June 6, 2007

Thomas J Osler

1. *Leibniz rule for fractional derivatives generalized and an
application
to infinite*

*series*, SIAM J. Appl. Math., 18 (1970), pp. 658-674. MR 41#5562
(download from JSTOR) download PDF
file

2. *The fractional derivative of a composite function*, SIAM
J.
Math. Anal, 1 (1970),

pp. 288-293. MR 41#5563 download
PDF file

3. *Taylor’s series generalized for fractional derivatives and
applications*,
SIAM J.

Math. Anal. 2 (1971), pp. 37-48. MR 45#3682 download PDF file

4. *Fractional derivatives and leibniz rule*, Amer. Math.
Monthly,
78 (1971),

pp. 645-649. (download from JSTOR) download
PDF file

5. *A further extension of Leibniz rule to fractional derivatives
and its relation to Parseval’s formula*, SIAM J. Math. Anal., 3
(1972),
pp. 1-16. MR 48#2323a download PDF
file

6. *An integral analogue of Taylor’s series and its use in
computing
Fourier*

*transforms*, Math. Comp., 26 (1972), pp. 449-460. MR 46#5950.
download
PDF file

*7. The integral analog of the Leibniz rule*, Math. Comp., 26
(1972),
pp. 903-915.

MR 47#2792. download PDF file

8. *A correction to Leibniz rule for fractional derivatives*,
SIAM
J. Math. Anal., 4 (1973), pp. 456-459. MR 48#2323b download
PDF file

9. *Differences of arbitrary order *(With J. B. Diaz), Math.
Comp.,
28 (1974),

pp. 185-202. MR 49#11077 (download from JSTOR) download
PDF file

10. *Fundamental properties of fractional derivatives via
Pochhammer
integrals*.(With J. L. Lavoie and R. Tremblay). A paper in
"Fractional
Calculus and Its Applications" edited by B. Ross, Springer-Verlag, New
York, 1975, pp. 323-356.

MR 57#16490

11*. Open questions for research*. (Proc. Internat. Conf. Univ.
New Haven, West

Haven, Conn., 1974) pp. 376-381. Lecture Notes in Math., Vol. 457,
Springer,

Berlin, 1978. (A. M. Brickner) MR 57#16493

12. *An indentity for simplifying certain generalized
hypergeometric
functions*, Math Comp., 29 (1975), pp. 888-893. MR 51#10710 download
PDF file

13. *Leibniz rule for fractional derivatives used to generalize
formulas
of Walker and Cauchy*, Bul. Inst. Polit, Jasi, 21-(25), 1-2, (1975),
pp. 21-24. MR 52#8822 download
PDF file

14. *Fractional derivatives and special functions*, SIAM
Review,
18 (1976),

pp. 240-268. MR 53#13666 download
PDF file

15. *A quick look at Lyapunov space*, Mathematics and Computer
Education,

28 (1994), pp. 183-197.

16. *A mathematical art exhibit*, Mathematics and Computer
Education,
29 (1995),

pp. 245-252.

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. download
PDF version

18. *The trinomial triangle, *(with James Chappell, student),
The
College Mathematics Journal, Vol. 30, No. 2, 1999, pp. 141-142. download
PDF version

19. *Extending the Babylonian algorithm, *Mathematics and
Computer
Education, Vol. 33, No. 2, 1999, pp. 120-128. download
PDF version

20. *The tautochrone under arbitrary potentials using fractional
derivatives,
*(with
Eduardo Flores), American Journal of Physics, (Am. J. Phys.), 67(1999),
pp. 718- 722. download PDF version

21. *The united Vieta’s and Wallis’s products for pi,*
American
Mathematical Monthly, 106 (1999), pp. 774-776. download
PDF version

22. *Fractal Movies,* Mathematics and Computer Education, Vol.
33 (1999), pp. 236-243. download PDF
version

*23. A child’s garden of fractional derivatives, *(with Marcia
Kleinz), The College Mathematics Journal, Vol. 31, No. 2, (2000), pp.
82-887
download
PDF version

*24. The binomial to binomial theorem,* The College Mathematics
Journal, Vol. 31, No. 3, (2000), pp. 211-212. download
PDF version

*25. Spacetime numbers the easy way, *(with Nick Borota and
Eduardo
Flores), Mathematics and Computer Education, Vol. 34, No. 2, (2000),
pp.
159-168. download PDF version

*26. Playing with partitions on the computer,* (with Abdul
Hassen),
Mathematics and Computer Education , Vol. 35, No. 1, (2001), pp. 5-17.
download
PDF version

*27. Mutations of the Mandelbrot set, *(with Jae
Hattrick-Simpers,
student), Mathematics and Computer Education, Vol. 35, No. 1, (2001),
pp.
18-26. download PDF version

*28. The remarkable incircle of a triangle*. (with Ira Fine),
Mathematics
and Computer Education, Vol. 35, No. 1, (2001), pp. 44-50. download
PDF version

*29. Cardan polynomials and the reduction of radicals, *Mathematics
Magazine, Vol 47, No. 1, (2001), pp. 26-32. download
PDF version

*30. The rotating tautochrone, *(with Eduardo Flores), Journal
of Applied Mechanics,

68(2001), pp. 353-356. download PDF version

31. *Rearranging terms of a harmonic-like series, *Mathematics
and Computer Education, 35(2001), pp. 136-139. download
PDF version

32. *Fun with 0.999...* , The AMATYC Review, 22(2001), pp.
53-56.
download
PDF version

33. A*n unusual approach to Kepler’s first law*, American
Journal of Physics, 69(2001), pp. 1036-8. download
PDF version

34. *An unusual view of the ellipse*, Mathematics and Computer
Education, 35,(2001), pp. 234-236. download PDF
version

35. *Variations on Vieta’s and Wallis’s products for pi,*
(with
Michael Wilhelm), Mathematics and Computer Education, 35(2001), pp.
225-232.
download
PDF version

36. *A tale of two series*, (with Marcus Wright),
The
College Mathematics Journal, 33(2002), pp. 99-106. download
PDF file

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. download
PDF version

38. *Fermat’s little theorem from the multinomial theorem*,
The
College Mathematics Journal, 33(2002), p. 239. download
PDF version

39. *A table of the partition function*, (with Abdul Hassen
and
T. R. Chandrupatla), The Mathematical Spectrum, 34(2001/2002), pp.
55-57.
download PDF version

40. *Visual Basic for QuickBasic Programmers*, (with Seth
Bergmann
and T. R. Chandrupatla), Mathematics and Computer Education, 36(2002),
pp. 133-138. download PDF file

41. *Functions of a spacetime variable*, (with Nicolae A.
Borota),
Mathematics and Computer Education, 36(2002), pp. 231-239. Download
PDF file

42. *An easy introduction to biplex numbers*, (with Dipti
Bardhan),
Mathematics and Computer Education, 36(2002), pp. 278-286. Download
PDF file

43. *An easy look at the cubic formula*, Mathematics and
Computer
Education, 36(2002), pp. 287-290. Download
PDF file

44. *Proof without words: Integral of sine squared, *The
AMATYC
Review, 24(2002), p. 65. Download
PDF file

45. *A computer hunt for Apery's constant, *(with Brian
Seaman),
Mathematical Spectrum, 35(2002/2003), No.1, pp. 5-8. Download
PDF file

46. *A magic trick from Fibonacci*, (with James Smoak), The
College
Mathematics Journal, 34(2003), pp. 58-60. Download
PDF file

47. *Variations on a theme from Pascal's triangle*,
The College Mathematics

Journal, 34(2003), pp. 216-223.
Download PDF file

48. *Visual proofs of two integrals, *The College
Mathematics
Journal, 34(2003), p.231-232.. Download
PDF file

49. *An unusual product for sin z and variations of Wallis’s
product,
*The Mathematical Gazette, 87(2003), pp. 134-139. Download
PDF file

50. *Finding Zeta(2p) from a product of sines. *The
American Mathematical Monthly, 111(2004), pp. 52-54. Download
(PDF) original version containing motivational material.

Download (PDF) final
accepted
version (more formal with less motivation)

51. *Another intuitive approach to Stirling’s formula*,
International Journal of Mathematical Education in Science and
Technology, 35(2004), pp.111-118. Download
PDF file.

52. *Geometric construction of Pythagorean triangles, *(with
Tirupathi
R. Chandrupatla), Mathematics and Computer Education, 38(2004), pp.
90-91.

Download PDF file

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. Download
(PDF) version.

54. *Extending Theon's ladder to any square root, *(with
Shaun
Giberson), The College Mathematics Journal, 35(2004), pp. 222-226. Download PDF file

55. *Problems on divisibility of binomial coefficients*, (with
James Smoak). The AMATYC Review, 25(2004), pp. 17-21.Download PDF file.

56. Generalizing integrals
involving
x^x and series involving n^n, (with Jeffrey Tsay). Mathematics
and Computer Education, 39(2005), pp. 31-36. Download PDF File

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. Download
PDF file

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. Download
PDF file

59. *Unexpected constructable numbers*, The AMATYC Review,
26(2005), no. 2, pp. 2-3. Download
PDF file

60. Some* unusual expressions for the inradius of a triangle, *(with
Tirupathi R. Chandrupatla), The AMATYC Review, 26(2005), no.2, pp.
12-17. Download
PDF file

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. Download PDF file

62. *Proof Without Words: Arc length of the cycloid, *
The Mathematical Gazette, 89(2005), no. 515, page 250. Download PDF file.

63. Ptolmey vs. Copernicus. (With
Joseph Diaco.) The Mathematical Spectrum, 38(2005/2006), pp.
3-6. Download
PDF File

64. The general Vieta-Wallis product for pi, The Mathematical Gazette, 89(2005), pp. 371-378. Download PDF file

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. Download
PDF file

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. Download
PDF file

68. A mechanical view of
Archimedes quadrature of the parabola. The
College Mathematics Journal, 37(2006), pp. 24-28. Download
PDF file

69. Interesting finite and
infinite products from simple algebraic identities. The
Mathematical Gazette, 90(2006), pp. 90-93. Download
PDF File.

71. A spiral of triangles related to the great pyramid, with Matthew Oster. The Mathematical Spectrum 38(2005/2006), pp. 108-112,. Download PDF File

72. An asymptotic approach to constructing the hyperbola, with David Grochowski. The Mathematical Spectrum 38(2005/2006), pp. 113-115. Download PDF File

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. Download PDF file

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/. Download
PDF file

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/. Download
PDF file

76. Translation with notes of
Euler’s
paper
E796 ( with Kristen
McKeen), 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.”, on the web at
the Euler Archive http://www.math.dartmouth.edu/~euler/. Download
PDF file .

77. Synopsis by section of Euler's
paper E769 ( with
Kristen McKeen), 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”, on
the web at the Euler Archive http://www.math.dartmouth.edu/~euler/.
Download
PDF file

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.) On
the web at the Euler Archive
http://www.math.dartmouth.edu/~euler/. Download
PDF file

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.) on
the web at the Euler Archive
http://www.math.dartmouth.edu/~euler/. Download PDF file

80. The integers of James Booth, (with John F. Kennedy), Mathematical Spectrum, 39(2006/2007), pp. 71-72. Download PDF file

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. Download PDF file

82. Some cosine relations and the regular heptagon, ( with Phongthong Heng) Mathematics and Computer Education, (41)2007, pp. 17-21. Download PDF file

83. Developing formulas by skipping rows in Pascal's triangle (with Robert J. Buonpastore). Mathematics and Computer Education, (41)2007, pp. 25-29. Download PDF file

84. Some long telescoping series. The Mathematical Gazette, 91(2007), pp. 104-5. Download PDF file

85. Finding Zeta(2n) from a recursion relation for Bernoulli numbers (with Jim Zeng), The Mathematical Gazette, 91(2007), pp. 123-6. Download PDF file

86. The quadratic equation as solved by Persian mathematicians of the middle ages, (with Mohamed Teymour). Mathematical Spectrum, 39(2006/2007), pp. 115-8. Download PDF file

87. Lucky fractions: Where bad arithmetic gives correct results, Mathematics and Computer Education, 41(2007), pp.162-167.

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. Download PDF file

89. The unlikely connection between partitons and divisors, (with Abdul Hassen and T. R. Chandrupatla). To appear in The College Mathematics Journal.

90. Geometric constructions
approximating pi related to Vieta's product of nested radicals. To
appear in The Mathematical Spectrum.

92. An unusual proof that Fm divides Fmn for Fibonacci numbers using hyperbolic functions, (with Adam Hilburn). To appear in The Mathematical Gazette November 2007.

93. Another geometric vision of the hyperbola. To appear in The Mathematical Spectrum.

94.

95. Euler's little summation formula and sums of powers, (with Andrew Robertson). To appear in The Mathematical Spectrum.

96. Oblique-angled diameters and the conic sections, with Edward Greve. To appear in The Mathematical Spectrum.

97. Euler's little summation formula and special values of the zeta function. To appear in The Mathematical Gazette in July 2008.