Ajima Naonobu



, also known as Ajima Manzō Chokuyen, was a Japanese
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
of the
Edo period The or is the period between 1603 and 1867 in the history of Japan, history of Japan, when Japan was under the rule of the Tokugawa shogunate and the country's 300 regional ''daimyo''. Emerging from the chaos of the Sengoku period, the Edo perio ...
.Smith, David. (1914). His
Dharma name A Dharma name or Dhamma name is a new name acquired during both lay and monastic Buddhist initiation ritual The Lay Buddhist Ordination (, Japanese language, Japanese: , Korean language, Korean: ''sugye'' (수계) refers to the public ordina ...
was (祖眞院智算量空居士).


Ajima is credited with introducing
calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizati ...
into Japanese mathematics. The significance of this innovation is diminished by a likelihood that he had access to European writings on the subject. Ajima also posed the question of inscribing three mutually tangent circles in a triangle; these circles are now known as
Malfatti circles In geometry, the Malfatti circles are three circles inside a given triangle such that each circle is Tangent circles, tangent to the other two and to two sides of the triangle. They are named after Gian Francesco Malfatti, who made early studies ...
after the later work of Gian Francesco Malfatti, but two
triangle center In geometry, a triangle center (or triangle centre) is a point in the plane that is in some sense a Centre (geometry), center of a triangle akin to the centers of square (geometry), squares and circles, that is, a point that is in the middle of t ...
s derived from them, the Ajima–Malfatti points, are named after Ajima. Ajima was an astronomer at the Shogun's Observatory (''Bakufu Temmongaki'').Jochi, Shigeru. (1997).


In 1976, the
International Astronomical Union The International Astronomical Union (IAU; french: link=yes, Union astronomique internationale, UAI) is a nongovernmental organisation with the objective of advancing astronomy in all aspects, including promoting astronomical research, outreach ...
(IAU) honored Ajima by identifying a crater on the
moon The Moon is Earth's only natural satellite. It is the List of natural satellites, fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth ( ...
with his name. Naonobu is a small lunar
impact crater An impact crater is a circular depression (geology), depression in the surface of a solid astronomical object formed by the hypervelocity collision, impact of a smaller object. In contrast to volcanic craters, which result from explosion or in ...
located on the eastern
Mare Fecunditatis Mare Fecunditatis (Latin ''fēcunditātis'', the "Sea of Fecundity" or "Sea of Fertility") is a lunar mare The lunar maria (; singular: mare ) are large, dark, basalt Basalt (; ) is an aphanite, aphanitic (fine-grained) extrusive ign ...
, to the northwest of the prominent crater Langrenus.

Selected works

In a statistical overview derived from writings by and about Ajima Naonobu,
OCLC OCLC, Inc., doing business as OCLC, See also: is an American nonprofit cooperative organization "that provides shared technology services, original research, and community programs for its membership and the library community at large". It was ...
WorldCat WorldCat is a union catalog that itemizes the collections of tens of thousands of institutions (mostly libraries), in many countries, that are current or past members of the OCLC global cooperative. It is operated by OCLC, Inc. Many of the ...
encompasses roughly 20+ works in 30+ publications in two languages and 40+ library holdings. *
OCLC 017232052
collected works *
OCLC 057185881
algorithms considered * (''Introduction of the 'Works and Days Calendar) * (''Ajima's Studies for Western Calendars'') * (''Methods of Professor Ajima's'' '') * (''Introduction of Eclipses of the Sun and the Moon'') * (''Methods of Three Diagonals and Three Circles'')Jochi, * (''Periods of Decimal Fractions'')

See also

Sangaku Sangaku or San Gaku ( ja, 算額, lit=calculation tablet) are Japanese geometrical problems or theorems on wooden tablets which were placed as offerings at Shinto shrine A is a structure whose main purpose is to house ("enshrine") one or m ...
, the custom of presenting mathematical problems, carved in wood tablets, to the public in
shinto shrines A is a structure whose main purpose is to house ("enshrine") one or more ''kami'', the deities of the Shinto religion. Overview Structurally, a Shinto shrine typically comprises several buildings. The ''honden''Also called (本殿, meanin ...
Soroban The is an abacus developed in Japan. It is derived from the History of Science and Technology in China, ancient Chinese suanpan, imported to Japan in the 14th century. Like the suanpan, the soroban is still used today, despite the proliferation ...
, a Japanese
abacus The abacus (''plural'' abaci or abacuses), also called a counting frame, is a calculating tool which has been used since Ancient history, ancient times. It was used in the ancient Near East, Europe, China, and Russia, centuries before the ado ...
Japanese mathematics denotes a distinct kind of mathematics which was developed in Japan Japan ( ja, 日本, or , and formally , ''Nihonkoku'') is an island country in East Asia. It is situated in the northwest Pacific Ocean, and is bordered on the west by t ...



* Endō Toshisada (1896). . Tōkyō: _____
OCLC 122770600
* Oya, Shin'ichi. (1970). "Ajima Naonobu" in ''
Dictionary of Scientific Biography The ''Dictionary of Scientific Biography'' is a scholarly reference work that was published from 1970 through 1980 by publisher Charles Scribner's Sons, with main editor the science historian Charles Gillispie, from Princeton University. It cons ...
,'' Vol. 1. New York: Charles Scribner's Sons. * Restivo, Sal P. (1992)
''Mathematics in Society and History: Sociological Inquiries.''
Dordrecht: Kluwer Academic Publishers.
OCLC 25709270
* Selin, Helaine. (1997)
''Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures.''
Dordrecht: Kluwer/
Springer Springer or springers may refer to: Publishers * Springer Science+Business Media, aka Springer International Publishing, a worldwide publishing group founded in 1842 in Germany formerly known as Springer-Verlag. ** Springer Nature, a multinationa ...
OCLC 186451909
David Eugene Smith David Eugene Smith (January 21, 1860 – July 29, 1944) was an Americans, American mathematician, educator, and editor. Education and career David Eugene Smith is considered one of the founders of the field of mathematics education. Smith was bo ...
Yoshio Mikami was a Japanese mathematician and historian of ''Japanese mathematics''. He was born February 16, 1875, in Kotachi, Hiroshima prefecture. He attended the High School of Tohoku University, and in 1911 was admitted to the Imperial University of Tok ...
. (1914)
''A History of Japanese Mathematics.''
Chicago: Open Court Publishing
OCLC 1515528-- note alternate online, full-text copy at archive.org
{{DEFAULTSORT:Ajima, Naonobu 1732 births 1798 deaths 18th-century Japanese mathematicians Japanese writers of the Edo period Japanese Buddhists