.de/DiaSte.pdf (Cubic QA-Cu1)

[15d] 04-5 Vierecksbezogene Inversionen:

http://eckartschmidt.de/STEIN.pdf (QL-Tf1: Clawson-Schmidt Conjugate)

[15e] 11-1 Die Brennpunktkurve eines Vierecks:

http://eckartschmidt.de/Focus.pdf (QL-Cu1: QL-Quasi Isog. Cubic)

[15f] 11-3 Miquel-, Poncelet- und Bennett-Punkt eines Vierecks:

http://eckartschmidt.de/Pktve.pdf (QL-P1/-P2/-P4)

[15g] 08-6 Miquel Points and Inscribed Triangles:

http://eckartschmidt.de/ (QA-P23)

[15h] 11-2 Parallelogramme eines Vierecks:

http://eckartschmidt.de/ (QA-P23)

[15i] 04-3 Euler-Gerade eines Vierecks:

http://eckartschmidt.de/ (QG-L4)

[16] Daniel Baumgartner, Roland Stärk, Ein merkwürdiger Punkt des Vierecks, available at

http://geometria.ch/geometrie/empdv.pdf

https://studylibde.com/doc/1096915/ein-merkw%C3%BCrdiger-punkt-des-vierecks-1

[17] Bernard Gibert, http://bernard-gibert.fr/index.html

[17a] Points and Mappings:

http://bernard-gibert.fr/gloss/pointsandmapping.html

[17b] Jean-Pierre Ehrmann and Bernard Gibert,

Special Isocubics in the Triangle Plane, available at:

http://bernard-gibert.fr/files/isocubics.html

[17c] Note on Circular Isocubics,

http://bernard-gibert.fr/gloss/circularcubics.html

[17d] Inscribed Cardioids and Eckart Cubics,

http://bernard-gibert.fr/files/cardioids.html

[18] H.M. Cundy and C.F. Parry,

Geometrical properties of some Euler and circular cubics. Part 2.

Journal of Geometry 68, 2000,

p.63 on isoptic (or Bennett) point of a quadrangle

[19] Michael Fox, Constructions for Sketchpad

http://mysite.mweb.co.za/residents/profmd/constructions.pdf

[20] P.S. Modenow and A.S. Parkmohenko,
Geometric Transformations, Volume 2: Projective Transformations

p.24 Two fundamental Theorems on Projective Transformations

[21] Jim Loy, Jim Loy's Mathematics Page

* Inscribing a Square in a Quadrilateral: http://www.jimloy.com/geometry/inscribe.htm

[22] J.W. Clawson, The complete Quadrilateral – American Mathematical Monthly, Volume 20 (1919) pages 232-262,

available at: http://www.jstor.org/stable/1967118

[23] Eckart Schmidt, Mittelsenkrechtenvierecke eines Vierecks, PM 2/44 (Jg. 2002), S. 84-87

available at: http://www.fachportal-paedagogik.de/fis_bildung/suche/fis_set.html?FId=617395

[24] Lang Fred, The pedal circle center transformation. – July 9, 2007.

available at: http://home.citycable.ch/langfamille/PagesWEB/PedalCircleCenterTransformation.pdf

[25] J.L. Coolidge, Harvard University, Two geometrical applications of the method of least squares,

available at: http://www.jstor.org/stable/2973072

[26] Chris van Tienhoven, Perspective Fields,

[26a] Perspective Fields part I

[26b] Perspective Fields part II

available at: http://www.chrisvantienhoven.nl/index.php/mathematics/perspective-fields.

[27] Olga Radko and Emmanuel Tsukerman - The perpendicular bisector construction, isoptic point and Simson line, 161—189,

Forum Geometricorum, Volume 12 (2012),

available at http://forumgeom.fau.edu/FG2012volume12/FG2012index.html

See note at [4].

[28] A.V. Akopyan, A.A. Zaslavski, Geometry of Conics, American Mathematical Society. ISBN 978-08218-4323-9

[29] C.M. Herbert, The inscribed and Circumscribed Squares of a Quadrilateral and Their Significance in Kinematic Geometry – Annals of Mathematics, Second Series, Vol. 16, No 1/4 (1914 – 1915), pages 38-42,

available at: http://www.jstor.org/stable/1968039

[30] Alexei Myakishev, On two remarkable lines related to a quadrilateral, Forum Geometricorum, 6 (2006) 289--295.

available at http://forumgeom.fau.edu/FG2006volume6/FG200634index.html

See note at [4].

[31] J.W. Clawson, More theorems on the Complete Quadrilateral – American Mathematical Monthly, Volume 23, No. 1 (Sep., 1921) pages 40-44,

available at: http://www.jstor.org/stable/1967780

[32] Eisso J. Atzema - An Elementary Proof of a Theorem by Emelyanov, Forum Geometricorum 8 (2008) 201-204

available at: http://forumgeom.fau.edu/FG2008volume8/FG200829.pdf

See note at [4].

[33] Anopolis, Internet forum for discussions on Elementary Geometry,

This former Yahoo-forum was closed at December 2019.

Unfortunately there is no more online program for viewing messages.

However many of the Anopolis-messages also were placed in Hyacinthos (see [11]), but not all of them.

[34] Quadri-Figures-Group, Internet forum for discussions on topics related to Quadrilaterals, Quadrangles, etc.

This former Yahoo-forum was closed at December 2019.

1. The archive is available at: https://groups.io/g/Quadri-Figures-Group

When you are looking for a QFG-message with a specific number (e.g. #255), then use the Search option with keyword “Message: 255” and you will be directed to the right message.

2. Also available at: www.qfg.epizy.com

You can go to a specific message with number nnnn by typing:
www.qfg.epizy.com/message.php?msg=nnnn

You can go to a specific topic with number tttt by typing:
www.qfg.epizy.com/message.php?topic=tttt

[35] Wikipedia, The Free Encyclopedia, about the Möbius Transformation.

Available at: http://en.wikipedia.org/wiki/M%C3%B6bius_transformation

[35b] Wikipedia, The free Encyclopedia, about the Petr-Douglas-Neumann Theorem.

Available at: https://en.wikipedia.org/wiki/Petr%E2%80%93Douglas%E2%80%93Neumann_theorem

[36]Benedetto Scimemi, Central Points of the Complete Quadrangle - Milan. J. Math., 75 (2007) 333–356.

Available at: http://link.springer.com/article/10.1007%2Fs00032-007-0076-6

[37] F. Morley, Extensions of Clifford’s Chain-Theorem, Amer J Math, 51 (1929) 465-472.

Available at: http://www.jstor.org/discover/10.2307/2370734?uid=3738736&uid=2&uid=4&sid=21102545290233

[38] S. Kantor,Quelques théorèmes nouveaux sur l’hypocycloïde à trois rebroussements,

Bulletin des sciences mathématiques et astronomiques (1879).

Available at : http://archive.numdam.org/ARCHIVE/BSMA/BSMA_1879_2_3_1/BSMA_1879_2_3_1_136_1/BSMA_1879_2_3_1_136_1.pdf

[39]M. Victor Thébault, Sur le quadrilatere complet, C. R. Acad. Sci., Paris 217, 97-99 (1943),

Available at: http://gallica.bnf.fr/ark :/12148/bpt6k31698/f97.image

[40] J.W. Clawson, An Inversion of the complete Quadrilateral – American Mathematical Monthly, Volume 24, No 2 (Feb., 1917) pages 71-73,

available at: http://www.jstor.org/stable/2972702

[41] Martin Josefsson - Characterizations of Trapezoids, Forum Geometricorum Volume 13 (2013) 23–35.

available at http://forumgeom.fau.edu/FG2013volume13/FG201305.pdf

See note at [4].

[42] Darij Grinberg,Poncelet points and antigonal conjugates,

available at: http://www.mathlinks.ro/Forum/viewtopic.php?t=109112.

[43] Bernard Keizer,La Géométrie du Quadrilatère Complet.

available at http://bernardkeizer.blogspot.fr/

[44] Schwerpunkte von Vierecken (I),Wurzel 48-2/2014, 35-41 (mit Günter Pickert)

English Version: Rudolf Fritsch and Guenter Pickert, The Seebach-Walser Line of a Quadrangle.

CRUX Mathematicorum 39-4/2014, 178-184

[45] M. Léon Ripert, Notes sur le quadrilatère, available at:

https://archive.org/stream/compterenduvolu03sciegoog#page/n114/mode/2up

(pages 106-118)

[46] H.V. Mallison, Pedal Circles and the Quadrangle.

Math. Gazette 42 (1958), 17-20,

available at: http://www.jstor.org/discover/10.2307/3608347

[47]F. Morley, On Reflexive Geometry, Trans Amer Math Soc, 8 (1907) 14-24

available at:

http://www.ams.org/journals/tran/1907-008-01/S0002-9947-1907-1500771-4/S0002-9947-1907-1500771-4.pdf

[48]F. Morley, On the Metric Geometry of the N-Line, Trans Amer Math Soc, 1 (1900) 97-115

available at:

http://www.ams.org/journals/tran/1900-001-02/S0002-9947-1900-1500528-8/S0002-9947-1900-1500528-8.pdf

[49]F. Morley, Orthocentric properties of the plane n-Line, Trans Amer Math Soc, 4 (1903) 1-12

available at:

http://www.ams.org/journals/tran/1903-004-01/S0002-9947-1903-1500618-2/S0002-9947-1903-1500618-2.pdf

[50] Advanced Plane Geometry, an Internet forum for discussions on Advanced Plane Geometry,

This former Yahoo-forum was closed at December 2019.

1. The archive is available at: www.adgeom.epizy.com

You can go to a specific message with number nnnn by typing:
www.adgeom.epizy.com/message.php?msg=nnnn

You can go to a specific topic with number tttt by typing:
www.adgeom.epizy.com/message.php?topic=tttt

2. A file with all messages can be downloaded at this page:

http://garciacapitan.blogspot.com/2020/12/links-related-to-triangle-geometry.html

[51] M. Chasles, Annales De Mathematique 18 (1827-1828), p.297,

available at: http://www.numdam.org/item?id=AMPA_1827-1828__18__277_0

[52] Paris Pamfilos, Gallery Geometrikon,

The item “All rectangular hyperbolas tangent to four lines”

Available at: http://www.math.uoc.gr/~pamfilos/eGallery/problems/RectHyperbolasTangent4Lines.html

[53] H.S.M. Coxeter - The Real Projective Plane. Springer-Verlag, 1993

[54] Angel Montesdeoca - Apuntes de Geometrıa Proyectiva Conicas y Cuadricas

Available at: http://amontes.webs.ull.es/apuntes/gdh.pdf

[55] Goormaghtigh, R., The Hervey Point on the general n-Line, The American Mathematical Monthly, Vol. 54, No. 6 (Jun. - Jul., 1947), pp. 327-331,

available at: https://www.jstor.org/stable/2305206?seq=1#page_scan_tab_contents

[56] Edward C. Phillips, On the Pentacardioid, University of Michigan, 1909.

[57] Guy, R. K.. (2007). The Lighthouse Theorem, Morley & Malfatti: A Budget of Paradoxes. The American Mathematical Monthly, 114(2), 97–141.

Available at: http://www.jstor.org/stable/27642143

[58] Clark Kimberling, "Hofstadter points", Nieuw Archief voor Wiskunde 12 (1994) 109-114.

[59] Art of Problem Solving (AoPS), an Internet forum for High School Olympiads.
Available at: https://artofproblemsolving.com/community/c6_high_school_olympiads

[59a] Vu Thunh Tang - 4 Orthotransversals are concurrent

Available at: https://artofproblemsolving.com/community/c6h1106953p5076972

[59b] Vu Thunh Tang - Points of Concurrent orthotransversals Problem

Available at: https://artofproblemsolving.com/community/c6h1112485p5079962

[59c] Telv Cohl – Radical center of Five circles

Available at: https://artofproblemsolving.com/community/c6h1813119p12086815

[60] Rolinek, Michal & Anh Dung, Le. The Miquel points, pseudocircumcenter, and Euler-Poncelet point of a complete quadrilateral. Forum Geometricorum, 14 (2014) 145--153.
Available at: http://forumgeom.fau.edu/FG2014volume14/FG201413.pdf

See note at [4].

[61] Jacob Steiner, Jacob Steiner’s Gesammelte Werke, vol. I.
Auflösung einer geometrischen Aufgabe aus Gergonne’s Annales de Mathem. t. XVII, p. 284.

Available at: https://books.google.nl/books?id=6Y-HAAAAQBAJ&pg=PR5&lpg=PR5&dq=Steiner+gesammelte+werken&source=bl&ots=NxyXryFrB_&sig=ACfU3U3QFUdHS7SxncmGTovQqQcP_cIp4w&hl=nl&sa=X&ved=2ahUKEwiz34Gql6bhAhWMPFAKHW7VB9gQ6AEwB3oECAkQAQ#v=onepage&q=ellipse&f=false, page 123.

[62] Mathcurve, ENCYCLOPÉDIE DES FORMES MATHÉMATIQUES REMARQUABLES, subpage: Anallagmatic Curve

Available at: https://www.mathcurve.com/courbes2d.gb/anallagmatic/anallagmatic.shtml

[63] Roger Cuppens, Faire de la Géomètrie supérieure en jouant avec Cabri-Géomètre II, Tome II

APMEP Brochure no 125, ISBN: 2-912846-38-2

[64] A.S. Hart - Construction by the Ruler alone to determine the ninth Point of Intersection of two Curves of the third Degree. Cambridge and Dublin Mathematical Journal 6 (1851) 181-182.

[65] Math Forum, about “Naming Polygons and Polyhedra”

Available at: http://mathforum.org/dr.math/faq/faq.polygon.names.html

[66] Quadri-and-Poly-Geometry (QPG), Internet forum for discussions on topics related to the Geometry of Quadrilaterals & Polygons,

Available at: https://groups.io/g/Quadri-and-Poly-Geometry

[67] Sandor Nagydobai Kiss, On the Wittenbauer Type Parallelograms, INTERNATIONAL JOURNAL OF GEOMETRY, Vol. 4 (2015), No. 1, 27 – 36

Available at: https://ijgeometry.com/wp-content/uploads/2015/03/4.pdf

[68] Dario Pellegrinetti, The six-point circle for the quadrangle, INTERNATIONAL JOURNAL OF GEOMETRY, Vol. 8 (2019), No. 2, 5 – 13

Available at: https://ijgeometry.com/wp-content/uploads/2019/09/5-13a.pdf

[69] Qingchun Ren, Jürgen Richter-Gebert & Bernd Sturmfels (2015) Cayley–Bacharach Formulas, The American Mathematical Monthly, 122:9, 845-854, DOI: 10.4169

Available at: https://arxiv.org/pdf/1405.6438v2.pdf

[70] Tran Quang Hung - Some new theorems on Pentagon and Pentagram,

Available at: https://arxiv.org/abs/1908.00974

[71] Cabri Geometry - Solution of a difficult problem: the Quartic page

Available at: http://www.cabri.net/cabri2/Quartic.html

[72] Euclid, Internet forum for discussions on topics related to Triangles

Available at: https://groups.io/g/Euclid

[73] Chris van Tienhoven, Dario Pellegrinetti - Quadrigon Geometry: Circumscribed Squares and Van Aubel Point, Journal for Geometry and Graphics, Volume 25 (2021), No. 1, 053—059

Available at: https://www.heldermann.de/JGG/JGG25/JGG251/jgg25005.htm

[74] Michael de Villiers - Van Aubel's Theorem and some Generalizations

Available at: http://dynamicmathematicslearning.com/aubelparm.html

Chris van Tienhoven,

e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

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