NAM Newsletter - University of Evansville

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Volume XLII Number 1The National Association of Mathematicians (NAM)publishes the NAM Newsletter four times per year.EditorDr. Talitha M. WashingtonUniversity of Evansvillenam_newsletter@yahoo.comhttp://faculty.evansville.edu/tw65/Editorial Board Find NAM NewsletterDr. Edray Herber Goinson Facebook!Purdue Universityegoins@math.purdue.eduhttp://www.math.purdue.edu/~egoins/Dr. Mohammad K. AzarianUniversity of Evansvilleazarian@evansville.eduhttp://faculty.evansville.edu/ma3/Newsletter Websitehttp://faculty.evansville.edu/tw65/NAM.htmThis website has a list of open job and summer positions.It also features past editions of the Newsletter and editionsfrom 41.1 to present are in color.From the EditorAs I sit in church, I can hear the constant babbling ofbabies and the wild chatter of children. I admit that sometimesI am disquieted as I am trying to hear the stories beingtold. All of the sudden, my pastor, Rev. Adrian M.Brooks, Sr., interrupts his message to remind us that ―youknow when an organization is alive. You see and hear theyouth. A dying organization is void of the young.‖NAM‘s efforts to cultivate, nourish and grow the nextcrop of mathematical researchers are highly commendable.At NAM‘s Undergraduate MATHFest 2010, budding students,intrigued by the rigor and beauty of mathematics,gained invaluable connections (page 7). At the Joint MathematicsMeetings 2011, the new Ph.D. session showeddiversity within areas of research, as well as diversitywithin the NAM community (page 8). All the while, Dr.Azarian reminds us that, as we move forward, it is vital topreserve our past, and remember the mathematicians whocame before us (page 3). We are also encouraged to preserveour own works, and Carol Mead of the Archives ofAmerican Mathematics Archives shows us how (page 6).Fortunately, at times, a family member will document thejoys and conflicts that exist in every family, as with Dr. J.Ernest Wilkins‘ family (page 4).Letters to the editor should be addressed to Dr. TalithaM. Washington, University of Evansville, Department ofMathematics, 1800 Lincoln Avenue, Evansville, Indiana47722 or by email to nam_newsletter@yahoo.com.Email is preferred.Subscription and membership questions should bedirected to Dr. Roselyn E. Williams, Secretary-Treasurer,National Association of Mathematicians, P.O. Box 5766,Tallahassee, Florida 32314-5766; (850) 412-5236; email:Roselyn.Williams@famu.eduNAM’s Official Webpage http://www.nam-math.orgNAM’s History and Goals: The National Associationof Mathematicians, Inc., known as NAM was founded in1969. NAM, a nonprofit professional organization, hasalways had as its main objectives, the promotion of excellencein the mathematical sciences and the promotion andmathematical development of under-represented minoritymathematicians and mathematics students. It also aims toaddress the issue of the serious shortage of minorities inthe workforce of mathematical scientists.David Bressoud (MAA President2009-2010) and Talitha WashingtonHowever,we do nothave to proceedby ourselves.Overthe years, wehave receivedgenerous supportfor ourefforts fromthe mathematicsinstitutesfrom across the country (page 7). Through connectionswith other professional organizations such as theMathematical Association of America, our efforts are supportedand amplified.As NAM proceeds forward, we are reminded to includethe young, to make connections with those aroundus, and to provide both the courage and support to moveour community forward so that the next generation ofscholars can travel a smoother road that leads to mathematicalgreatness.Enjoy!2NAM Newsletter
Spring 2011The Second Ptolemy: Persia's Fifteenth CenturyMathematical GeniusMohammad K. AzarianGhiyāth al-Dīn Jamshīd Masūdal-Kāshī was one of the most renownedmathematicians and astronomersin Persian history, as well asone of the most fascinating medievalmathematicians in the world. InIran and other Persian speaking societies,he is called by his PersianMohammad Azarian name, Kāshānī. Kāshānī‘s exactdate of birth is not known, but it was sometime during thesecond half of the fourteenth century. Most likely, he wasborn in the Tamerlane empire in the city of Kāshān in centralIran about 160 miles south of the capital Tehran, andabout 300 miles from the Caspian Sea. Kāshānī died onthe morning of Wednesday, June 22, 1429 (Ramadān 19,832 AHL) outside of Samarqand, at the observatory he hadhelped to build in Uzbekistān, in northeast Iran.Kāshānī was known for his extraordinary ability toperform very difficult mental computations. The manynicknames given to Kāshānī include ―the second Ptolemy‖,―the pearl of the glory of his age‖, ―the king of engineers‖,―the reckoner‖, and ―our master of the world‖.Although Kāshānī‘s interests were in mathematics andastronomy, he was actuallya physician. Like manyother scientists of theMiddle Ages, he dedicatedmost of his known scientifictreatises to monarchsor other influentialrulers of his time in orderto receive compensation.Kāshānī was Persian,but, in order to increasehis readership, he wrotemost of his mathematicalwork in Arabic. Most ofhis work was written insexagesimal system, asystem where the digitsare separated by commas, and the integral and fractionalparts by semicolons. (For example, ―1, 23; 45, 57‖ in base60 is1 × 60 + 23 × 60 0 + 45 × 60 -1 + 35 × 60 -2 in base 10.) Today,his best-known work has been translated into English,French, German, and Russian. For a more detailed discussionof Kāshānī‘s life and his mathematical achievements,we refer the reader to the references provided for this article,especially [5].Mathematical Achievements―The Treatise on the Circumference‖ was completedin Arabic as Al-Risāla al-muhītīyya in July of 1424(Sha‘bān 827 AHL). In this masterpiece of computationaltechniques, Kāshānī used his fundamental theorem fromthis risāla to calculate the value of Л, correct to 16 decimalplaces. He used inscribed and circumscribed polygons,each with 805,306,368 sides. This approximation ofЛ was a remarkable achievement for that time. It far surpassedall approximations of Л by all previous mathematiciansthroughout the world, including Archimedes, Ptolemy,and Muhammad al-Khwārizmī. Archimedes‘ approximationwas 3.14 (250 BC); Ptolemy‘s result was 3.14166(150 AD); and al-Khwārizmī‘s approximation was 3.1416(800 AD). It took European scientists 186 years to improveon Kāshānī‘s approximation of Л.―The Treatise on the Chord and Sine‖ was completedin Arabic as Risāla al-watar wa’l-jaib around 1427. Themain part of this work involves the creation of and solutionsto the cubic equation ax = b + x 3 where a and b areconstants. He then found an approximation of sin 1 o viatrigonometric identity sin 3x = 3sin x - 4sin 3 x. By usingan iterative method, today known as the fixed-point method,he found thatsin 1 o = .0174524064372835103712which is correct to 22 decimal places (and is equivalent tosin 1 o = 1;2,49,43,11,14,44,16,26,17, correct to ten sexagesimalplaces). This was the first approximation methodin the history of mathematics and the most significantachievement in medieval algebra. Before this work, thebest known approximation was found in the tenth centuryAD by Abu‘l-Wafā and Ibn Yūnus but they were correct toonly four sexagesimal places.―The Key of Arithmetic‖ or ―The Calculators‘ Key‖was completed in Arabic as Miftāh al-hisāb on March 2,1427 (Jamādi al-awwal 3, 830 AHL). It took Kāshānīmore than 7 years to complete this work. It was writtenprimarily as a textbook and was used for more than fivecenturies as a textbook as well as an encyclopedia. Itserved many generations of students, accountants, astronomers,architects, engineers, land surveyors, and merchants.Side NoteThe start of the Islamic calendar is the year 622 AD inthe Western calendar, the year the prophet Muhammadmade the hijra, his migration Mecca to Medina. There aretwo Islamic calendars in use: the lunar, which is 354 daysand the solar, which is 365 days. In this article, ―AHL‖and ―AHS‖ are used for these two calendars, respectively.NAM Newsletter 3
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