Paul Yiu
Department of Mathematical Sciences
Florida Atlantic University

Papers in Classical Euclidean Geometry

46. Lines simultaneously bisecting the perimeter and area of a triangle, (preprint).
45. (With Francisco Javier Garcia Capitan) Three mutually tangent congruent circles tangent to the sidelines of a triangle, (preprint).
44. Collinearity of the reflections of the intercepts of a line in the angle bisectors of a triangle, (preprint).
43. Iterations of sum of powers of digits, (preprint).
42. The Kariya problem and related constructions, Forum Geom., 15 (2015) 191--201.
41. Three constructions of Archimedean circles in an arbelos, Forum Geom., 14 (2014) 255--260.
40. (With Sandor N. Kiss) The touchpoints triangles and the Feuerbach hyperbolas, Forum Geom., 14 (2014) 63--86.
39. On the conic through the intercepts of the three lines through the centroid and the intercepts of a given line, Forum Geom., 13 (2013) 87--102.
38. Conic construction of a triangle from its incenter, nine-point center, and a vertex, Journal for Geometry and Graphics, 16 (2012) 171--183.
37. Geometry of sum-difference numbers, College Math. Journal, 43 (2012) 408--409.
36. Sherman's fourth side of a triangle, Forum Geom., 12 (2012) 219--225.
35. (With N. Dergiades) The golden section with a collapsible compass only, Forum Geom., 11 (2011) 255--259.
34. Rational Steiner porism, Forum Geom., 11 (2011) 237--249.
33. Polygonal triples and the double ruling of a hyperboloid, Int. J. Math. Educ. Sci. Technol., 43 (2012) 831--839.
32. The circles of Lester, Evans, Parry, and their generalization, Forum Geom., 10 (2010) 175--209.
31. (With A. P. Hatzipolakis) Reflections in triangle geometry, Forum Geom., 9 (2009) 301--348.
30. Heptagonal triangles and their companions, Forum Geom., 9 (2009) 125--148.
29. (With K. R. S. Sastry and S. Gao), Heron sequences and their modifications, Combinatorial Number Theory, pp. 199--204, de Gruyter, 2009.
28. Conic construction of a triangle from the feet of its angle bisectors, Journal for Geometry and Graphics, 12 (2008) 171--182.
27. Dynamic triangle geomety: families of lines with equal intercepts, Int. J. Comput. Math. Learning, 13 (2008) 159--170.
26. Conic solution of Euler's triangle determination problem, Journal for Geometry and Graphics, 12 (2008) 75--80.
25. (With F. M. van Lamoen) Construction of Malfatti squares, Forum Geom., 8 (2008) 49--59.
24. (With C. Pohoata) On a product of two points induced by their cevian triangles, Forum Geom., 7 (2007) 169--180.
23. Some constructions related to the Kiepert hyperbola, Forum Geom., 6 (2006) 343--357.
22. (With B. Suceava) The Feuerbach point and Euler lines, Forum Geom., 6 (2006) 191--197.
21. On Emelyanov's circle theorem, Journal for Geometry and Graphics, 9 (2005) 155--167.
20. (With M. Hoffmann) Moving central axonometric reference systems, Journal for Geometry and Graphics, 9 (2005) 133--140.
19. Elegant geometric constructions, Forum Geom., 5 (2005) 75--96.
18. Generalized Apollonian circles, Journal for Geometry and Graphics, 8 (2004) 225--230.
17. (With N. Dergiades) Antiparallels and concurrent Euler lines, Forum Geom., 4 (2004) 1--20.
16. The congruent incircle cevians of a triangle, Missouri J. Math. Sci., 15 (2003) 21--32.
15. (With D. Grinberg) The Apollonius circle as a Tucker circle, Forum Geom., 2 (2002) 175--182.
14. On the Fermat lines, Forum Geom., 3 (2003) 83--91.
13. (With F. M. van Lamoen) The Kiepert pencil of Kiepert hyperbolas, Forum Geom., 1 (2001) 125 -- 132.
12. The volume of an isosceles tetrahedron and the Euler line, Mathematics and Informatics Quarterly, 11 (2001) 15 -- 19.
11. (With A. P. Hatzipolakis) Pedal triangles and their shadows, Forum Geom., 1 (2001) 81--90.
10. (With A. P. Hatzipolakis) The Lucas circles of a triangle, Amer. Math. Monthly, 108 (2001) 444--446.
9. (With A. P. Hatzipolakis, F. M. van Lamoen, and B. Wolk) Concurrency of four Euler lines, Forum Geom., 1 (2001) 59--68.
8. Heronian triangles are lattice triangles, Amer. Math. Monthly, 108 (2001) 261--263.
7. The length of x_1^4+x_2^4+x_3^4+x_4^4 as a sum of squares, Journal of Pure and Applied Algebra, 156 (2001) 367--373.
6. The uses of homogeneous barycentric coordinates in plane euclidean geometry, Int. J. Math. Educ. Sci. Technol., 31 (2000) 569--578.
5. Mixtilinear incircles, Amer. Math. Monthly, 106 (1999) 952--955.
4. (With C. Dodge, T. Schoch, and P. Woo) Those ubitiquous Archimedean circles, Math. Mag., 72 (1999) 202--213.
3. Construction of indecomposable Heronian triangles, Rocky Mountain Journal of Mathematics, 28 (1998) 1189--1202.
2. Isosceles triangles equal in perimeter and area, Missouri J. Math. Sci., 10 (1998) 106--111.
1. Heronian triangles with associated inradii in arithmetic progression, Crux Math., 23 (1997) 146--149.

Course Notes

Notes on Euclidean Geometry, 1998
Elementary Mathematical Works of Leonhard Euler, 1999
Introduction to the Geometry of the Triangle, 2001 (with corrections 2013)
Recreational Mathematics, 2003
Algebraic Topology, 2006
Number Theory, 2007

Lectures

A tour of Triangle Geometry via the Geometer's Sketchpad, 2004
A short tour of Triangle Geometry around the nine-point circle, 2007
Regular heptagon by angle trisection and other constructions, 2007
Heron triangles which cannot be decomposed into two integer right triangles, 2008
The circles of Lester, Evans, Parry, and their generalizations, 2008
Heptagonal triangles and their companions, 2009

Last update: October 20, 2015.