**August 22, 2015**

**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.

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) *s*ubmitted 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.

72. *An asymptotic approach
to constructing the hyperbola*, with David Grochowski.
The Mathematical Spectrum, 38(2005/2006), pp. 113-115. Submitted to the
Mathematical Spectrum on October 12, 2005. Revision requested November 3, 2005
and sent via email with bios on November 11, 2005. Accepted November 16, 2005.

73. *A collection of numbers whose proof of irrationality is like that of the
number e, *(with Nicholas Stugard). Mathematics
and Computer Eduation, 40(2006), pp. 103-107.
Accepted February 10, 2006. Submitted to Mathematics and Computer Education
on May 3, 2005. Revision sent October 13, 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.

81. *A simple geometric
method of estimating the error in using Vieta's
product for pi*, International Journal of Mathematics Education in Science
and Technology, (38)2007, pp. 136-142. Submitted to the International Journal
of Mathematics Education in Science and Technology on August 16, 2005 and **accepted
on August 24, 2006.** Revision requested June 15, 2006. Revised version sent
June 30, 2006**.** Abstract sent July 11, 2006.

82. *Some cosine relations and the regular heptagon, *( with Phongthong Heng) Mathematics and
Computer Education, (41)2007, pp. 17-21. . Submitted by email to Mathematics
and Computer Education on February 22, 2006 and accepted **August 11, 2006**.
Page proof sent August 18, 2006. Originally submitted to The College
Mathematics Journal on September 6, 2004. Resubmitted on January 26, 2006
because the original editor failed to process the paper. Rejected February 14,
2006.

83. *Developing formulas by skipping rows in Pascal's triangle *(with
Robert J. Buonpastore). Mathematics and Computer
Education, (41)2007, pp. 25-29. Submitted to Mathematics and Computer
Education on July 4, 2006, and **accepted on October 16, 2006**. Originally
submitted to The Mathematical Spectrum on June 28, 2006 and rejected July 2,
2006.Submitted to Mathematics and Computer Education on July 4, 2006, and **accepted
on October 16, 2006**. Originally submitted to The Mathematical Spectrum on
June 28, 2006 and rejected July 2, 2006.

84. *Some long telescoping series. *The Mathematical Gazette, 91(2007),
pp. 104-5. Submitted to The Mathematical Gazette on September 15, 2005 and
accepted on September 27, 2005. Scheduled to appear March 2007. Corrected proof
sent Jan 3, 2007.

85. *Finding Zeta(2n) from a recursion relation for Bernoulli numbers *(with
Jim Zeng), The Mathematical Gazette, 91(2007), pp. 123-6*. *Accepted April
25, 2005, and due to appear March 2007. PDF and WORD versions emailed on May 6,
2005. Submitted to The Mathematical Gazette on February 22, 2005. Corrested proof sent Jan 3, 2007. Originally submitted to
the American Mathematical Monthly on February 26, 2004 and rejected on
July 15, 2004 because they do not have room for it. Next submitted to
Mathematics Magazine on July 19, 2004, and rejected on Feb. 17, 2005.

86.** ***The quadratic equation as solved by Persian mathematicians of the
middle ages, *(with Mohamed Teymour). Mathematical
Spectrum, 39(2006/2007), pp. 115-8. Submitted to The Mathematical Spectrum on
June 23, 2005.** Accepted July 1, 2005.**

87. *Lucky fractions: Where bad arithmetic gives correct results,** *Mathematics and Computer Education,
41(2007), pp.162-167.Submitted to Mathematics and Computer Education on
November 22, 2006.

88. *Constructing a line segment whose length is equal to the measure of a
given angle*, (with Walter Jacob, IV), International Journal of Mathemeatical Education in Science and Technology,
38(2007), pp. 529-230. Submitted to the International Journal of Mathemeatical Education in Science and Technology on
February 6, 2006 and accepted on August 25, 2006. Revised version sent June 28,
2006 via email. Originally submitted to The Mathematical Gazette on January 10,
2006, and rejected February 1, 2006.

89. *Surprising connections between partitons
and divisors*, (with Abdul Hassen and T. R. Chandrupatla), The College Mathematics Journal, 38(2007),
pp. 278-287. 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.

90. *Oblique-angled diameters and the conic sections*, with Edward Grev, Mathematical Spectrum, 40(2007/2008), pp. 26-30..
Submitted to The Mathematical Spectrum on December 11, 2006 and accepted **January
4, 2007.** Revisions sent Jan 21, 07.

93. *An unusual proof
that Fm divides Fmn for
Fibonacci numbers using hyperbolic functions, (with Adam Hilburn).
*The Mathematical Gazette, 91(2007), pp. 510-512. Submitted to The
Mathematical Gazette on March 15, 2006 and accepted on April 22, 2006.
.Originally submitted to the American Mathematical Monthly on May 2, 2005, and
rejected August 2, 2005. Then submitted to Mathematics Magazine on August 9,
2005 and rejected March 6, 2006.

98. Exact values of the hyperbolic functions. Mathematics and Computer Education, 42(2008), pp. 58-59. Submitted to Mathematics and Computer Education on January 3, 2007 via email. Accepted August, 2007.

** **100.
*Translation with notes of Euler's paper E83,* (with __Edward Greve__)On some properties of conic sections
that are shared with infinitely many other curved lines. On the web at the
Euler Archive http://www.math.dartmouth.edu/~euler/

101. *Synopsis of Euler's paper E83,* On some
properties of conic sections that are shared with infinitely many other
curved lines. On the web at the Euler Archive http://www.math.dartmouth.edu/~euler/

.

Submitted to The Mathematical Specrum on October 30, 2007. Accepted November 23, 2007.

105.
*A remarkable formula for approximating the sum of alternating series. *The Mathematical Gazette, 93(2009),
pp. 76-82. Submitted to The Mathematical Gazette on October 30, 2007 and
accepted on January 14, 2008. Scheduled to appear March 2009. Corrected
page proof returned Jan 18, 2009.

110*. On numbers equal
to the sum of two squares in more than one way,* (with Ming-Sun
Li, Kathryn Robertson, Abdul Hassen, Christopher S.
Simons and Marcus Wright). Mathematics and Computer Education, 43(2009), pp.
102-108. Submitted March 4, 2008 to Mathematics and Computer Education, and
accepted about November 1, 2008.

111. *Conjectures from a historic table by John Wallis*, with Lee Collins.
Mathematical Spectrum, 42(2009/2010), pp. 14-19. Submitted to The Mathematical
Spectrum on December 24, 2008. Revisions requested and sent on Feb 14, 2009 and
accepted Feb 25, 2009.

112. *Triangles of equal area in a hyperbola*, with Adam Romasko. Mathematical Spectrum, 42(2009/2010), No. 2, pp.
70-74. Submitted to The Mathematical Spectrum on December 24, 2008. Revisions
requested and sent on Feb 14, 2009 and accepted Feb 25, 2009.

113. *Euler and the functional equation for the zeta function*. Mathematical Scientist, 34(2009), pp. 62-73.
Submitted electronically and one hard copy to The Mathematical Scientist on
February 6, 2009 and accepted Feb 26, 2009. To appear December 2010. Originally
submitted (electronically) to International Journal of Mathematical Education
in Science and Technology on December 28, 2008 and rejected on February 6,
2009.

114 *The tables of John Wallis and the discovery of his product for pi. *The
Mathematical Gazette, 94(2010), pp. 430-437. Submitted to The Mathematical
Gazette on January 2, 2009. Revisions requested on Feb 14, 2009. Revised
version sent by email on Feb 16, 2009. Accepted March 3, 2009.

115. *Five historic formulas for pi*. Mathematics and Computer Education,
43(2009), pp. 250-258. Submitted to Mathematics and Computer Education on
December 13, 2008, and accepted on April 14, 2009.

117. *Lord Brouncker’s forgotten sequence of
continued fractions for pi.*, International Journal of Mathematical
Education in Science and Technology, Volume 41, Issue 1 January 2010 , pages 105 – 110.
Submitted to International Journal of
Mathematical Education in Science and Technology on February 16, 2009 and
accepted on June 22, 2009. Originally submitted to the American Mathematical
Monthly on January 20, 2009 and rejected Feb 8 2009.

118. *Translation with notes of Euler's paper E745,*
(with Christopher Tippie and Kristin Masters) On the continued fractions of Wallis. on the web at the Euler Archive

119. *Reflections and
Notes on Euler’s paper E745, *(with Christopher Tippie
and Kristin Masters) On the continued fractions of
Wallis. on the web at the Euler
Archive

120. *Synopsis of
Euler’s paper E745, *(with Christopher Tippie and
Kristin Masters) On the continued fractions of Wallis. on the web at the Euler Archive

121.* Euler’s parallel oblique angled diameters,* The Mathematical Gazette,
95(2011), pp. 40-48.

*S*ubmitted to The Mathematical Gazette
on December 14, 2008 and returned on May 31 with request that the two papers be
combined into one. Revision combining two papers sent July 1, 2009. Accepted on
September 1, 2009/

122. *Translation of Euler's paper ,* (with Jasen Scaramazza) Memoire sur la plus grande
equation des planets,** **(Memoir on the Maximum value of an Equation
of the Planets). on the web at the Euler Archive http://www.math.dartmouth.edu/~euler/.

123. N*otes on
Euler's paper ,* (with Jasen Scaramazza) Memoire sur
la plus grande equation des planets,** **(Memoir
on the Maximum value of an Equation of the Planets). on the web at the Euler Archive http://www.math.dartmouth.edu/~euler/.

124. Synopsis *of Euler's paper ,* (with Jasen Scaramazza) Memoire sur la plus grande equation des
planets,** **(Memoir
on the Maximum value of an Equation of the Planets). on the web
at the Euler Archive http://www.math.dartmouth.edu/~euler/

125. *The perimeter of an ellipse*, (with Tirupathi
R. Chandrupatla). The Mathematical Scientist,
35(2010), pp. 122-131. Submitted to The Mathematical Scientist on March 1,
2010, and request for revisions on March 15, 2010. Accepted on March 30, 2010.
Originally submitted to Mathematics and Computer Education on March 26, 2009
and rejected March 1, 2010.

126. *An interesting generalization of the half angle formulas to complex
numbers, *(with Marcus Wright), The Mathematical Gazette, 95(2011), p.
327. Submitted on March 2, 2010 and
accepted on April 14, 2010 by The Mathematical Gazette. Due to appear July
2011.

127. *Euler’s method of integration by parts* (with Steve Donahue).
The Mathematical Gazette, 96(2012), pp. 115=116. Submitted to the Mathematical
Gazette on September 1, 2010. Assigned the number 4314 and accepted on
September 15, 2010.

128. *Planar
biarc curves – A geometric view, *(with T. R. Chandrupatla). The Mathematical Scientist, 36(2011),
pp. 126-132. Submitted to The Mathematical Scientist on October 4,
2010. Revisions requested on October 28, 2010 and sent on November 9, 2010.
Paper accepted on November 15, 2010.

129. *Law of cosines generalized for any polygon and any polyhedron, *(with
Lee Collins), The Mathematical Gazette, 95(2011), pp. 240-243. Submitted to The Mathematical Gazette on
January 7, 2010 and review sent March 1, 2010. We did not like the requested
changes and asked for another referee to examine the paper. Second referee’s
report received April 29, 2010 and revised version sent by email on May 8,
2010. Accepted January 7, 2011. To
appear November 2011.

130. *The missing fractions in Brouncker’s sequence
of continued fractions for pi. *The Mathematical Gazette, 96(2012), pp.
221-225. Accepted by The Mathematical Gazette on October 5, 2011 and due to
appear July, 2012. Submitted to the Mathematical Gazette on January 31, 2011.
Revision 1 sent May 19, 2011. Revision 2 sent September 19, 2011. Revision 1
sent May 19, 2011. Revision 2 sent September 19, 2011. Originally submitted to
the American Mathematical Monthly on December 29, 2010 and rejected on January
15, 2011.

131. *How Euler found the eccentricity of planetary orbits, *(with Jasen Scaramazza). The Mathematical
Scientist 32(2014), pp. 89-96. Submitted
on November 20, 2011 to The Mathematical Scientist via email and snail mail and
accepted on November 28, 2011. To appear December 2012.

132. Diophantine approximation and the irrationality of certain numbers, (with Eric Jones). Mathematics and Computer Education, 46(2012), pp. 125 - 130. Download PDF file

Submitted to Mathematics and Computer Education on December 23, 2010. Accepted December 22, 2011.

133. *Partial sums of divergent series that cannot be an integer.* The
Mathematical Gazette, 96(2012), pp. 515-519. .Submitted on December 13, 2011 to
The Mathematical Gazette. Small revisions sent by email on about January 18 and
accepted on January 24, 2012. Due to appear November 2012,

134. *The devil’s series –* *Did it
fool Euler. *(with Steven Donahue), The Mathematical Gazette, 97(2013), pp.
133 – 137. Submitted on December 16,
2011 to The Mathematical Gazette. Accepted March 15, 2012

135. *An interesting bilateral series generalizing the series for zeta of 2, *(with
Cory Wright), The Mathematical Gazette, 97(2013), pp. 131 – 133. Submitted February 8, 2012 to The
Mathematical Gazette.

136 .*Unexpected connections between three famous formulas for pi. *Submitted
to the Fibonacci Quarterly on November 14, 2011, and rejected on February 11,
2012.

137.* Four derivations of an interesting bilateral series generalizing the
series for zeta of 2. *(with Cory Wright). The International Journal of
Mathematical Education in Science and Technology, 44(2013), pp. 456 – 461.

138. *Interesting subseries of the harmonic series*. Mathematics and Computer Education, 46(2012),
pp. 169 – 173. Submitted on December 4,
2011 to Mathematics and Computer Education.

139. *Recursive formulas related to the AGM, *(with Tirupathi R. Chandrupatla). The
Mathematical Gazette, 98(2014), pp. 484-486. Submitted January 18, 2013 to The Mathematical Gazette. Revision
requested on December 9, 2013. Paper accepted on December 22, 2013.

140 *Vieta’s** product for
Pi from Archimedes, *The Mathematical Gazette, 98(2014), pp. 429-431.
Submitted to The Mathematical Gazette on January
6, 2014. Revision requested on February 14, 2014 and revised paper sent on
March 23, 2014. Accepted on March 24, 2014. Due to appear November 2014.

141 *Can
divergent series be of value?. *The Mathematical Scientist 39(2014), pp.
100-106. Submitted to The Mathematical Scientist on March 26, 2014 via email.
Accepted on April 2, 2014.

142 *A
higher look at vertical motion. *The Mathematical Scientist 39(2014), pp
138-142. Submitted on November 21, 2011 to The Mathematical Scientist via email
and snail mail. Referee’s report received on June 21, 2012 requesting extensive
revision. Revised version sent on March 30, 2014

143 A novel approach to integral csc x, (with Walter Jacob). The Mathematical Gazette, 98(2014), pp. 518-519. Submitted to the Mathematical Gazette on May 7, 2014 and accepted on May 13, 2014. Due to appear in November 2014.

145 *Short and
fuzzy derivations of five remarkable formulas for primes, *The Mathematical
Gazette, 99(2015) pp. 220 – 225. Submitted to The Mathematical Gazette on March 26, 2014 and
rejected on September 4, 2014. Resubmitted on September 19, 2014..

**II.
Papers accepted for publication and awaiting printing**

144 *A product of nested radicals for the AGM.*, Accepted July 20, 2014 by The American Mathematical
Monthly. Due to appear in mid to late 2015, Submitted on March 23, 2014 as a
note to the American Mathematical Monthly. Positive referee’s report received
on April 23, 2014 and revision sent May 3, 2014.

146 *Iterations for
the lemniscate constant resembling the Archimedean
algorithm for pi. *Accepted by The
American Mathematical Monthly on May 27,
2015. Submitted on January 4, 2015.

147.* A table of definite integrals from the
marriage of power and Fourier series, *(with James Rosado). Accepted on June
24, 2015 by Revista
Scientia.
Submitted to Revista Scientia
on January 1, 2015. Submitted to International Journal of Pure and Applied
Mathematics on September 19, 2014, bur no response from this journal.
Originally submitted to The Proceedings of the American Mathematical Society on
August 22, 2014 and rejected on September 14, 2014..

**III
Papers submitted and being reviewed **

*1.
**Some
Definite Integrals from Fourier Series *(with James Resado).
Submitted to The mathematical Gazette on March 26, 2014.

*2.
**A table of definite integrals from the marriage of
power and Fourier series, *(with James
Rosado). Submitted to Revista Scientia on January 1,
2015. Submitted to International Journal of Pure and Applied Mathematics on
September 19, 2014, bur no response from this journal. Originally submitted to
The Proceedings of the American Mathematical Society on August 22, 2014 and
rejected on September 14, 2014..

3. An unusual series summed by Goldbach and Euler. Submitted as a note to the American Mathematical Monthly on October 27, 2007, and rejected October 28, 2008.

*4.Four Arc Approximation of Ellipses*, (with Tirupathi R. Chandrupatia). Submitted
to The Mathematical Scientist on October 24, 2007.

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 **

14.
*Morphing Lord Brouncker’s
Continued Fraction for pi into the Product of Wallis. *Presented at the
National Meeting of the American Mathematical Society on January 9 2009 in
Washington, D.C.

15.
*Euler and the continued fractions of
Wallis and Brouncker. *Presented at the Eighth
annual meeting of The Euler SocietyAt Rodger Williams
University, Bristol, RI on July 14, 2009.

16.
*Another look at Euler’s parallel oblique
angled diameter*. Presented at the
National Meeting of the American Mathematical Society on January 9 2010 in San
Francisco.

17.
*How Euler found the functional equation
for the zeta function. *Presented at Temple University on March 23, 2010.

18.
*Euler’s paper E83 in which he finds
curves that share properties with the conic sections*. Presented at the Ninth
Annual Meeting of the Euler Society at Adelphi Univeristy,
Garden City, NY on July 20, 2010.

19. *Unexpected
connections between three old famous formulas for pi. *Presented at
"The DIMACS-Rutgers Experimental Math Seminar."

20.
*Expressions with Pi and the lemniscates constant expanded as infinite products and
continued fractions. *Presented at the National Meeting of the American
Mathematical Society on January 8 2011 in*
*New Orleans.

21. *The devil’s
series - Did it fool Euler?, *Presented at the National
Meeting of the American Mathematical Society on January 4, 2012 in Boston.

22.
*A new look at several old formulas for
Pi. * Presented at the National
Meeting of the American Mathematical Society on January 4, 2013.

**VII.
Solutions to Journal Problems Submitted **

**VIII.
Sponsoring Student Research **

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

44. Sponsored the project of Christopher Tippie, *Euler and the continued fractions of John
Wallis *at the STEM Symposium, April 17, 2009.

45. Sponsored the project of Jonathon Weisbrod, *A tree of primitive Pythagorean triples *at
the STEM Symposium, April 17, 2009.

46. Sponsored the project of Jasen Scaramassa, *Euler and
the equations of the planets *at the STEM Symposium, April 17, 2009.

47. Sponsored the project of Jasen Scaramassa, *How Euler
found the eccentricity of the planets *at the Undergraduate Poster Session
of the National Meeting of the American Mathematical Society in San Francisco
on January 15, 2010.

48. Sponsored the project of Lee Collins, *A generalization of the law of cosines *at the Undergraduate Poster
Session of the National Meeting of the American Mathematical Society in San
Francisco on January 15, 2010.

49. Sponsored the project of Jonathan Weisbrod, *Patterns associated with the Barning tree of primitive Pythagorean triples *at the
Undergraduate Poster Session of the National Meeting of the American
Mathematical Society in San Francisco on January 15, 2010.

50. Sponsored the project of Steven Donahue, *Translation of Leonhard Euler’s paper “An exercise in analysis in which
a very general summation of series is found” *at the STEM Symposium, April
23, 2010.

51. Sponsored the project of Eric Jones, *A
selection of numbers whose irrationality can be determined by Diophantine
approximation at the *Undergraduate Poster Session of the National Meeting
of the American Mathematical Society in New Orleans on January 8, 2011.

52. Sponsored the project of James Rosado, *The marriage of Taylor and Fourier series to evaluate definite
integrals. *At the STEM Symposium, April 25, 2014.

53. Sponsored the project of Sky Waterpeace,* Using the Archimedean algorithm to find Vieta’s product of nested radicals for Pi. . *At the
STEM Symposium, April 25, 2014.* *