# Katsuura, Hidefumi

## Date Updated

5-20-2024

## Department

Mathematics and Statistics, College of Science

## Academic Rank

Professor

## Year Retired from SJSU

2023

## Educational Background

1984 Ph.D. in mathematics from University of Delaware.

1980 M.S. in mathematics from University of Delaware, Newark, Delaware.

1978 B.A. in mathematics from the College of Charleston, Charleston, SC.

## Dissertation Title

Set Functions and Continuous Mappings

## Administrative and Professional Experience

1994 – 2023 San Jose State University, Professor of Mathematics.

1989 – 1994 SJSU, Associate Professor of Mathematics.

1984 – 1989 SJSU, Assistant Professor of Mathematics.

## Selected Publications

1. In and Ex Spheres of a Tetrahedron, submitted to the Journal for Geometry and Graphics on March 27, 2024. (JGG #24/28)

2. Converse of Ptolemy’s Theorem, was accepted to appear on the Proceedings of the 21st International Conference in Geometry and Graphics (ICGG2024) on 4-1-2024.

3. Introduction to Analysis; theorems and examples, book contract with Springer-Nature was signed on December 20, 2023.

4. Central and Twin Tetrahedra, the Journal for Geometry and Graphics, vol. 27 (2023) No. 2, 119 – 126.

5. Problem 2177 in the Mathematics Magazine, vol. 96, no. 4, 2023, page 468 Problem 2177: Prove that in any triangle with side length 𝑎, 𝑏, 𝑐, inradius 𝑟 and circumradius 𝑅, we have a/(b+c) + b/(a+c) + c/(a+b) + r/R ≤ 2.

6. How to Cut Cubes into Dodecahedra and Icosahedra, The Mathematical Gazzet, Volume 107 (2023) No. 569, 332 – 340.

7. Three Collinear Points Generated by a Tetrahedron, Journal for Geometry and Graphics, Volume 27 (2023), No. 1, 29 – 37.

8. Concurrent Segments in a Tetrahedron-Applications of Ceva’s and Carnot’s Theorems, Journal for Geometry and Graphics, Volume 26 (2022), No. 2, 289 – 300.

9. Characterization of Arcs by Products and Diagonals, is published electronically in November, 2022, and will be paper published in the Topology Proceedings Volume 63 (2024).

10. Angles of Isosceles Tetrahedra, Journal for Geometry and Graphics, Vol. 25 (2021), No. 2, 243 -251.

11. Dihedral Angles of 4-Ball Tetrahedra, Journal for Geometry and Graphics, Vol. 25 (2021), No.2, 197 – 204.

12. Geometric Inequalities on Parallelepipeds and Tetrahedra, with Alana Bailey, Journal for Geometry and Graphics, Vol. 24 (2020), No. 2, 193 – 196.

13. Problem 12189 on Integration, American Mathematical Monthly Problem Section, Vol. 127 on June-July 2020, page 563.

14. Solid Angle Sum of a Tetrahedron, Journal for Geometry and Graphics, Vol. 24 (2020), No.1, 29 – 34.

15. Problem 12172; A Problem on a Tetrahedron, American Mathematical Monthly, March 2020, page 275.

16. Three-Dimensional Viviani Theorem on a Tetrahedra, Journal for Geometry and Graphics, Vol. 23 (2019), No. 2, 179 – 182.

17. Problem 391; Hyperrational Cheese, Math Horizons, September 2019. Not only I proposed this problem, my solution also appeared in Math Horizons, February 2020, 31 – 32.

18. Characterization of an Isosceles Tetrahedron, the Journal of Geometry and Graphics, 23 (2019), 37 - 40.

19. An Ancient Astronomer Aristarchus tells the history of science, self-published, April 2015. Available at SJSU MLK Library at: http://scholarworks.sjsu.edu/faculty_books/114/#.VUk0eet-vbc.email

20. A New InXinite Series Representation of , The American Mathematical Monthly 122 (2015), 376.

21. Cutting Right Triangles Right!, with Wasin So, Geombinatorics Quarterly, XXIII (2014), 170 – 176.

22. Extending Alternating Series Test, College Math. J., 43 (2012) 325 – 330.

23. Trigonometric Inequalities of Sine and Tangent, College Math Journal, Vol.42, September 2011, 338.

24. Summations Involving Binomial CoefXicients, College Math Journal, Vol.40, September 2008, 284 – 287.

25. Inequalities Involving Trigonometric and Hyperbolic Functions, with Samih Obaid of SJSU, Mathematical Inequalities and Applications, Vol.10, April 2007, 243 – 250.

26. Fixed Points of k-to-one Maps on a Circle and on a Torus, Continuum Theory: In Honor of Professor David P. Bellamy on the Occasion of his 60th Birthday, Sociedad Mathematica Mexicana, 2007.

27. Problem 186, Math Horizon, Vol.12, September 2004, page 32.

28. A Generalization of the Arithmetic-Geometric Mean Inequality and a Three Dimensional Puzzle, College Mathematical Journal, Vol.34, September 2003, 280-282.

29. From Euler to Fermat, College Mathematical Journal, Vol.30, March 1999, 118-119.

30. *Triangles Within Triangles*, this is a column written by David Gale based on my paper Star of David in Mathematical Intelligencer, and re-published in his book, Tracking the Automatic Ant, 126 – 128, Springer-Verlag, 1998.

31. On the Summation of Squared Integers, American Mathematical Monthly, March 1998, Vol.105, page 245.

32. Star of David, SJSU Department of Mathematics and Computer Science Newsletter, XVII, No.1, Spring 1996, page 7. This was also published in a column by David Gale in Math. Intelligencer.

33. Computational Aspects of Kolmogorove’s Superposition Theorem, with David A. Sprecher of University of California at Santa Barbara, Neural Networks, Pergamon Press, New York, 7(1994), 455-461

34. Pseudo-Contraction and Homotopy of the sin(1/x) Curve, Proceedings of Amer. Math. Soc., 115(1992), 1129-1138.

35. Japanese Education Revisited, The AMATYC Review of Amer. Math. Assoc. of Two-year Colleges, 13(1991), 72-75.

36. The Non-Existence of a Continuous Surjection from a Continuum onto its Square, Proceedings of Amer. Math. Soc., 111(1991), 1129-1140.

37. On a Continuous Nowhere-Differentiable Function-An Application of Contraction Mappings, American Mathematical Monthly, 98(1991), 411-416.

38. Dispersion Points and Continuous Functions, Topology and Its Applications, North Holland, 28(1988), 233-240.

39. Concerning Generalized Connectedness Im Kleinen of a Hyperspace, Houston Jour. of Math., 14(1988), 227-233.

40. K-to-1 Function on (0,1), Real Analysis Exchange, 12(1987), 516-527.

41. K-to-1 Function on an Arc, with Kenneth Kellum of SJSU, Proceedings of Amer. Math. Soc., 101(1987), 629-633.