Thomas J. Osler
Mathematics Department

Mathematical Activities since December, 1997.

I. Papers published

Papers 1 to 16 published before 1995

17. Get billions and billions of digits of pi from a wrong formula,  Mathematics and Computer Education , Vol. 33, No. 1, 1999, pp.40-45.
 Submitted August 4, 1998.  Accepted October 24, 1998.

18. The trinomial triangle, (with James Chappell, student),  The College Mathematics Journal, Vol. 30, No. 2, 1999, pp. 141-142.
Submitted on March 24, 1998.  Accepted August 4, 1998.

19. Extending the Babylonian algorithm, Mathematics and Computer Education, Vol. 33, No. 2, 1999, pp. 120-128.
Submitted  on October 6, 1998. Accepted January 19, 1999.

20.  The tautochrone under arbitrary potentials using fractional derivatives, (with Eduardo Flores),  American Journal of Physics, (Am. J. Phys.), 67(1999), pp. 718-722.  Submitted on September 11, 1998. Accepted November 13, 1998. Revised version sent on December 10, 1998. Revised Table sent on December 17, 1998

21. The united Vieta’s and Wallis’s products for pi, American Mathematical Monthly, 106 (1999), pp. 774-776.
Submitted on September 10, 1998. Accepted December 17, 1998. Final version submitted January 7, 1999.

22. Fractal Movies, Mathematics and Computer Education,  Vol. 33 (1999), pp.  236-243. Submitted on December 8, 1997.  Returned for revision on  June 30, 1998. Revised version submitted on July 15, 1998. Accepted April 1999.

23. A child’s garden of fractional derivatives, (with Marcia Kleinz), The College Mathematics Journal, Vol. 31, No. 2, (2000), pp. 82-88.
Submitted on July 9, 1998. Returned for revision October 5, 1998. Resubmitted on November 13, 1998. Returned again for revision on December 7, 1998. Revised and resubmitted on December 30, 1998. Accepted January, 1999. Editorial changes requested February 14, 1999.

24. The binomial to binomial theorem, The College Mathematics Journal, Vol. 31, No. 3, (2000), pp. 211-212.
Submitted on January 7, 1998. Returned for revision on June 8, 1998. Revised version resubmitted on July 6, 1998. E-mail correspondence with editor Tom Farmer on July 10 & 11. Resubmitted again on July 13, 1998. Accepted August 4, 1998.

25. Spacetime numbers the easy way,  (with Nick Borota and Eduardo Flores), Vol. 34, No. 2, (2000), pp. 159-168.
Submitted on June 29, 1999 to The College Mathematics Journal as a feature article. Informed September 1, 1999 that the paper was accepted, but there is no room to print it. Submitted to Mathematics and Computer Education on September 7, 1999. Accepted March 16, 2000.

26. Playing with partitions on the computer, (with Abdul Hassen), Mathematics and Computer Education , Vol. 35, No. 1, (2001), pp. 5-17.
Submitted on August 23, 1999. Returned for revision in January, 2000. Revised version (with Abdul Hassen) submitted on June 14, 2000. Accepted August 14, 2000. Page proof corrected and returned August 18, 2000.

27. Mutations of the Mandelbrot set, (with Jae Hattrick-Simpers, student), Mathematics and Computer Education, Vol. 35, No. 1, (2001), pp. 18-26.
Submitted on November 1, 1999 to. Returned for revision on January 28, 2000. Revised version submitted on June 12, 2000. Accepted August 21, 2000. Copyright forms mailed on Sep 6, 2000. Page proof returned on Sep. 14, 2000.

28. The remarkable incircle of a  triangle. (with Ira Fine), Mathematics and Computer Education, Vol. 35, No. 1, (2001), pp. 44-50.
Submitted on April 18, 2000. Returned July 16, 2000 with favorable referee’e report, however revisions are required. Revised version sent August 8, 2000. Paper accepted and page proof sent to us on Sep. 12, 2000. Page proof returned on Sep. 18, 2000.

29. Cardan polynomials and the reduction of radicals,  Mathematics Magazine, Vol 47, No. 1, (2001), pp. 26-32.
Submitted to Mathematics Magazine on January 7, 1998 and returned on April 17, 1998 with the recommendation that the paper be shortened. Revised version submitted on July 15, 1998. Get encouraging e-mail note that paper is being returned with revisions requested on July 15, 1999. Revised version submitted on October 27, 1999. Returned for editorial revisions on May 24, 2000. Revised and submitted on June 19, 2000. Email correspondence with the editor Paul Zorn on July 19-20, 2000. Slight revison sent via email on July 20, 2000. Letter from new editor Frank A Farris received July 27, 2000. This letter indicates that he is not aware of my revisions with Paul Zorn. I e-mail him and he responds. Revisions sent to Paul Zorn on September 1, 2000. Electronic version returned to me by Zorn on Sep12. Hard copy and electronin copy sent to Paul Zorn and to Frank Farris on Sep. 14, 2000. Official letter of acceptance received from Paul Zorn on Sep. 12, 2000.

30. The rotating tautochrone, (with Eduardo Flores), Journal of Applied Mechanics, 68(2001), pp. 353-356.
Submitted to The American Journal of Physics, February 11, 1999. Rejected February 1999. Revised and submitted to SIAM Journal on Applied Mathematics on October 18, 1999. Returned as unsuitable for this journal on November 15, 1999. Submitted to the Journal of Applied Mechanics on March 28, 2000. Accepted subject to revisions on July 3, 2000. Revised version sent on July 20, 2000. Final request for changes sent via email from A A Ferri on Sep. 13, 2000. Changes made and mailed to AA Ferri on Sep. 14, 2000.

31oof  returned on January 22, 2001. Page proof mailed back to MACE on January 26, 2001.

32 Fun with 0.999... , The AMATYC Review , 22(2001), pp. 53-56. First submitted to The College Mathematics Journal as a Classroom Capsule on June 28, 1999. Regected January 10, 2000. Next submitted to The AMATYC Review on February 7, 2000. Acceptance indicated on June 27, 2000 subject to revisions. Revised version sent by email on July 18, 2000. Short biography and Rowan logo sent by email on March 7, 2001. Page proof corrected by email on April 24, 2001.

33. An unusual approach to Kepler’s first law, American Journal of Physics, 69(2001), pp. 1036-8. Submitted to The American Journal of Physics on January 22, 2001. Letter expressing confusion on part of editors as to appropriateness of this paper for AJP received February 21, 2001. Revised version submitted on February 27, 2001. Accepted March 9, 2001 with small revisions requested. Revised version mailed March 20, 2001. Transfer of copyright sent 3/28/01, and email confirming approval of changes made by the editor. Page proof received over the web, corrected and faxed back on May 30, 2001.

34. An unusual view of the ellipse, Mathematics and Computer Education, 35,(2001), pp. 234-236. Submitted on January 5, 2001. Revisions requested on May 16, and returned on May 21, 2001. Accepted on May 25, 2001. Page proof and copyright agreement mailed May 31, 2001.

35. Variations on Vieta’s and Wallis’s products for pi, (with Michael Wilhelm), Mathematics and Computer Education, 35(2001), pp. 225-232. Submitted on May 25, 2000. Returned for revision on January 9, 2001. Revised version submitted on January 24, 2001. Accepted on May 23, 2001. Copyright agreement mailed May 31, 2001.

36.  A tale of two series, (with Marcus Wright), The College Mathematics Journal, 33(2002), pp. 99-106. Submitted to The College Mathematics Journal on March 30, 2000. Accepted subject to revisions on July 10, 2000. Ask Marcus Wright to make revisions on August 16, 2000. Mail revised version on May 2, 2001. Revisions requested (mostly cosmetic) on May 22, 2001 along with transfer of copyright agreement. Revisions sent on July 17, 2001. Electronic versions sent by email on July 30, 2001.

37.  Divergence of the harmonic series, p series and others by rearrangement, (with Bernard August, Emeritus), The College Mathematics Journal, 33(2002), pp. 233-4. Submitted to The College Mathematics Journal as a Classroom Capsule on July 3, 2001. Accepted July 23, 2001. Revisions sent July 30, 2001.

38. Fermat’s little theorem from the multinomial theorem, The College Mathematics Journal, 33(2002), p. 239.  Submitted to The College Mathematics Journal on August 14, 2001 as a Classroom Capsule. Accepted on September 19, 2001.

39. A table of the partition function, (with Abdul Hassen and T. R. Chandrupatla), The Mathematical Spectrum, 34(2001/2002), pp. 55-57. Submitted to The Mathematical Spectrum on June 4, 2001 and accepted on July 13, 2001 with cosmetic revisions. Revisions sent on July 30, 2001. Electronic version sent October 22, 2001. Previously submitted to Mathematics and Computer Education on January 4, 2001. (under the title More playing with partitions) –Rejected on May 23, 2001. (This is a completely rewritten version of Counting partitions the transparent way, with T. R. Chandrupatla which was submitted on October 4, 1999 to Mathematics and Computer Education and rejected on January 28, 2000.)

40. Visual Basic for QuickBasic Programmers, (with Seth Bergmann and T. R. Chandrupatla), Mathematics and Computer Education, 36(2002), pp. 133-138. Submitted to Mathematics and Computer Education on June 6, 2001. Accepted December 1, 2001. Transfer of Copyright sent January 7, 2002.

41. Functions of a spacetime variable, (with Nicolae A. Borota), Mathematics and Computer Education, 36(2002), pp. 231-239. Submitted to Mathematics and Computer Education on January 19, 2001 and rejected July 15, 2001. Revised and resubmitted on October 17, 2001. Editor sends second referee's report. Reply to report sent March 8, 2002. Accepted on March 28, 2002. Corrected page proof and Copyright Agreement sent April 10, 2002.

42. An easy introduction to biplex numbers, (with Dipti Bardhan), Mathematics and Computer Education, 36(2002), pp. 278-286. Accepted on July 27, 2002 by Mathematics and Computer Education. Originally submitted to The  College Mathematics Journal on June 14, 2001. Returned August 20, 2001 for revision. Submitted to The Mathematical Spectrum on October 19, 2001. Rejected on November 7, 2001. Revised and submitted to Mathematics and Computer Education on April 12, 2002. Returned on July 7, 2002 with a request for revision.

43. An easy look at the cubic formula, Mathematics and Computer Education, 36(2002), pp. 287-290. Accepted on August 5, 2002 by Mathematics and Computer Education. Originally submitted to The AMATYC Review on June 20, 2001. Returned for revision on September 24, 2001. Revised version mailed on October 16, 2001. Rejected February 25, 2002. Submitted to Mathematics and Computer Education on April 11, 2002.

44. Proof without words: Integral of sine squared, The AMATYC Review, 24(2002), p. 65. Submitted to The AMATYC Review on April 22, 2002. Accepted September 1, 2002.

45.  A computer hunt for Apery's constant, (with Brian Seaman), Mathematical Spectrum, 35(2002/2003), No. 1, pp. 5-8. Submitted to The Mathematical Spectrum on April 24, 2002. Accepted on April 29, 2002.

46. A magic trick from Fibonacci, (with James Smoak), The College Mathematics Journal, 34(2003), pp. 58-60. Submitted as a classroom capsule to The College Mathematics Journal on May 16, 2002. Accepted June 26, 2002. Revised version and copyright transfer sent July 9, 2002.

47. Variations on a theme from Pascal's triangle, The College Mathematics
Journal, 34(2003), pp. 216-223. Submitted on October 15, 2001. Accepted on November 2, 2001 with minor changes requested. Page proof corrected and returned on January 23, 2003.Due to appear in May, 2003.

48. Visual proofs of two integrals, The College Mathematics Journal, 34(2003), p.231-232. Submitted on March 26, 2002. Accepted  on May 6, 2002. Page proof corrected and returned on January 23, 2003.

49. An unusual product for sin z and variations of Wallis’s product, The Mathematical Gazette, 87(2003), pp. 134-139.  Accepted December 5, 2001. Page proof returned by email on April 11, 2002. Originally submitted to The American Mathematical Monthly as a Note on June 19, 2000. Rejected on July 26, 2000 with the recommendation that it be resubmitted to the problem section. Submitted to The Mathematical Gazette on May 30, 2001. Returned for revision on September 29, 2001. Revised version mailed on October 16, 2001.

50 Finding Zeta(2p) from a product of sines. The American Mathematical Monthly, 111(2004), pp. 52-54.  Submitted on May 28, 2002. Returned for revision on August 16, 2002. Revised version sent Sept. 3, 2002. Returned for a second revision on November 19, 2002. Second revision sent on December 2, 2002. Accepted on January 7, 2003. Transfer of copyright sent January 11, 2003. Editorial addjustments sent March 3, 2003. Page proof checked on September 28, 2003.

51. Another intuitive approach to Stirling’s formula, International Journal of Mathematical Education in Science and Technology, 35(2004), pp.111-118. Submitted on on September 3, 2002. Returned on April 2, 2003 with a request for revision. Revised version sent August 4, 2003. Accepted on September 16, 2003. Hard and soft copies of final version mailed to editor on October 10, 2003. Page proof emailed and copyright agreement mailed on December 4, 2003. Originally submitted to The College Mathematics Journal on June 27, 2001 as a Classroom Capsule. Rejected August 26, 2001. Revised version submitted to The Mathematical Spectrum on October 16, 2001. Rejected November 13, 2001.

52. Geometric construction of Pythagorean triangles, (with Tirupathi R. Chandrupatla).Mathematics and Computer Education, 38(2004), pp. 90-91. Submitted to Mathematics and Computer Education on November 27, 2002. Email question received and answered regarding the originality of the work on November 19, 2003. Accepted November 20, 2003. Page proof and copyright agreement mailed on December 1, 2003. Originally submitted to The College Mathematics Journal on August 30, 2002. Rejected October 25, 2002.

53. Variations on the linear first order ODE, (with Brian Seaman), International Journal of Mathematical Education in Science and Technology, 35(2004), pp.309-315. Submitted to the International Journal of Mathematical Education in Science and Technology  on February 26, 2003. Accepted on November 13, 2003. Hard and soft copies of final version mailed to editor on Decenber 5, 2003. Originally submitted to Mathematics and Computer Education on October 23, 2001.Returned July 31, 2002 for revision. Revised version sent September 7, 2002. Rejected February 20, 2003.

54. Extending Theon's ladder to any square root, (with Shaun Giberson), The College Mathematics Journal, 35(2004), pp. 222-226. Submitted on April 8, 2003 to The College Mathematics Journal. Accepted June 27, 2003 pending modifications. Revised version sent June 30, 2003. Transfer of copyright sent December 15, 2004.

55. Problems on divisibility of binomial coefficients, (with James Smoak). The AMATYC Review, 25(2004), pp. 17-21. Submitted to The AMATYC Review on July 24, 2002. Returned December 2, 2002 for revision. Revised version sent January 12, 2002. Accepted March 17, 2003. Biographies and Rowan letter head sent February 4, 2004. Page proof and abstract returned on Feb. 25, 2004. Originally submitted to Mathematics and Computer Education on August 14, 2001.Returned December 18, 2001 for revision. Revised version submitted February 25, 2002. Rejected, July 22, 2002.

56. Generalizing integrals involving x^x and series involving n^n, (with Jeffrey Tsay). Mathematics and Computer Education, 39(2005), pp. 31-36. Submitted to Mathematics and Computer Education on February 11, 2004. Accepted October 29, 2004. Copyright and journals request sent November 2, 2004.

57. Theon's ladder for any root (with Marcus Wright and Michael Orchard, International Journal of Mathematical Education in Science and Technology, 36(2005), pp. 389-398. Submitted to the International Journal of Mathematical Education in Science and Technology  on January 29, 2004. Accepted September 27, 2004. Hardcopy and diskette sent October 13, 2004. Page proof and transfer of copyright sent Nov 28, 2004. Originally submitted to The Fibonacci Quarterly on August 11, 2003 and returned on September 22, 2003. We were asked to resubmit when a reference is accepted. Paper resubmitted on October 10, 2003 with an abstract, a new final section 8, and eight new references added. Rejected as "not substantial enough for FQ" on December 31, 2003.

58. Why sin 80x looks like sin x on my TI-89, (with Jim Zeng).International Journal of Mathematical Education in Science and Technology, 36(2005), pp. 437-441. Submitted to the International Journal of Mathematical Education in Science and Technology  on December 1, 2003. Minor revisions requested June 30, 2004 and revisions sent on July 8, 2004. Accepted September 27, 2004. Hardcopy and diskette sent October 12, 2004. Page proof and transfer of copyright sent Nov 28, 2004. Originally submitted to Mathematics and Computer Education on November 2, 2001. Returned August 1, 2002 for revision. Revised version mailed August 12, 2002. Rejected February 20, 2003.  Next submitted to The College Mathematics Journal on March 4, 2003 and rejected on November 25, 2003.

59. Unexpected constructable numbers, The AMATYC Review, 26(2005), no. 2, pp. 2-3. Submitted to The AMATYC Review on June 10, 2003. Returned for revision on September 2, 2003. Revised version sent on September 28, 2003. Second revision requested on July 5, 2004. Revision sent on August 10, 2004. Accepted September 18, 2004 with requests for minor changes which were emailed the same day. Approval of proofs faxed Feb 2, 2005. Expected to appear Spring 2005. Originally submitted as a classroom capsule to The College Mathematics Journal on September 15, 2002. Rejected on October 1, 2002. Next submitted to Mathematics and Computer Education on November 26, 2002 and rejected on May 29, 2003.

60. Some unusual expressions for the inradius of a triangle, (with Tirupathi R. Chandrupatla), The AMATYC Review, 26(2005), no.2, pp. 12-17.  Submitted to The AMATYC Review on August 7, 2003. Accepted December 16, 2004. Revision and bios sent on December 20, 2004. Proofs approved and faxed Feb 2, 2005. Originally submitted to The College Mathematics Journal on August 30, 2002. Rejected October 25, 2002. Next submitted to Mathematics and Computer Education on November 27, 2002. Rejected August 4, 2003.

61  A simple geometric construction of the harmonic mean of n variables (with Jim Zeng,  Mathematical Spectrum, 37(2004/2005), No. 3, pp. 109-111. Submitted to the Mathematical Spectrum on January 14, 2004. Accepted January 21, 2004.

62. Proof Without Words: Arc length of the cycloid,  The Mathematical Gazette, 89(2005), no. 515,  page 250. Submitted on May 28, 2003. Improved version sent by email on October 10, 2003. Accepted on September 9, 2003. Page proof and copy Right sent March 24, 2005. Originally submitted to Mathematics and Computer Education on April 10, 2002, and rejected on June 22, 2002. Then (second) submitted  to Mathematics Magazine on July 1, 2002 and rejected February 11, 2003.Submitted (third) to the International Journal of Mathematical Education in Science and Technology on March 5, 2003, and rejected on May 21, 2003.

63. Ptolmey vs. Copernicus. (With Joseph Diaco.) The  Mathematical Spectrum, 38(2005/2006), pp. 3-6.  Submitted on on February 18, 2004. Accepted May 11, 2004.

64.  The general Vieta-Wallis product for pi, The Mathematical Gazette, 89(2005), pp. 371-378. Submitted to The Mathematical Gazette on September 26, 2003. Returned on October 26, 2003 with the option of requesting another referee's report. I request another referee's report on November 5, 2003. Second referee's report is favorable, but the editor requests that I shorten section 6. Revised verson mailed on January 5, 2004. Accepted on January 13, 2004. Scheduled to appear in November, 2005. Electronic version sent on January 20, 2004. Page proof and copyright sent July 15, 2005. Originally submitted to The Fibonacci Quarterly on August 21, 2003, and rejected on September 22, 2003.

65. Using simple harmonic motion to help in the search for tautochrone curves, (with Tirupathi R. Chandrupatia), International Journal of Mathematical Education in Science and Technology, 37 ( 2006),  pp, 104-9.. Submitted to the International Journal of Mathematical Education in Science and Technology on July 28, 2004. Accepted February 24, 2005. Proof sheets examined and Copyright form signed May 19 and 24, 2005. Originally submitted to The American Journal of Physics on April 15, 2004, and rejected July 29, 2004 after a positive recommendation from the referee. The editor felt that it was a "weak recommendation".

66.  Motivation for finding Zeta(2p) from a product of sines, International Journal of Mathematical Education in Science and Technology, 37(2006), pp. 231-235.  Submitted to the International Journal of Mathematical Education in Science and Technology  on March 18, 2004. Returned for revision on Sept. 10, 2004. Revision sent via email on May 12, 2005. Accepted June 23, 2005. Originally submitted to The Mathematical Gazette on February 25, 2004. Rejected March 14, 2004.

67. A mechanical view of Archimedes quadrature of the parabola. The College Mathematics Journal, 37(2006), pp. 24-28. Submitted to The College Mathematics Journal on  November 4, 2004. Revisons requested March 31, 2005 and submitted via email on May 11, 2005. Accepted July 22, 2005. Revision sent August 4, 2005 with copyright notics, bio, abstract and photo. Figures 1 to 5 mailed Sep 19, 2005.

68. A proof of the continued fraction for e^1/M, American Mathematical Monthly, 113(2006), pp. 62-66. Submitted to the American Mathematical Monthly on February 26, 2003. Returned for revision on January 2, 2004. Revised version sent January 17, 2004. Returned for a second revision on July 27, 2004. Second revision sent August 13, 2004. Accepted January 23, 2005. Revisions sent January 24, 2005. Revisions requested April 28 and sent  via email on May 10, 2005. More revision and diskette snail mailed on May 25, 2005.

69.  Interesting finite and infinite products from simple algebraic identities. The Mathematical Gazette, 90(2006), pp. 90-93. Submitted to The Mathematical Gazette on January 5, 2003. Returned for revision February 7, 2004. Revised version mailed February 16, 2004. Accepted on February 23, 2004.  Electronic files sent February 29, 2004. Originally submitted to The American Mathematical Monthly on August 6, 2003, and rejected on December 16, 2003.

70.  Proof with few words: Quadratic convergence of the AGM. The Mathematical Gazette, 90(2006), p 116-117. .Submitted to The Mathematical Gazette on January 14, 2004. Returned on February 23, 2004 with favorable response and a request for revision. Revision sent February 29, 2004. Accepted on March 14, 2004. Originally submitted to Mathematics Magazine on April 22, 2002. Rejected January 5, 2004.

71. A spiral of triangles related to the great pyramid, with Matthew Oster. The Mathematical Spectrum, 38(2005/2006), pp. 108-112. Submitted to the Mathematical Spectrum on October 28, 2005 and accepted on November 3, 2005. Revision with bios sent via email on November 11, 2005.

74. Translation with Notes of Euler's  paper "Remarks on a beautiful relation between direct as well as reciprocal series" (E352),(with Lucas Willis), on the web at the Euler Archive, http://www.math.dartmouth.edu/~euler/. Submitted to the online "Euler Archive" on July 27, 2006. Accepted August 21, 2006.

75. Synopsis of Euler's paper "Remarks on a beautiful relation between direct as well as reciprocal series" (E352),(with Lucas Willis), on the web at the Euler Archive http://www.math.dartmouth.edu/~euler/. Submitted to the online "Euler Archive" on July 27, 2006. Accepted August 21, 2006.

76. Translation with notes of Euler’s paper E796, Recherches sur le problem de trois nombres carres tels que la somme de deux quelconques moins le troisieme fasse un nombre carre,“Research into the problem of three square numbers such that the sum of any two less the third one provides a square number.” ( with Kristen McKeen) . Submitted to the Euler Archive on Nov.16, 2006 Accepted Dec 4, 2006.

77. Synopsis by section of Euer's paper E769, Recherches sur le problem de trois nombres carres tels que la somme de deux quelconques moins le troisieme fasse un nombre carre,“Research into the problem of three square numbers such that the sum of any two less the third one provides a square number.” ( with Kristen McKeen) . Submitted to the Euler Archive on Nov.16, 2006. Accepted Dec 4, 2006.

78. Translation with notes of Euler's paper E46, Methodus Universalis Serierum Convergentium Summas Quam Proxime Inveniendi, (A general method for finding approximations to the sums of convergent series). (with Walter Jacob.)Submitted to the Euler Archive on December 12, 2006 and accepted January 2, 2007.

79. Synopsis of Euler's paper E46, Methodus Universalis Serierum Convergentium Summas Quam Proxime Inveniendi, (A general method for finding approximations to the sums of convergent series). (with Walter Jacob.)Submitted to the Euler Archive on December 12, 2006 and accepted January 2, 2007.

80.  The integers of James Booth, (with John F. Kennedy), Mathematical Spectrum, 39(2006/2007), pp. 71-72. Submitted to The Mathematical Spectrum on May 11, 2005. Accepted May 18, 2005, subject to revision.

II. Papers accepted for publication and awaiting printing

1  The unlikely connections between partitons and divisors, (with Abdul Hassen and T. R. Chandrupatla). Submitted to The College Mathematics Journal on August 28, 2003. Request for revision set July 9, 2004. (Request that marriage allegory be removed.) Revision submitted on August 11, 2004. Accepted on Nov. 15, 2004. Revisions sent January 4, 2005 by email. Third revision sent June 30, 2006. Fourth revision sent August 17, 2006 by email. Fifth revision sent Feb 12, 2007 with photos and mini biographies.

3. Vieta-like products of nested radicals with Fibonacci and Lucas numbers. Submitted to the Fibonacci Quarterly on June 20, 2005. Abstract  and AMS Classification numbers added on July 5, 2005. Accepted on September 26, 2005. Originally submitted to the American Mathematical Monthly on February 7, 2005, and rejected June 10, 2005.

5.. Another geometric vision of the hyperbola,  submitted  to  The Mathematical  Spectrum  on October  24, 2006, and accepted on November 2, 2006. Revised version sent by email Jan 3, 2007.

6.  Approximating the path of a celestial body with a circular orbit from two close observations, with Joseph Palma.  Submitted to The Mathematical Scientist on October 24, 2006. Revision sent Nov 15, 2006. Accepted Noember 21, 2006. Originally submitted to The American Journal of Physics on July 24, 2002. Major revisions requested on October 8, 2002. Revised version sent October 21, 2002. Small revisions requested on November 12, 2002. Second revision sent on December 1, 2002. Third revision requested on January 9, 2003. Third revision sent on January 12, 2003. Reply from editor on Feb. 3, 2003. Fourth version sent June 24, 2003. Rejected March 5, 2004. Submitted to the International Journal of Mathematical Education in Science and Technology on July 28, 2004 and rejected on December 17, 2004. Submitted to Celestial Mechanics and Dynamical Astronomy on January 4, 2005.

7. Euler's little summation formula and sums of powers, (with Andrew Robertson), submitted to The Mathematical Spectrum on December 4, 2006 and accepted pending minor revisions on December 19, 2006. Revisions sent Jan 21, 07.

8. Oblique-angled diameters and the conic sections, with Edward Greve. Submitted to The Mathematical Spectrum on December 11, 2006 and accepted January 4, 2007. Revisions sent Jan 21, 07.

9. Euler's little summation formula and special values of the zeta function, submitted to The Mathematical Gazette on October 20, 2006 and accepted on February 26, 2007 with a few changes requested. Scheduled to appear in July 2008. Originally submitted to The American Mathematical Monthly on August 30, 2006 and rejected on October 19, 2006.

??. On generalizations of Lambert’s series, Submitted on February 23, 2007 to International Journal of Pure and Applied Mathematics and accepted on March  5, 2007. Editor wants me to convert the paper to a Latex file, and I am not sure if I can do this. Originally submitted to the Rocky Mountain Journal of Mathematics on September 1, 2002.  Positive referee's report received on September 23, 2002 with revision requested. Revised version submitted on August 18, 2003 but rejected in February 2007. Originally submitted to the International Journal of Mathematics and Mathematical Sciences on October 6, 1998. Rejected April 1999.

III Papers submitted and being reviewed

1. A binomial telescope.  Originally submitted to The American Mathematical Monthly on June 6, 2002. Rejected August 7, 2002 with the recommendation that it be resubmitted for the Problems Section.Submitted to The Mathematical Gazette on August 14, 2002, and rejected September 17, 2002.

V. Manuscripts in preparation

1. Fractional derivatives and the tautochrone problem, (with Stacie Rueblinger)

2. Pascal's triangle and modular arithmetic, Brian Reed

3. Theon's ladder and cubic equations, with Jaclyn Letton

4. Solving cubics by intersecting circles and hyperbolas, with Elizabeth Klinglesmith.

5. A trigonometric table of exact values, with Kristy Erickson.

VI. Talks at other Universities

1. Cardan polynomials and the reduction of radicals, delivered to the Mathematics Seminar at Drexel University on January 14, 1998.

2. Cardan polynomials and the reduction of radicals, delivered to the Number Theory Seminar at Temple University on March 25, 1998.

3. Cardan polynomials and the reduction of radicals, delivered to the Mathematics Seminar at Saint Joseph’s University on March 26, 1998.

4. Using the  history of mathematics in your classroom. delivered to  the South Jersey Math Alliance  at Rowan University, May  22, 1998

5. Lessons from the history of mathematics, delivered to DelMATYC (Del. Math. Assoc. of Two-Year Colleges), at the Buena Vista Conference Center, Delaware on June 9, 1998.

6. An unusual approach to Kepler’s first law, delivered to Spring Meeting of the Mathematical Association of America, New Jersey Section, at Rowan University on April 21, 2001.

7. Finding Zeta(2p) from a product of sines, delivered at the Annual Meeting of the American Mathematical Society in Baltimore on January 15, 2003.

8. On generalizations of Lambert's series, delivered at the Annual Meeting of the American Mathematical Society in Phoenix on January 8, 2004.

9. The general Vieta-Wallis product for pi. Presented at the National Meeting of the American Mathematical Society on January 7, 2005 in Atlanta.

10. Another proof of the continued fraction expansion of  exp(1/M). Presented at the National Meeting of the American Mathematical Society on January 13, 2006 in San Antonio.

11. Euler’s little summation formula and special values of the zeta function. Presented at the National Meeting of the American Mathematical Society on January 6, 2007 in New Orleans.

12. The Joy of Student-Professor Collaboration in Translating Euler’s Papers. Plenary talk delivered at the Euler 300^th Anniversary Meeting, The Mathematical Association of America, New Jersey Section at Rowan University, March 31, 2007.

VII. Solutions to Journal Problems Submitted

1. Problem 1529, “An Integral Sum of Cube Roots”, from Mathematics Magazine, 70(1997). Proposed by David C. Kay, University of South Carolina at Asheville. Submitted November 26, 1997 with James Chappell, Rowan student. Solution recorded correct in Math. Mag., 71(1998), pp. 316-317.

2. Problem 334, “Gravity problem”, from Mathematics and Computer Education,  (1997), p. 307. Proposed by Allen Barnes and Jeffery Hascheck, Queensborough Community College, NY. Submitted  February 4, 1998.

3. Problem 343  “Repeated radicals”, from Mathematics and Computer Education, (1997),  Proposed by K. R. S. Sastry, Bangalore, India. Submitted February 9, 1998.

4. Problem 1533, “A quadratic recurrence relation”, from Mathematics Magazine, 70(1997), p. 299. Proposed by Joaquin Gomez Rey, I. B. “Luis Bunuel”, Alcorcon, Madrid, Spain.  Submitted February 17, 1998. Solution recorded correct in Math. Mag., 71(1998), pp. 321-322.

5. Problem 1530, “Tower of Bubbles”, from Mathematics Magazine, 70(1997), p. 298.
Proposed by Allen J. Schwenk of Western Michigan University.  Submitted February 25, 1998. Solution recorded as correct in Math. Mag., 71(1998), pp. 317-319.

6. Problem 82.A, “A Fibonacci sum”, from The Mathematical Gazette, (1998), p. 129. Proposed by J. R. Goggins. Submitted May 21, 1998.

7. Problem 345, “An area problem”, from Mathematics and Computer Education, (1998),
Proposed by Juan-Bosco Romero Marquez, Universidad de Valledolid, Spain. Submitted August 31, 1998. My solution published in Vol. 33, 1999, pp. 289-290.

8. Problem 678 “A double sum”, from The College Mathematics Journal, 31(2000). Proposed by David Atkinson, Olivet Nazarene University, Kankakee, IL. Submitted May 31, 2000. Solution recorded as correct in 32(2001), p. 214.

9. Problem no. 676 “A family of limacons” ,  from The College Mathematics Journal, Vol 31, No. 3, May, 2000. Proposed by Rick Mabry, LSU-Shreveport, Shreveport, LA, and Paul Deiermann, Lindenwood University, St. Charles, MO. Submitted June 7, 2000. Solution recorded as correct in 32(2001), pp. 212-213.

10. Problem no. 10809 “An identity for partitions of integers”, from The American Mathematical Monthly, Vol. 107, No. 6, (2000), p. 566. Proposed by David Beckwith, Sag Harbor, NY. Submitted November 25, 2000. Solution recorded as correct in 109(2002), p. 477.

11. Problem AM-2, “A polynomial root”, from The AMATYC Review, 22(2001), p. 80.
Proposed by Michael S. McClendon, University of Central Oklahoma, Edmond, OK. Solution submitted on June 4, 2001.

12. Problem AM-4, “A radical recursion”, from the AMATYC Review, 22(2001), p. 80. Proposed by Russell Euler and Jawad Sadek, Northwest Missouri State University, Marysville, MO. Solution submitted on June 20, 2001.

13. Problem 720, “A limit of differences”, from The College Mathematics Journal, 33(2002), p.55. Proposed by Andrew Cusumano, Great Neck, NY. Submitted January 29, 2002.

VIII.  Sponsoring Student Research

1. Edited the first two issues of The Rowan University Math/Physics Student Research Newsletter, Fall, 1998 and Fall, 1999.

2. Sponsored the project of James Chappell, The trinomial triangle, at the STEM Exhibit, Rowan University, April 1998.

3. Sponsored the project of Nicolae Borota, The spacetime numbers, at the STEM Exhibit, Rowan University, April 1999.

4. Thesis advisor for Nicolae Borota (Master’s), The spacetime numbers, May, 1999.

5. Sponsored the project of Dipti Bardham, The biplex number system, at the STEM Exhibit, April 1999.

6. Sponsored the project of Marcia Kleinz, A child’s garden of fractional derivatives, at the Stem Exhibit, April 1999.

7. Sponsored the project of Jae Hatchrick - Sempers, Mutations of the Mandelbrot set, at the Stem Exhibit, April, 1999.

8. Sponsored the project of Ira Fine, The remarkable incircle of a triangle, at the STEM Symposium, April 7, 2000.

10. Sponsored the project of John Atzu-Swanzy, Simulation with discrete dynamical systems,  at the STEM Symposium on April 7, 2000.

11. Sponsored the project of Michael Wilhelm, The union of Vieta’s and Wallis’s products for pi, at the STEM Symposium, April 7, 2000.

12. Sponsored the project of Matthew Flacche, Pascal’s triangle and Sierpinski’s triangle: An incredible link, at the STEM Symposium, April 7, 2000.

13. Sponsored the project of David W. Thibault Jr., Estimating the orbit of an asteroid, at the STEM Symposium, April 6, 2001.

14. Sponsored the project of Kristy A. Erickson and David W. Thibault Jr., A simple ephemeris, at the STEM Symposium, April 6, 2001.

15. Sponsored the project of John Atsu-Swanzy, Exact solutions of the n body problem, at the STEM Symposium, April 6, 2001.

16. Sponsored the project of Douglas Eaton, Pascal's triangle and modular arithmetic, at the STEM Symposium, April 26, 2002.

17. Sponsored the project of Joseph Palma, Predicting the orbit of a new asteroid, at the STEM Symposium, April 26, 2002.

18. Sponsored the project of Danielle Pennino, Fractional derivatives and Cauchy's integral formula, at the STEM Symposium, April 26, 2002.

19. Sponsored the project of Brian Seaman, A computer hunt for Apery's constant, at the STEM Symposium, April 26, 2002.

20. Sponsored the project of Brian Seaman and Shaun Giberson, Variations on two standard ordinary differential equations, at the STEM Symposium, April 26, 2002.

21. Sponsored the project of Todd Pelletier and Kevin Hughes, A one-to-one function mapping (0,1) onto [0,1] at the STEM Symposium, April 25, 2003.

22. Sponsored the project of  Michelle Briles, The unlikely marriage of partitions and divisors, at the STEM Symposium, April 25, 2003.

23. Sponsored the project of  Shaun Giberson, Extending Theon's ladder to any square root,   at the STEM Symposium, April 25, 2003.

24. Sponsored the project of  Robert Ciccozzi, Parametric generation of Heronian triangles, at the STEM Symposium, April 25, 2003.

25. Sponsored the project of Christina Miles, Cardan Polynomials and Cardan sequences, at the STEM Symposium, April 25, 2003.

26. Sponsored the project of Joseph Palma, Approximating the orbit of a new asteroid,  at the STEM Symposium, April 25, 2003.

27. Sponsored the project of Joseph Diaco, A simple ephemeris, Part II,  at the STEM Symposium, April 25, 2003.

28. Sponsored the project of Brian Reed, The hidden side of Pascal's triangle at the STEM Symposium, April 23, 2004.

29. Sponsored the project of Michael Orchard, Theon's ladder for any root at the STEM Symposium, April 23, 2004.
 
30. Sponsored the project of  Elizabeth Ann Klinglesmith, When conic sections collide at the STEM Symposium, April 23, 2004.

31. Sponsored the project of  Jaclyn Letton, Using Theon's ladder to solve cubic equations at the STEM Symposium, April 23, 2004. 

32. Sponsored the project of  Kristy Ericson, A table of exact trigonometric values, at the STEM Symposium, April 23, 2004.

33. Sponsored the project of  Jeffrey Tsay, Generalizing integrals involving x^x and series involving n^n at the STEM Symposium, April 23, 2004.

34.  Sponsored the project of  Nick Stugard, Irrational numbers whose proof of irrationality resembles that of the number eat the STEM Symposium, April 22, 2005.

35. Sponsored the project of John F. Kennedy, The remarkable numbers of Rev. James Booth at the STEM Symposium, April 22, 2005.

36. Sponsored the project of Adam Hilburn, An unusual proof that the Fibonacci number Fm divides Fmn at the STEM Symposium, April 22, 2005.

38. Sponsored the project of Mohamed Teymour, The quadratic equation as solved by Persian mathematicians of the middle ages at the STEM Symposium, April 21, 2006.

39. Sponsored the project of William T. Osler, Fractal banners at the STEM Symposium, April 21, 2006.

40. Sponsored the project of Matthew R. Oster, A spiral of triangles related to the great pyramid  STEM Symposium, April 21, 2006.

41. Sponsored the project of Walter Jacob, A simple construction to approximate any angle at the STEM Symposium, April 21, 2006

42.  Sponsored the project of  David Grochowski, An asymptotic approach to constructing the hyperbola at the STEM Symposium, April 21, 2006.

43.  Sponsored the project of Walter Jacob, Euler's E46 and finding sums of series at the STEM Symposium, April 20, 2007.

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