Paul Yiu
Department of Mathematics
Florida Atlantic University


An Introduction to the Geometry of the Triangle, 2001 [ps file][pdf]
Notes on Euclidean Geometry, 1998
Elementary Mathematical Works of Leonhard Euler, 1999 [ps file][pdf]
                 with a chronologial listing of Euler's works [ps file][pdf]
Recreational Mathematics, 2003

Number Theory, 2007


A Tour of Triangle Geometry, February 2004
A Short Tour of Triangle Geometry Around the Nine-point Circle (GSP), April 2007
Regular Heptagon by Angle Trisection and Other Constructions [ps][pdf], April 2007
Heron triangles which cannot be decomposed into two integer right triangles  [ps] [pdf],  February 2008
The circles of  Lester, Evans, Parry, and their generalizations, August 2008.
Heptagonal  triangles and their companions  [ps] [pdf], February 2009.




Geometry Papers:
  1.     Construction of integer right triangles with consecutive legs in the tradition of Jiuzhang Suanshu, (Chinese) EduMath. no.3, (1996) 26 -- 32.
  2.     Heronian triangles with associated inradii in arithmetic progression, Crux Math., 23 (1997) 146 -- 149.
  3.     Isosceles triangles equal in perimeter and area,  Missouri J. Math. Sci., 10 (1998) 106 -- 111.
  4.     Construction of indecomposable Heronian triangles,  Rocky Mountain Journal of Mathematics, 28 (1998) 1189 -- 1202.
  5.     (with Clayton Dodge, Thomas Schoch, and Peter Woo) Those ubitiquous Archimedean circles, Math. Mag., 72 (1999) 202 -- 213. 
  6.     Mixtilinear incircles,  Amer. Math. Monthly, 106 (1999) 952 -- 955. 
  7.     The uses of homogeneous barycentric coordinates in plane euclidean geometry, Int. J. Math. Educ. Sci. Technol., 31 (2000) 569 -- 578. 
  8.     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.
  9.     Heronian triangles are lattice triangles,  Amer. Math. Monthly, 108 (2001) 261 -- 263. 
  10.    (with A.P. Hatzipolakis, F.M. van Lamoen and Barry Wolk), Concurrency of four Euler lines, Forum Geom., 1 (2001) 59 -- 68. 
  11.    (with A.P. Hatzipolakis) The Lucas circles of a triangle,  Amer. Math. Monthly, 108 (2001) 444 -- 446. 
  12.    (with A.P. Hatzipolakis), Pedal triangles and their shadows,  Forum Geom., 1 (2001) 81--90. 
  13.    The volume of an isosceles tetrahedron and the Euler line,  Mathematics and  Informatics Quarterly, 11 (2001) 15 -- 19.
  14.    (with F.M. van Lamoen) The Kiepert pencil of Kiepert hyperbolas, Forum Geom., 1 (2001) 125 -- 132;
  15.    Over de lijnen van Fermat (Dutch translation by Floor van Lamoen),  Euclides, 77 (2002) 188 -- 193;  with minor revision,  On the Fermat lines,  Forum Geom., 3 (2003) 83--91.
  16.    (with D. Grinberg) The Apollonius circle as a Tucker circle, Forum Geom., 2 (2002) 175--182.
  17.    The congruent - incircle cevians of a triangle, Missouri J. Math.Sci., 15 (2003) 21--32.
  18.    (with N. Dergiades) Antiparallels and concurrent Euler  lines, Forum Geom., 4 (2004) 1--20.
  19.    Generalized Apollonian circles, Journal for Geometry and Graphics, 8 (2004) 225--230.
  20.    Elegant geometric constructions, in N.Y. Wong, C.K. Leung, M.Y. Tang (Eds.), Revisiting Mathematics Education in Hong Kong for the New Millennium, Hong Kong Association for Mathematics Education, pp.173--203; also in Forum Geom., 5 (2005) 75--96. 
  21.    (with M. Hoffmann) Moving central axonometric reference systems, Journal for Geometry and Graphics, 9 (2005) 133--140.  
  22.    On Emelyanov's circle theorem,  Journal for Geometry and Graphics,  9 (2005) 155--167.
  23.    (with B. Suceava), The Feuerbach point and Euler lines,  Forum Geom., 6 (2006) 191--197. 
  24.     Some constructions related to the Kiepert hyperbola, Forum Geom., 6 (2006) 343--357.
  25.    (with C. Pohoata) On a product of two points induced by their cevian triangles, Forum Geom., 7 (2007) 169--180.
  26.    (with F. M. van Lamoen) Construction of Malfatti squares, Forum Geom., 8 (2008) 49 -- 59.
  27.    Conic solution of Euler's triangle determination problem, Journal for Geometry and Graphics, 12 (2008) 75--80.
  28.    Dynamic triangle geomety: families of lines with equal intercepts, Int. J. Comput. Math. Learning, 13 (2008) 159--170.
  29.    Conic construction of a triangle from the feet of its angle bisectors, Journal for Geometry and Graphics, 12 (2008) 171--182.
  30.    (with K. R. S. Sastry and S. Gao) Heron sequences and their modifications, Combinatorial Number Theory, pp. 199--204, de Gruyter, 2009.
  31.    Heptagonal triangles and their companions, Forum Geom., 9 (2009)  125--148.
  32.    (with A. P. Hatzipolakis) Reflections in triangle geometry, Forum Geom., 9 (2009) 301--348.


Last modified: January 7, 2010.