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Artzt parabolas of a triangle

Published online by Cambridge University Press:  02 November 2015

John Sharp
John Sharp*
Affiliation:
20 The Glebe, Watford WD25 0LR, e-mail: sliceforms@yahoo.co.uk
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Type
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Information
The Mathematical Gazette , Volume 99 , Issue 546 , November 2015 , pp. 444 - 463
Copyright
Copyright © Mathematical Association 2015

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References

1. Artzt, August, Untersuchungen über ähnliche Punktreihen auf den Seiten eines Dreiecks und auf deren Mittelsenkrechten, sowie über kongruente Strahlenbüschel aus den Ecken desselben; ein Beitrag zur Geometrie des Brocardschen Kreises, Programm des Gymnasiums zu Recklinghausen 54, pp. 3–22 (1884).Google Scholar
2. Bullard, J. A., Properties of parabolas inscribed in a triangle, American Mathematical Monthly, 42 (December 1935) pp. 606–610.Google Scholar
3. Bullard, J. A., Further Properties of parabolas inscribed in a triangle, American Mathematical Monthly, 44 (June-July 1937) pp. 368–371.Google Scholar
4. Eddy, R. H. and Fritsch, R, The conics of Ludwig Kiepert: a comprehensive lesson in the geometry of the triangle. Math. Mag. 67, (1994) pp. 188–205.10.1080/0025570X.1994.11996212Google Scholar
5. Advanced Plane Geometry Group, available at http://groups.yahoo.com/AdvancedPlaneGeometry Google Scholar
6. Forum Geometricorum (2015), available at http://forumgeom.fau.edu Google Scholar
7. GeoGebra (2015), available at http://www.geogebra.org Google Scholar
8. Dorrie, H., 100 great problems of elementary mathematics, Dover (1965).Google Scholar
9. Yates, Robert C., A handbook on curves and their properties, Edwards, Ann Arbor (1947).Google Scholar
10. Lambert, Johann Heinrich, Insigniores orbitae cometarum proprietates (1761) Section I §§15–16 and Figure 3.Google Scholar
11. Heath, T. L., The works of Archimedes with the method of Archimedes, Cambridge (1897), republished by Dover (2003).Google Scholar
12. Varigié, Emile, Les progrès de la géometrié du triangle en 1890, Journal de Mathématiques Spéciales, 3rd series 15 (1891) pp. 8, 28, 56, 80.Google Scholar
13. Brocard, H., Proprietés de l’hyperbole des neuf points et de six paraboles remarkables, Journal de Mathématiques Spéciales, 2nd series 4 (1885) pp. 12, 30, 58, 76, 104, 123.Google Scholar
14. Brocard, Henri, Propriétés d’un groupe de trois paraboles, Mathesis 7 (1887). Appendix extracted from Mémoires de L’Académie de Montpellier, Section de Sciences (1886) pp. 1–8.Google Scholar
15. de Longchamps, G., Sur les paraboles de M. Artzt, Journal de Mathematiques Spéciales 3rd series 4 (1890) pp. 149–153.Google Scholar
16. Thébault, Victor, Parabolas associated with a triangle, American Mathematical Monthly, 64 (1957) pp. 10–16.Google Scholar
17. Honsberger, Ross, Mathematical morsels, Mathematical Association of America (1978) problem 91.Google Scholar
18. Lawrence, B. E., A property of a parabola inscribed in a triangle, Math. Gaz. 15 (December 1930) pp. 259–260.Google Scholar
19. Cremona, Luigi, Elements of projective geometry, Oxford University Press (1893).Google Scholar
20. Hatton, J. L. S., The principle of projective geometry applied to the straight line and the conic, Cambridge University Press (1913).Google Scholar
21. Borwein, Jonathan and Bailey, David, Mathematics by experiment, plausible reasoning in the 21st Century, CRC Press (2008).Google Scholar
22. Steiner, Jacob, Aufgaben und Lehrsätze, erstere aufzulösen, letztere zu beweisen. Geometrische Lehrsätze, Journal für die reine und angewandte Mathematik (Crelle’s Journal), Vol II (1826) p. 190.Google Scholar
23. Steiner, Jacob, Géométrie pure. Développement d’une série de théorèmes relatifs aux sections coniques, Annales de Mathématiques Pure et Appliqués 19 (1828) pp. 37, 64.Google Scholar
24. Miquel, A., Théorèmes de Géométrie, Journal de Mathématiques Pure et Appliqués, 1 (1838) pp. 485–487.Google Scholar
25. de Villiers, Michael, A variation of Miquel’s theorem and its generalisation, Math. Gaz. 98 (July 2014) p. 334.10.1017/S002555720000142XGoogle Scholar
26. Miquel, A., Memoire de Géométrie part 2, Journal de Mathématiques Pure et Appliqués, 10 (1845) pp. 347–350.Google Scholar
27. William Kingdom Clifford, A synthetic proof of Miquel’s theorem, Oxford, Dublin and Cambridge Messenger of Mathematics vol v pp. 124–141, also in his collection of mathematical papers p. 38.Google Scholar
28. Klaoudatosa, Nikos, The parabolas of Artzt in the solution of a geometric problem of minimum length, International Journal of Mathematical Education in Science and Technology, 42, Issue 2 (2011) pp. 239–245.Google Scholar