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Occasion of Receiving the Seki-Takakazu Prize
特集:日本数学会関孝和賞受賞 On the occasion of receiving the Seki-Takakazu Prize Jean-Pierre Bourguignon, the director of IHÉS A brief introduction to the Institut des Hautes Études Scientifiques The Institut des Hautes Études Scientifiques (IHÉS) was founded in 1958 by Léon MOTCHANE, an industrialist with a passion for mathematics, whose ambition was to create a research centre in Europe, counterpart to the renowned Institute for Advanced Study (IAS), Princeton, United States. IHÉS became a foundation acknowledged in the public interest in 1981. Like its model, IHÉS has a small number of Permanent Professors (5 presently), and hosts every year some 250 visitors coming from all around the world. A Scientific Council consisting of the Director, the Permanent Professors, the Léon Motchane professor and an equal number of external members is in charge of defining the scientific strategy of the Institute. The foundation is managed by an 18 member international Board of Directors selected for their expertise in science or in management. The French Minister of Research or their representative and the General Director of CNRS are members of the Board. IHÉS accounts are audited and certified by an international accountancy firm, Deloitte, Touche & Tomatsu. Its resources come from many different sources: half of its budget is provided by a contract with the French government, but institutions from some 10 countries, companies, foundations provide the other half, together with the income from the endowment of the Institute. Some 50 years after its creation, the high quality of its Permanent Professors and of its selected visiting researchers has established IHÉS as a research institute of world stature. -
JRASC-2007-04-Hr.Pdf
Publications and Products of April / avril 2007 Volume/volume 101 Number/numéro 2 [723] The Royal Astronomical Society of Canada Observer’s Calendar — 2007 The award-winning RASC Observer's Calendar is your annual guide Created by the Royal Astronomical Society of Canada and richly illustrated by photographs from leading amateur astronomers, the calendar pages are packed with detailed information including major lunar and planetary conjunctions, The Journal of the Royal Astronomical Society of Canada Le Journal de la Société royale d’astronomie du Canada meteor showers, eclipses, lunar phases, and daily Moonrise and Moonset times. Canadian and U.S. holidays are highlighted. Perfect for home, office, or observatory. Individual Order Prices: $16.95 Cdn/ $13.95 US RASC members receive a $3.00 discount Shipping and handling not included. The Beginner’s Observing Guide Extensively revised and now in its fifth edition, The Beginner’s Observing Guide is for a variety of observers, from the beginner with no experience to the intermediate who would appreciate the clear, helpful guidance here available on an expanded variety of topics: constellations, bright stars, the motions of the heavens, lunar features, the aurora, and the zodiacal light. New sections include: lunar and planetary data through 2010, variable-star observing, telescope information, beginning astrophotography, a non-technical glossary of astronomical terms, and directions for building a properly scaled model of the solar system. Written by astronomy author and educator, Leo Enright; 200 pages, 6 colour star maps, 16 photographs, otabinding. Price: $19.95 plus shipping & handling. Skyways: Astronomy Handbook for Teachers Teaching Astronomy? Skyways Makes it Easy! Written by a Canadian for Canadian teachers and astronomy educators, Skyways is Canadian curriculum-specific; pre-tested by Canadian teachers; hands-on; interactive; geared for upper elementary, middle school, and junior-high grades; fun and easy to use; cost-effective. -
Historical Development of the Chinese Remainder Theorem
Historical Development of the Chinese Remainder Theorem SHEN KANGSHENG Communicated by C. TRUESDELL 1. Source of the Problem Congruences of first degree were necessary to calculate calendars in ancient China as early as the 2 na century B.C. Subsequently, in making the Jingchu [a] calendar (237,A.D.), the astronomers defined shangyuan [b] 1 as the starting point of the calendar. If the Winter Solstice of a certain year occurred rl days after shangyuan and r2 days after the new moon, then that year was N years after shangyuan; hence arose the system of congruences aN ~ rl (mod 60) ~ r2 (mod b), . ~ ' where a is the number of days in a tropical year and b the number of days in a lunar month. 2. Sun Zi suanjing [c] (Master Sun's Mathematical Manual) Sun Zi suanjing (Problem 26' Volume 3) reads: "There are certain things whose number is unknown. A number is repeatedly divided by 3, the remainder is 2; divided by 5, the remainder is 3; and by 7, the remainder is 2. What will the num- ber be ?" The problem can be expressed as x --= 2 (mod 3) ~ 3 (mod 5) ~- 2 (rood 7). SUN ZI solved the problem as we do, giving x ~ 140 + 63 -k 30 ~=- 233 ~ 23 (rood 105). 1 Shangyuan is a supposed moment that occurred simultaneously with the midnight of jiazi [v] (the first day of the 60 day cycle), the Winter Solstice and the new moon. 286 SHEN KANGSHENG In speaking of the algorithm yielding these addends in the solution he continued: "In general, for G1 ~ 0(mod 5) ~ 0 (mod 7) = 1 (rood 3), take G1 = 70, G2 ~ 0(rood 3) ~ 0(mod 7) ~ 1 (mod 5), take G2 = 21, G3 ~ 0 (mod 3) ~ 0 (mod 5) ~ (1 rood 7), take G3 = 15. -
ON MATHEMATICAL TERMINOLOGY: CULTURE CROSSING in NINETEENTH-CENTURY CHINA the History of Mathematical Terminologies in Nineteent
ANDREA BRÉARD ON MATHEMATICAL TERMINOLOGY: CULTURE CROSSING IN NINETEENTH-CENTURY CHINA INTRODUCTORY REMARKS: ON MATHEMATICAL SYMBOLISM The history of mathematical terminologies in nineteenth-century China is a multi-layered issue. Their days of popularity and eventual decline are bound up with the complexities of the disputes between the Qian-Jia School who were concerned with textual criticism and the revival of ancient native Chinese mathematical texts, and those scholars that were interested in mathematical studies per se1 (and which we will discuss in a more detailed study elsewhere). The purpose of the following article is to portray the ‘introduction’ of Western mathematical notations into the Chinese consciousness of the late nineteenth century as a major signifying event, both (i) in its own right within the context of the translation of mathematical writ- ings from the West; and (ii) with respect to the way in which the tradi- tional mathematical symbolic system was interpreted by Qing commentators familiar with Western symbolical algebra. Although one might assume to find parallel movements in the commentatorial and translatory practices of one and the same person, nineteenth-cen- tury mathematical activities will be shown to be clearly compartmen- talized. In fact, for the period under consideration here, it would be more appropriate to speak of the ‘reintroduction’ of Western mathematical notations. Already in 1712 the French Jesuit Jean-François Foucquet S. J. (1665–1741) had tried to introduce algebraic symbols in his Aer- rebala xinfa ̅ (New method of algebra). This treatise, which was written for the Kangxi emperor, introduced symbolical 1 In particular, the ‘three friends discussing astronomy and mathematics’ (Tan tian san you dž ) Wang Lai (1768–1813), Li Rui (1763–1820) and Jiao Xun nj (1765–1814). -
Muramatsu's Method Aryabhata (499 AD) Brahmagupta (640 AD
π in Other Eastern Countries Japan India In the Edo Period of Japan (1603 to 1868), 3.16 was used for π. But Aryabhata (499 AD) as people recognized that this value was not accurate, different values for π were calculated. Wasan scholars such as Muramatsu Shigekiyo, Seki Takakazu, Kamata Toshikiyo, Takebe Katahiro, and Matsunaga Aryabhata usedp the perimeter of a 384-sided poly- Yoshisuke all made calculations of π, and accomplished results gon to find π ≈ 9:8684. Later Aryabhata would comparable to their European mathematician counterparts. publish an “approximation” for his square root value, 3.1416. Note that his approximation is Muramatsu’s Method more accurate than his official value! Shigekiyo Muramatsu published Sanso in 1663. Muramatsu served the Asano family and possibly had a math insti- Brahmagupta (640 AD) tute in Edo (present day Tokyo). In his Brahmagupta used a pattern of inscribed polygons that work, Sanso, Muramatsu arranged prob- increased in the number of sides to calculate the perime- lems published earlier in Japanese math- ter of a circle.p Using these data points, he came to believe ematics texts without answers. Mura- that π = 10: matsu classified these problems into dif- ferent levels according to how difficult he thought they’d be to learn. Asano Crest It is in this book that he also showed the calculation of π from the regular inscribed polygon of 32,768 sides. He correctly obtained the Ramanujan (1887-1920) value 3.1415926. Thus, this book was the first to contain a mathematical calculation of π in Japan. 1 Srinivasa Ramanujan found several formulas for π. -
Mathematical Philosophy of Takebe Katahiro
数理解析研究所講究録 第 1831 巻 2013 年 57-65 57 Mathematical Philosophy of Takebe Katahiro Morimoto, Mitsuo 1 Seki Kowa Institute of Mathematics, Yokkaichi University Professor Emeritus, Sophia University Abstract Takebe Katahiro (1664-1739) was a Japanese mathematician, who exposed his philosophy on Mathematics itself and on Mathematical Research. In the Taisei Sankei (1711), he wrote Chapter 4 entitled the “Three Essentials” describing four classes of mathematical problems, the status of parameters in a problem and the classffica- tion of numbers. Note that his thought was based on Chinese traditional philosophy and on the achievement of Japanese mathematics in the early Edo period. Note also he recognized some numbers are not algebraic. In the Tetsujutsu Sankei (1722) he recommended the inductive heuristic method in mathe- matical research and recognized a mathematical research would be successful once the character of a mathematical object and that of a mathematician were accommodated to each other, com- paring his method of calculation of the circular $co$ efficient with that of his master Seki Takakazu and citing his own discovery of the infinite power series expansion formula of an inverse trigono- metric function. The Meiji Restoration (1868) was a tuming point in the history of Japan from the feudalism to the constitutional monarchism. The “ordinance on school system” (1872) of the new gov- emment defined mathematics in Japanese schools to be of “European style” thus abandoning the Japanese traditional mathematics. This policy was proved to be efficient at least for a half century and Takebe’s philosophy on Mathematics was buried in the complete oblivion. 1 Takebe Katahiro Takebe Katahiro 建部賢弘 (1664-1739) was one of great mathematicians in the Edo Period (1603- 1868) of Japan. -
A Review of the History of Japanese Mathematics
Revue d’histoire des math´ematiques, 7 (2001), p. 137–155. A REVIEW OF THE HISTORY OF JAPANESE MATHEMATICS Tsukane OGAWA (*) ABSTRACT. — This review aims to introduce Japanese mathematics to a non- expert and a non-Japanese readership. It briefly characterizes mathematics in Japan, surveys its history, as it developed over the last century, and provides a large (if not exhaustive) bibliography of works in the primary European languages. RESUM´ E´.—APERC¸ U SUR L’HISTOIRE DES MATHEMATIQUES´ JAPONAISES. Le but de cette note est de pr´esenter les math´ematiques japonaises `a un public non sp´ecialis´e dans le domaine. Les math´ematiques au Japon sont bri`evement caract´eris´ees, leur histoire, telle qu’elle s’est d´evelopp´ee durant le dernier si`ecle, est pass´ee en revue et finalement une importante bibliographie dans les principales langues europ´eennes est propos´ee, mˆeme si elle ne peut pr´etendre `a l’exhaustivit´e. 1. INTRODUCTION – NOT ONLY SANGAKU The custom of hanging sangaku ( ), wooden plates on which are inscribed mathematical problems and their answers, under the roofs of shrines in the Edo period (1603–1867) in Japan is familiar enough to have been illustrated and described in Scientific American, May 1998 [Rothman 1998]. It is, however, obvious that sangaku is not all there is to Japanese mathematics. It would be fallacious to consider that the essence of Japanese mathematics reveals itself in sangaku. As a beginning, this essay attempts briefly to introduce Japanese mathematics to a non-Japanese readership. It will answer the following questions : 1) What kind of mathematical disciplines developed in Japan ? 2) How were mathematical expressions written in vertical typesetting ? 3) How did the Japanese calculate ? 4) Is it true that, lacking proofs, Japanese mathematics was not logical ? (*) Texte re¸cu le 7 mars 1999, r´evis´e le 11 novembre 2000. -
Navigating the Mid September Night Sky
Navigating the mid September Night Sky For observers in the middle The stars plotted represent those which northern latitudes, this chart North can be seen from areas suffering is suitable for early Sept. from moderate light pollution. In larger cities, less than at 10:00 p.m. and late Sept. Capella at 9:00 p.m. 100 stars are visible, while from dark, rural areas well over ten times Perseus that amount Double are found. Cluster Polaris, Pointer Stars1 to the North Star the North Star D Andromeda Cepheus Cassiopeia 2 Mars M31 Milky Way + E Moon C 3 Sep 5 M13 D Deneb Arcturus East Vega The The Zenith Northern Great 4 The Crown Square The+ Keystone West Summer Pegasus Cygnus Triangle 5b Coathanger Cluster Great Rift Moon Altair D Sep 20 Aquila 5a B D Numerous star clusters Saturn and nebulae Jupiter M22 Moon M8 Antares Relative sizes Sep 25 Moon Fomalhaut The and distances Sep 24 Teapot in the sky can be deceiving. For The Ecliptic represents Sagittarius instance, 360 "full the plane of the solar moons" can be placed system. The sun, the moon, side by side, extending from and the major planets all lie on or horizon to horizon. near this imaginary line in the sky. South Relative size of the full moon. Navigating the mid September night sky: Simply start with what you know or with what you can easily find. 1 Extend a line north from the two stars at the tip of the Big Dipper's bowl. It passes by Polaris, the North Star. -
NASA Night Sky Notes: Observe the Milky Way and the Great Rift
NASA Night Sky Notes July 2021 This article is distributed by NASA Night Sky Network The Night Sky Network program supports astronomy clubs across the USA dedicated to astronomy outreach. Visit nightsky.jpl.nasa.gov to find local clubs, events, and more! Observe the Milky Way and Great Rift David Prosper Summer skies bring glorious views of our own Milky Way galaxy to observers blessed with dark skies. For many city dwellers, their first sight of the Milky Way comes during trips to rural areas - so if you are traveling away from city lights, do yourself a favor and look up! To observe the Milky Way, you need clear, dark skies, and enough time to adapt your eyes to the dark. Photos of the Milky Way are breathtaking, but they usually show far more detail and color than the human eye can see – that’s the beauty and quietly deceptive nature of long exposure photography. For Northern Hemisphere observers, the most prominent portion of the Milky Way rises in the southeast as marked by the constellations Scorpius and Sagittarius. Take note that, even in dark skies, the Milky Way isn’t easily visible until it rises a bit above the horizon and the thick, turbulent air which obscures the view. The Milky Way is huge, but is also rather faint, and our eyes need time to truly adjust to the dark and see it in any detail. Try not to check your phone while you wait, as its light will reset your night vision. It’s best to attempt to view the Milky Way when the Moon is at a new or crescent phase; you don’t want the Moon’s brilliant light washing out any potential views, especially since a full Moon is up all night. -
THE MILKY WAY from AQUILA to CYGNUS Space Density Function and the Distribution of the Dark Nebulae
VoL. 23, 1937 ASTRONOMY: F. D. MILLER 405 NOTE ON GALACTIC STRUCTURE: THE MILKY WAY FROM AQUILA TO CYGNUS By FREEMAN D. MILLER SWASEY OBSERVATORY, DENISON UNIVERSITY Communicated June 15, 1937 Analyses of general star-counts are ofX value in detailed descriptions of extended regions of the Milky Way. The observations summarized below, covering the area between galactic longitudes 300 and 550, and latitudes - 100 and + 150, were made for the purpose of investigating the stellar space density function and the distribution of the dark nebulae. 1. The observations depend chiefly upon plates taken with a 4-inch Ross camera at the Oak Ridge Station of the Harvard College Observatory. Part of the plates are half-hour exposures showing stars to the fifteenth magnitude, and the remainder are short exposure polar-comparisons for photometric purposes. Supplementary information concerning stars be- tween the thirteenth and sixteenth magnitudes was obtained from the original negatives of Ross's Atlas of the Milky Way.' A number of Harvard patrol and polar comparison plates, taken with a 3-inch Ross camera, gave additional data on stars brighter than the thirteenth magnitude. 2. The most exacting requirement involved a homogeneous magnitude system covering several hundred square degrees. The Mount Wilson catalog of photographic magnitudes in the Selected Areas2 fills this need satisfactorily between the tenth and sixteenth magnitudes, but the number of brighter stars is small. For this reason, from three to five polar-com- parisons on each of the six Selected Areas were used in setting up sequences of stars between the eighth and twelfth magnitudes. -
August 2021 a Non-Profit Educational Association SDAA Update P.O
San Diego Astronomy Association Celebrating Over 50 Years of Astronomical Outreach https://www.sdaa.org/ August 2021 A Non-Profit Educational Association SDAA Update P.O. Box 23215, San Diego, CA 92193-3215 SDAA is now actively using online facilities like Zoom and YouTube to provide access to club meetings, events, and outreach programs in keeping with state and local mandates Next SDAA Business Meeting regarding physical distancing requirements during the COVID-19 pandemic. In-person August 10th at 7:00pm events will start again in 2021 as soon as allowed by state and local mandates. 10070 Willow Creek Rd Look for updates on the Lipp telescope. San Diego, CA 92131 Via Zoom Since TDS is private space there is no reason to lock down the facility but there are actions you can take to help keep the site safe for all of us. If you plan to visit and use the facility, Next Program Meeting please bring along some disinfectant wipes or disinfectant spray cleaner. When you finish August 18th at 7:00pm using the restrooms or the warming room, please wipe down the areas that you touched in Live Stream order to help prevent the spread of any viruses. As much as we love sharing the views of the night sky, try to maintain the recommended 6-foot physical distance guideline. August 18, 2021 Program Meeting CONTENTS August 2021, Vol LIX, Issue 8 Speaker: Dr. Julie Castillo-Rogez, JPL planetary scientist Published Monthly by the Topic: NASA Near Earth Object Missions San Diego Astronomy Association Incorporated in California in 1963 Dr. -
Adam Koloff - Offers This Panoramic Image of the Observatory Eastern Sky
<- M 86 <- M 84 Adam Koloff - offers this panoramic image of the observatory eastern sky Image was taken June 15 using his new Canon EOS R6 camera. This new mirrorless model features many new features with the ability to take 20 meg images in both still and video modes. Taken at ISO 4000 using a ten-frame panorama. The above image has been cropped and enhanced to bring out the Milky Way extending from Cygnus to Scorpius. Note the dark pipe smoke nebula on the right. Also note the long dark “Great Rift” in the central region. Read more in the NSN article on page You can see Adam’s full original 120 degree panorama on page 6. Want to try to take your own Milky Way photos this summer. Try this article on AstroBackyard https://astrobackyard.com/how-to-photograph-milky-way/ Lots of other tips on taking sky photos here also. Contents: 1 Observatory Eastern Sky panorama by Adam Koloff 2 Upcoming Observing Night Events - Links to online Spring meetings 3 Alcon 2021 - Aug. 19-21 and Okie-Tex Oct 1-9 Bortle Dark Sky Scale 4 President’s Message – by Tamara Green New Relaxed Observing Night Guidelines 5 Congratulations to Abby Bollenbach - One Year of her popular Astronomy video series Infinity and Beyond 6 What’s Up in Tonight’s Sky by John Land 7 Report on Ash Dome Observatory project by Skip Whitehurst 8 Land Title Update - by Don Bradford 9-10 Observe the Milky Way and Great Rift by David Prosper 11 Treasurer’s Report and New Members - by John Newton 12 Club Contacts - I Spy with my Little Eye Riddle Astronomy Club Events Check our website AstroTulsa.com events section for updates Observatory ONLY OPEN for SCHEDULED EVENTS.