Introduction
Teaching Interests
Professional Activities
Mathematical Bridge,
Queens College,
Cambridge
Sir Isaac Newton,
Trinity College
Charles L. Dodgson,
i.e., Lewis Carroll
Christ Church, Oxford
Carroll's "flowchart" for applying the propositions in
Euclid.
Medieval Illuminated MS.
An unknown woman teaching geometry to monks.
Archimedes
|
|
College of Natural and Social
Sciences
Department of Mathematics
Shirley B. Gray
Office: ST F218
Phone: (323) 343 - 2163 MATH
320
FAX: (323) 343 - 5071
Email: sgray@calstatela.edu
INTRODUCTION
Dr. Gray, Dr. Stewart Venit and
Dr.
Russ Abbott have created and maintained this web site under the
auspicies
of the National Science Foundation and the Arnold and Mabel Beckman
Foundation.
The prestigious journal Science
recognized our work in Fall, 2006. See <http://curvebank.calstatela.edu>
for a "FLASH" introduction as well as the Home Page <http://curvebank.calstatela.edu/home/home.htm>.
In addition to hosting the NCB web site, Dr. Gray enjoys teaching MATH
320
History of Mathematics. The CSULA campus has a
unique asset. Our campus is located near the Huntington Library
in San Marino,
CA. The Huntington's priceless collection of mathematical books
and
incunabula was recently augumented by the acquisition of 66.000 items
from
the Burndy Collection. Many works in both the old and new holdings are
rare
first editions. Thus, CSULA students have access to what may be
called
the finest collection in the history of mathematics and science in
North
America. Our History of Mathematics course offers students and
faculty
the unique pleasure of seeing these books and their magnificent
illustrations.
TEACHING INTERESTS
At the Huntington, we have examined the the following
titles:
A Sampler of the Huntington Collection
|
Date
|
Mathematician
|
Title
|
| 1279 |
Ptolemy |
Almagest |
| 1482 |
Euclid |
Elements (Several editions.) |
| 1543 |
Copernicus |
De Revolutionibus Orbium Coelestium |
| 1632 |
Galileo |
Dialogo Sopra Due Massimi Sistemi del Mondo |
| 1545 |
Cardano |
Ars Magna |
| 1637 |
Descartes |
Discours de la Méthode |
| 1687 |
Newton |
Principia |
| 1759 |
Châtelet |
Principia |
| 1748 |
Agnesi |
Instituzioni Analitiche
http://instructional1.calstatela.edu/sgray/Agnesi |
| 1716 |
L'Hôpital |
Analyse des Infiniment petits |
| 1777 |
Euler |
Introductio In Analysin Infinitorum |
| 1801 |
Gauss |
Disquisitiones arithmeticae |
| 1566 |
Apollonius |
Conics |
| 1543,1544 |
Archimedes |
Opera Omni |
| 1556 |
Juan Diez, O.F.M. |
Sumario Compendioso |
| 1557 |
Recorde
|
"The whetstone of witte, which is the
seconde
part of Arithmetike . . ."
|
1697
|
Johann Bernoulli
|
Acta
Eruditorium
|
| and many others. |
Highlights
of PROFESSIONAL
ACTIVITIES
Among other delights, Gray has been
privileged
to examine the Bodleian Library's copy of Euclid's Elements
(888 A.D.)
at Oxford University. This is the world's oldest dated edition. Another
historically
important edition, ca. 900 A.D., is housed in the Vatican
Library.
In 2004, Gray was permitted to examine this copy once stolen by
Napoleon
and now returned to the archives
of the Biblioteca Vaticana, Roma.
This trip also permitted her the time to be a Reader in the famed
Laurentian
Library in Florence, Italy. Later, in 2005, she viewed the oldest
surviving
copy of the Nine Chapters on
Mathematical
Art in the Shanghai Library. Dr. Gray concurred when a
student
once told her, "You are a very lucky woman."
A "short list" of other favorite
trips
and talks includes:
AMS-MAA National Meetings. The newly established National Curve
Bank.
Baltimore, MD, January 15, 2003 and all subsequent NSF Poster Sessions.
Brown Bag Lunch Series, The National Curve Bank,
Northwestern
University, March, 2003.
AMS - MAA National Meeting, San Antonio, Texas. The Lost Palimpsest
of
Archimedes: The Method. January, 1999.
Gray's first web project was on Maria Gaetana Agnesi and
includes
the first translation of the closing of her famous calculus book.
[ See < http://instructional1.calstatela.edu/sgray/Agnesi
>.]
Gray's first videotape project appeared on KLAC-TV Channel 58
and
featured students learning to use the rather new graphing calculators
in
April, 1997. Using a Graphing Calculator had five airings
of
the tape just prior to the AP Calculus Exam.
Gray has especially enjoyed the network of friends that was
created
by participating in
IHMT, Washington, D.C. Institute for the History of Mathematics in
Teaching
sponsored by the MAA/NSF. June, 1996 and June, 1997.
|
Flowers were a gift of MATH 320 History
of
Mathematics, Winter, 2006.
|
Date
|
Favorite Publications
|
2009
|
Gray, Shirley B., "BSHM
detective story continued" BSHM
Bulletin, 24 (3), 2009.
 ,  , Science and Culture Review, 6
(3), 2009.
Translation by Yibao XU.
|
| 2008 |
Gray, Shirley B., "A Centennial Celebration of Two Great
Scholars," Notices of the American
Mathematical Society, 55 (7), August, 2008, pp. 776-783.
Gray, Shirley B., "On the Equals Sign - Our 'Twins': A Tour through
Original Sources," The Mathematical Intelligencer, 30 (2),
2008, pp. 19-23.
|
| 2006 |
“Bent into Shape”, NETwatch (M. Leslie, ed.); Science,
2006, 314, 571. [(October
27, 2006)]
“A Renie for the Brachistochrone, Short Takes (F.
Gouvêa, ed.); Focus, 2006, 26(5),
21.
Gray, Shirley B. and Gordillo, Gustavo. “The
Brachistochrone: For the ‘shrewdest mathematicians of all the world’
“ CMC ComMuniCator. 30(3) 34 – 36, March, 2006.
Gray, Mary and Gray, Shirley B. “Calculus: A Play in
London” math HORIZONS, Mathematical
Association of America. February, 2006.
Gray, Shirley B., “A Multiplicity of Multiplications.” College
Mathematics Journal, 37, Spring, 2006.
|
| 2005 |
Gray, Shirley B. “National Curve Bank
Project” College Board AP Central. College Board
AP Calculus AB program. January, 2005.
Perkins, Gay with Shirley B. Gray “Life of a 1950s Homecoming
Queen,” The Western Scholar. Western Kentucky
University. Spring, 2005. |
| 2004 |
Gray, Shirley B., "Hypatia", Mathematics
for Students, Macmillan Reference USA. |
| 2003 |
Gray, Shirley B., "Agnesi", Mathematics
for Students, Macmillan Reference USA. |
| 2002 |
< http://curvebank.calstatela.edu
> < http://curvebank.calstatela.edu/home/home.htm
>
A National Science Foundation and Arnold and Mabel Beckman Foundation
supported project.
|
| 2001 |
MAA Online Book Review, Stephen
Smale: The Mathematician Who Broke the Dimension Barrier,
< http://maa.org.reviews/reviews.htm >, April, 2001. |
| 2001 |
< http://instructional1.calstatela.edu/sgray/Agnesi/
> |
| 2001 |
Gray, S. I. B. and Sandifer, C.
Edward, The Sumario Compendioso, Mexico City, 1556: The New
World's First Mathematics Book, Mathematics Teacher,
NCTM, 94 (2) 98 - 103. |
| 2000 |
Mathematics in the Age of Jane Austen: Essential
Skills of 1800. Mathematics Teacher. NCTM, 93 (8) 670-679. |
| 2000 |
CALTECH AT OXFORD, 40 YEARS ON. The American
Oxonian; A Publication of the American Rhodes Scholar Foundation,
LXXXVII (1) 1-8. |
| 1999 |
Gray, S. I. B., and Malakyan, Tagui, The Witch of
Agnesi: A Lasting Contribution from the First Surviving
Mathematical Work by a Woman. A commemorative on the 200th
Anniversary of her death. The College Mathematics Journal,Mathematical
Association of America. Cover article, 30 (4), September,
1999, 258 - 268. Ms. Malakyan was a student in MATH 320. |
| 1999 |
Gray, S. I. B., The Mathematics of Lewis
Carroll, math HORIZONS, Mathematical Association of
America. April, 1999, 18 - 23. |
| 1999 |
Gray, Shirley I. B., THESE RUINS ARE STILL
INHABITED: Caltech at Oxford. A Tribute to Muriel and
George Beadle, Update for 1998. Engineering and Science,
California Institutue of Technology, LXI (4), April, 1999. |
| 1999 |
Gray, S. I. B., Heiberg and the Lost
Palimpsest of Archimedes. The British Society for the History
of Mathematics Newsletter, Summer, (39) 26-31. |
| 1999 |
Gray, S. I. B., Mathematics Education Across the
Poind in Great Britain. CMC ComMuniCator,23 (4), June,
1999, 46 - 47. |
| 1998 |
Gray, S.I.B., A Mathematics Treasure in
California, The Mathematical Intelligencer, 20(2), 41-46. |
| 1997 |
Gray, Shirley B. and Mena, Robert A. Amusements in the
History of Mathematics, PRIMUS, VII(4), 317-328. |
| 1997 |
Gray, Shirley B., Producer and Director. Using a
Graphing Calculator, Department of Mathematics and Computer
Science, CSULA. A videotape featuring 25 students, faculty and staff. |
| 1996 |
Gray, Shirley B. Earthquake Mathematics: An Infant
Science. [This earthquake problem has been selected for LAUSD's
Standards for High School Curriculum as a model for all
students.]
http://forum.swarthmore.edu/nctm96/interdisc/gray/index.html |
| 1992 |
Gray, Shirley B. Fractal Math, Journal of Computers
in Mathematics and Science Teaching, 1(1), 31-38. |
| 1992 |
Gray, Shirley B. and Craig, Terence. G. Math Matching
Ideas: A Generic HyperCard-HyperTalk Program, Journal of Computers
in Mathematics and Science Teaching, 1(2), 235-250. |
|
~
Link
Notes ~
Comments
on some of the books CSULA students see at the Huntington Library.
|
Claudius Ptolemy
Ptolemy wrote the Almagest, or "the greatest,"
in
the second century A.D. He produced the definitive Greek work in
mathematical
astronomy for determining the location of the planets. His mathematics
and
its geocentric theory stood unchallenged for 1400 years until
Copernicus
proposed his heliocentric theory in 1513.
The surviving copy at the Huntington uses the sexagesimal
number
system. It is thought to have been produced in the south of France, but
the
monastery, or atelier, is unknown.
As for esthetics, this copy is illuminated with gold and color
adornment.
The hand-printed vellum is not thick, but has an unforgettable texture
of
strength tempered with the appeal of the finest of translucent
paper.
To view the Vatican's copy and other interesting titles: http://sunsite.unc.edu/expo/vatican.exhibit/exhibit/Main_Hall.html
Euclid
The Huntington has more than 30 editions of the Elements,
but counting the number of editions is arbitrary, for not all books
have
survived in all editions. This collection was expanded (Fall,
2006)
by the addition of the Burndy Library from M.I.T.
Following the invention of printing, Erhard Ratdolt's
translation
in 1482 was the first mathematics material to be printed. The
manuscript
opens immediately with 23 definitions, including those for the point,
line
and plane! Impressively, the Latin illustrations of "puntus, linea,
plana,"
are clear to English readers 500 years later. On later pages, students
will
immediately recognize the "windmill" or "bride's chair" proof of the
Pythagorean
Theorem.
The Huntington has two copies of the first English translation by Sir
Henry
Billingsley (London, 1570). It contains pop-up, three-dimensional
models,
embedded in the text. For example, the book includes fold-out models of
two
perpendicular planes, a tetrahedron and a pyramid.
Many of the authors of the other editions are, themselves, famous,
e.g.,
Lewis Carroll.
Copernicus
This first edition of Copernicus at the Huntington was
the gift of Edwin Hubble of the "Hubble Space Telescope." It is nearly
always
on display in the Main Reading Room of the Library. Most of the other
titles
are seldom seen by the public.
Maria Agnesi and the
Marquise
du Châtelet
There are very few famous women in
mathematics.
We select the following for special mention:
Hypatia
See: Gray, Shirley
B.
"Hypatia." An article requested for Mathematics for
Students,
an encyclopedia published by Macmillan Reference USA., 2002.
|
d. 415 AD
|
Châtelet
Emilie Breteuil, Marquise du Châtelet |
1701 - 1749
|
Maria Agnesi
< http://instructional1.calstatela.edu/sgray/Agnesi
>
Also see: Gray, Shirley
B.
"Agnesia." An article requested for Mathematics for
Students,
an encyclopedia published by Macmillan Reference USA.,2002.
|
1718 - 1799
|
| Sophie Germain |
1776 - 1831
|
| Sonya Kovalevsky |
1850 - 1891
|
| Emmy Noether |
1882 - 1935
|
| CSULA is proud of our
former
colleague, Dr. Evelyn Boyd Granville, one of the first African-American
women
to earn a Ph.D. in mathematics (Spring, 1949). |
|
Apollonius
The Library also has Sir Edmond Halley's edition of Apollonius' works.
Euler
The CSULA Spring, 1997 students remarked that of all the books we had
seen
in chronological order, this was the first to look like a "math" book.
By
the 18th century, the equation and notation had evolved, as well as
printing
techniques, to have math equations, not verbal explanations, embedded
in
the text. Calculus students will immediately recognize that Euler was
working
on infinite series.
Brother Juan Diez, O.F.M.
The Sumario Compendioso in Spanish is the first book other
than religious
instruction printed in the entire Western Hemisphere. With a
publication
date of 1556 in Mexico City, it predates all North American settlement,
e.g.,
Jamestown (1607), Plymouth Rock (1620), and Quebec City (1608).
The Huntinton Library has been the Sumario 's home
since
1920. It is one of three remaining known copies in the World, with the
other
two being in the British Museum in London and in the Biblioteca
Nacional
in Madrid.
The cover is primitive heavy leather. On opening the cover, the first
thing
one sees on the left is a recycled piece of printed matter that is
pasted
vertically. Paper must have been in very short supply in Mexico City in
1556.
A gorgeous frontispiece is on the right opening page, and bears
reference
to the kingdoms of Peru (sic ).
Return to Brother
Juan
Diez.
Robert Recorde
In the summer of 2006 a student asked who was the very first to use the
equals
sign. The question was answered by showing him Robert Recorde's " The whetstone of witte, which is the
seconde
part of Arithmetike . . ." published in London (1557) at
the
Huntington Library.
|
