References in 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://web.archive.org/web/20231003013612/https://jl.ayme.pagesperso-orange.fr/index.html vol. 4 

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

http://web.archive.org/web/20231003013612/https://jl.ayme.pagesperso-orange.fr/index.html vol. 6

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

http://web.archive.org/web/20231003013612/https://jl.ayme.pagesperso-orange.fr/index.html vol. 8

* Page 11 Synthetical proof midcircles are concurrent

[2d] Jean-Louis Ayme, ”LA CHAÎNE INACHEVÉE DE WILLIAM KINGDON CLIFFORD” , no longer available at the web.

[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 (204) 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/…/forum-geometricorum-all-volumes.pdf
• 2001–2019 — https://garciacapitan.blogspot.com/…/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

https://garciacapitan.epizy.com/baricentricas/?i=1

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

This former Yahoo-forum was closed at December 2019.

1. 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:

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

[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

[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/ (QL-P1, QA-P2, QA-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
Alternative link: https://studylibde.com/doc/1096915/ein-merkwürdiger-punkt-des-vierecks-1

[17] Bernard Gibert – personal homepage:
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 the isoptic (or Bennett) point of a quadrangle.

[19] Michael Fox, Constructions for Sketchpad
Available at: 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: Fachportal Pädagogik

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

Available at: Download PDF

[25] J.L. Coolidge, 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: chrisvantienhoven.nl

[27] Olga Radko and Emmanuel Tsukerman – The perpendicular bisector construction, isoptic point and Simson line

Forum Geometricorum, Volume 12 (2012), pp. 161–189.
Available at: forumgeom.fau.edu

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, Vol. 16, No. 1/4 (1914–1915), pp. 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), pp. 289–295
Available at: forumgeom.fau.edu

Dee note at [4].

[31] J.W. Clawson, More theorems on the Complete Quadrilateral – American Mathematical Monthly, Vol. 23, No. 1 (Sep. 1921), pp. 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), pp. 201–204
Available at: Download PDF

See note at [4].

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

This former Yahoo-forum was closed in December 2019.
Unfortunately there is no more online program for viewing messages.

[34] Quadri-Figures-Group, Internet forum for discussions on topics related to Quadrilaterals, Quadrangles, etc.
This former Yahoo-forum was closed in 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:
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[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

[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/…/BSMA_1879_2_3_1_136_1.pdf

[39] M. Victor Thébault, Sur le quadrilatère complet, C. R. Acad. Sci., Paris 217 (1943), 97–99.
Available at: http://gallica.bnf.fr/ark:/12148/bpt6k31698/f97.image

[40] J.W. Clawson, An Inversion of the Complete Quadrilateral – Amer. Math. Monthly, 24(2), (1917), 71–73.
Available at: http://www.jstor.org/stable/2972702

[41] Martin Josefsson, Characterizations of Trapezoids, Forum Geometricorum 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 (met Günter Pickert).
English version: R. Fritsch & G. Pickert, The Seebach–Walser Line of a Quadrangle, CRUX Math. 39-4/2014, 178–184.

[45] M. Léon Ripert, Notes sur le quadrilatère.
Available at: https://archive.org/stream/…#page/n114/mode/2up

[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/…/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/…/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/…/1500618-2.pdf

[50] Advanced Plane Geometry, an Internet forum for discussions on Advanced Plane Geometry. This former Yahoo-forum was closed in 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:
http://garciacapitan.blogspot.com/2020/12/links-related-to-triangle-geometry.html

[51] M. Chasles, Annales De Mathématique 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] Ángel Montesdeoca – Apuntes de Geometría Proyectiva: Cónicas y Cuádricas.
Available at: http://amontes.webs.ull.es/apuntes/gdh.pdf

[55] R. Goormaghtigh, The Hervey Point on the general n-Line, Amer. Math. Monthly 54 (1947), 327–331.
Available at: https://www.jstor.org/stable/2305206

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

[57] R.K. Guy – The Lighthouse Theorem, Morley & Malfatti: A Budget of Paradoxes, Amer. Math. Monthly 114(2), 97–141 (2007).
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), 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 – Gesammelte Werke, vol. I. Aufgabe aus Gergonne’s Annales de Math. XVII, p. 284.
Available at: https://books.google.nl/…id=6Y-HAAAAQBAJ

[62] Mathcurve – ENCYCLOPÉDIE DES FORMES MATHÉMATIQUES REMARQUABLES, subpage: Anallagmatic Curve.
Available at: https://www.mathcurve.com/…/anallagmatic.shtml

[63] Roger Cuppens – Faire de la Géométrie 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 Cubics. Cambridge & Dublin Math. Journal 6 (1851), 181–182.

[65] Math Forum – “Naming Polygons and Polyhedra”.
Available at: http://mathforum.org/dr.math/faq/faq.polygon.names.html

[66] Quadri-and-Poly-Geometry (QPG), Internet forum on Quadrilateral & Polygon Geometry.
Available at: https://groups.io/g/Quadri-and-Poly-Geometry

[67] Sandor Nagydobai Kiss – On the Wittenbauer Type Parallelograms. Int. J. of Geometry 4 (2015), No.1, 27–36.
Available at: https://ijgeometry.com/…/4.pdf

[68] Dario Pellegrinetti – The Six-Point Circle for the Quadrangle. Int. J. of Geometry 8 (2019), No. 2, 5–13.
Available at: https://ijgeometry.com/…/5-13a.pdf

[69] Qingchun Ren, Jürgen Richter-Gebert & Bernd Sturmfels – Cayley–Bacharach Formulas, The American Mathematical Monthly 122:9 (2015), 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 25(1) (2021), 53–59.
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

[75] Michela Artebani and Igor Dolgachev – The Hesse Pencil of Plane Cubic Curves.
Available at: https://dept.math.lsa.umich.edu/~idolga/hesserev.pdf
and at: https://arxiv.org/abs/math/0611590

[76] Araceli Bonifant and John Milnor – On Real and Complex Cubic Curves
Available at: https://arxiv.org/pdf/1603.09018

[77] Fred Lang – Geometry and Group Structures of Some Cubics, published in Forum Geometricorum, Vol. 2 (2002).
Available at: https://www.researchgate.net/publication/251442938_Geometry_and_Group_Structures_of_Some_Cubics

[78] Thomas Cotterill – A Geometrical Property of Curves of the third Order. The Cambridge and Dublin Mathematical Journal Vol VII, p.14, 1851

[79] Will Traves and David Wehlau – Ten Points on a Cubic
Available at: https://arxiv.org/format/2105.12058

[80] Ewalina Nawara – The Hesse pencil of plane curves and osculating conics
Available at: https://arxiv.org/pdf/2506.04662

[81] J. de Vries, On polar figures with respect to a plane cubic curve
Available at: https://dwc.knaw.nl/DL/publications/PU00013494.pdf

[82] Heinrich Edward Schroeter – Die theorie der ebenen Kurven dritter Ordnung
Available at: https://ia600208.us.archive.org/28/items/dietheoriedereb01schrgoog/dietheoriedereb01schrgoog.pdf

[83] Henry Martyn Cundy and Cyril Frederick Parry, Some cubic curves associated with a triangle, Journal of geometry Vol. 53 (1995)

[84] H. Durège – Die ebenen Kurven dritter Ordnung, Eine Zusammenstellung ihrer bekannteren Eigenschaften (1871)
Available at: https://books.googleusercontent.com/books/content?req=AKW5QadZJnnAZ1Q–GNev9S6DvyGHm1TZGh2nlnCC3EkwNxnSxeqcfsDDsBtlT31–HkqD-fobGre7i_wlTFXCxNBdrogh2l0wZxMg0DD3ZZUsC919qcy7s7Wu_DqIxTl6QHNwgugZ4uKcx_A0zn3fxy1wDoaaoWKmUZ8DD0VnCmVbrRIbJkYKds2o1g7sSgI8rf7tOhTzPzw2sHoTnK5FKjS_HnL01x_B_yLTTiUOQSgue_nN19FgonXKL4I26_vQzeqNSRb03sMyroQe0gEUzHHUoJUk2Rpg

x

x

[85] Hilton – Plane Algebraic Curves
Available at: https://jasoncantarella.com/downloads/hilton_plane_algebraic_curves.pdf

Chris van Tienhoven,

e-mail: van10hoven@gmail.com

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