Department of Mathematical Sciences

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Yiu, Paul
http://www.math.fau.edu/Yiu/Geometry.html
yiu@fau.edu

  •  (with K.Y.Lam) Beyond the impossibility of a 16-square identity, in K.Y.Chan and M.C.Liu (ed.), Five Decades as Mathematician and Educator, On the 80th Birthday of Professor Yung Chow Wong, pp. 137 -- 163, World Scientific, Singapore, 1995.
  • Para - Euclidean teaching of Euclidean geometry, in M.K.Siu (ed.), Mathematics Education in Hong Kong, Hong Kong University Press, 1995.
  •  (with J.Eells) Harmonic morphisms between euclidean spheres,  Proc. Amer. Math. Soc., 123 (1995) 2921 -- 2925.
  • Some upper bounds for composition numbers, Bol. Soc. Mat. Mexicana (ser. 3) 2 (1996) 65 -- 77.
  • Heronian triangles with associated inradii in arithmetic progression,  Crux Math., 23 (1997) 146 -- 149.
  • (with S.Kahlil) The Cayley - Dickson algebras, A Theorem of Hurwitz, and Quaternions, Bull. Soc. Sci Lettres  Lodz, 47 (1997) 117 -- 169. 
  • Notes on Euclidean Geometry, Florida Atlantic University Lecture Notes, 1998, 174 pages.
  • Isosceles triangles equal in perimeter and area,  Missouri J. Math. Sci., 10 (1998) 106 -- 111.
  • Construction of indecomposable Heronian triangles, Rocky Mountain Journal of Mathematics, 28 (1998) 1189 -- 1202.
  • (with Clayton Dodge, Thomas Schoch, and Peter Woo) Those ubitiquous Archimedean circles, Math. Mag., 72 (1999) 202 -- 213.
  • Mixtilinear incircles,  Amer. Math. Monthly, 106 (1999) 952 -- 955.
  • The Elementary Mathematical Works of Leonard Euler, Florida Atlantic University Lecture Notes, 1999,  161 pages.
  • The uses of homogeneous barycentric coordinates in plane euclidean geometry, Int. J. Math. Educ. Sci. Technol, 31 (2000) 569 -- 578.
  • 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.
  • Heronian triangles are lattice triangles, Amer. Math. Monthly, 108 (2001) 261 -- 263.
  • (with A.P.Hatzipolakis, F.M.van Lamoen and Barry Wolk), Concurrency of four Euler lines, Forum Geom., 1 (2001) 59 -- 68.
  • (with A.P.Hatzipolakis) The Lucas circles of a triangle,  Amer. Math. Monthly, 108 (2001) 444 -- 446.
  • (with A.P.Hatzipolakis), Pedal triangles and their shadows, Forum Geom., 1 (2001) 81--90.
  • The volume of an isosceles tetrahedron and the Euler line,  Mathematics and  Informatics Quarterly, 11 (2001) 15 -- 19.
  • (with F.M.van Lamoen) The Kiepert pencil of Kiepert hyperbolas, Forum Geom., 1 (2001) 125 -- 132.
  • Introduction to the Geometry of the Triangle, Florida Atlantic University Lecture Notes, 2001, 147 pages.
  • Over de lijnen van Fermat (Dutch translation by Floor van Lamoen), Euclides, 77 (2002) 188 -- 193;  (English version) On the Fermat lines, Forum Geom., 3 (2003) 83--91.
  • (with D.Grinberg) The Apollonius circle as a Tucker circle, Forum Geom., 2 (2002) 175--182.
  • The congruent - incircle cevians of a triangle,  Missouri J. Math.Sci., 15 (2003) 21--32.
  • Recreational Mathematics, Florida Atlantic University Lecture Notes, 2003,  360 pages.
  • (with N.Dergiades) Antiparallels and concurrent Euler lines, Forum Geom., 4 (2004) 1--20.
  • Generalized Apollonian circles, Journal for Geometry and Graphics, 8 (2004) 225--230.
  • 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: Hong Kong Association for Mathematics  Education, pp.173--203; also in Forum Geom., 5 (2005) 75--96.
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