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Topic: Sangaku

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Seki Kowa

1708

	sangaku math
		Sangaku are found in both Shinto shrines and Buddhist temples, but are found in twice as many Shinto shrines as Buddhist temples.
		A Sangaku from the Mie Prefecture was inscribed with the name of a merchant, one of the lowest castes in the Edo period.
		Sangaku theorems did not provide immediate societal benefit (they did not help crops grow), did not necessarily translate into large sums of money, and were being done by everyone in Japan from women and children to merchants and samurais.
	www.loyola.edu /maru/sangaku.html (5033 words)

	Sangaku was Sudoku for the 17th century :: Rebecca Blood
		» Sangaku was the Sudoku of the 17th century, complex math problems based on principles even a child could understand.
		Sangaku were more like math Olympics problems, or the sort of thing your teacher might have put on the wall for extra credit." Tony Rothman, Princeton physics lecturer.
		Also, the number of surviving tablets is so small relative to the population of Japan and the length of the seclusion period as to attach a big question mark to the popularity of sangaku.
	www.rebeccablood.net /archive/2006/08/sangaku_was_sudoku_for_the_17t.html (378 words)

	Princeton University - Rothman helps reveal intricacies of ancient math phenomenon
		“Sangaku tablets are perhaps unique among the world’s cultural creations, as they are simultaneously objects of art, religious offerings and a record of what we might call folk mathematics,” said Rothman, who is a lecturer in the physics department and Pulitzer Prize nominee for his writings on science for the public.
		While modern mathematical methods, such as calculus, can sometimes simplify a sangaku problem that requires pages of calculation, Rothman said that the advantage to the math used in sangaku problems was that it was simple enough for young children to use, which opened the problems up to nearly anyone who wished to try them.
		This portion of a wooden sangaku -- literally "mathematical tablet" -- is from one of approximately 900 that survive in Japan from as far back as the 17th century.
	www.princeton.edu /main/news/archive/S15/04/04O77/index.xml?section=featured (1463 words)

	Sacred Sites of Japan and Mt Fuji (Site not responding. Last check: 2007-11-02)
		Sangaku shinko should not however, be thought of in the narrow sense of mountain worship, but rather understood to have a broader meaning which includes the mythology, folk beliefs, rituals, shamanistic practices, and shrine structures that are associated with the religious use of particular mountains.
		By the middle of the Heian period the complex interaction of Sangaku shinko, Shintoism and Shingon Buddhism had given rise to one of the most unique and fascinating religious practices found anywhere in the world.
		A blend of pre-Buddhist folk traditions of Sangaku shinko and Shinto, Tantric Buddhism, and Chinese Yin-yang magic and Taoism, Shugendo may be roughly defined as the 'way of mastering magico-ascetic powers by retreat to and practice within the sacred mountains'.
	www.sacredsites.com /2nd56/intjapan.html (2981 words)

	collision detection: Sangaku: The Sudoku of the 17th century
		Behold an ancient Japanese "Sangaku" table -- the Sudoku of the 17th century.
		Sangaku emerged during the 100-year period that Japan forcibly cut itself off from West, allowing only one Dutch ship a year to dock.
		Anyway, Sangaku fell into disrepute during the 20th century, but Tony Rothman, a Princeton Nobel nominee, is helping spearhead a movement to restore what he calls the sudoku of the 17th century.
	www.collisiondetection.net /mt/archives/2006/07/what_developed.html (596 words)

	bit-tech.net \| Sangaku Japanese case mod (Site not responding. Last check: 2007-11-02)
		It's basic dimensions would clearly define it as a PC - the goal wasn't to try to create something really crazy like the guys at WCG 2005 with Alien heads and fish tanks etc. Something aesthetically pleasing that, first and foremost, looked like some badass Japanese woodwork, but was also a PC.
		Sangaku is the Japanese word for unique, wooden, mathematical tablets created during the Edo period (1603-1867) in Japan - a period when all Western influences were shunned.
		Back in the 21st Century, the spirit of the ancient sangaku lives on in the craftmanship and attention to detail of this project.
	www.bit-tech.net /modding/2006/04/06/japanese_case_mod_sangaku/1.html (545 words)

	A Modern-Day Sangaku (Site not responding. Last check: 2007-11-02)
		The traditional sangaku is a shaped wooden tablet on which a geometric problem or theorem is written with colorful paint.
		A mathematical understanding of the derivation is not necessary for participants to help assemble it or for viewers to appreciate the wonderful patterns and relationships within its complex structure.
		As with traditional sangaku, it will be a work of devotees colorfully celebrating the beauty of geometry.
	www.cs.sunysb.edu /~george/sangaku (570 words)

	Minbu Za Folk Dance (Site not responding. Last check: 2007-11-02)
		Sangaku did not just involve dance, it also encompassed such attractions as music, puppetry, and acrobatics.
		Sangaku does not exist as a separate form, but, as Japan has done with other bits of Chinese culture, been assimilated into Japanese culture.
		Sangaku became Sarugaku, a lively form of dance which was performed at various social functions.
	www.japanesefolkdance.org /MinbuFolkDance.htm (750 words)

	List of masterpieces of the oral and intangible heritage of humanity
		Nôgaku theatre developed in the fourteenth and fifteenth centuries but actually dates from the eighth century, when the “Sangaku” was transmitted from China to Japan.
		At the time, the "Sangaku" comprised various types of performances, with acrobats, song and dance as well as comic sketches.
		The Kyôgen is derived from the comic plays of the "Sangaku" and is based on comic dialogue with very little use of masks.
	www.unesco.org /culture/intangible-heritage/masterpiece.php?lg=en&id=12 (375 words)

	ljs17December2001.nb (Site not responding. Last check: 2007-11-02)
		Typically the texts on the tablets did not include proofs, and yet the people who created and admired these icons must have had considerable insights into geometry.
		Some of the sangaku require sophisticated mathematical tools for their solution.
		The article that first brought sangaku to my attention was published in the May 1998 issue of Scientific American.
	www.unl.edu /tcweb/fowler/myGeometry/sangaku (264 words)

	SANGAKU (Site not responding. Last check: 2007-11-02)
		These theorems appeared as beautifully colored drawings on wooden tablets which were hung under one of the roof in the precincts of a shrine or temple.
		The tablet was called a SANGAKU which means a mathematics tablet in Japanese.
		I would like to send some image files of SANGAKUs by the Internet because SANGAKU is one of the customs left only in Japan.
	www.wasan.jp /english (190 words)

	Scientific American: Feature Article: Japanese Temple Geometry: May 1998 (Site not responding. Last check: 2007-11-02)
		From a survey of the extant sangaku, the tablets seem to have been distributed fairly uniformly throughout Japan, in both rural and urban districts, with about twice as many found in Shinto shrines as in Buddhist temples.
		Fukagawa believes that Seki encountered sangaku on his way to the shogunate castle, where he was officially employed as court mathematician, and that the tablets pushed him to further researches.
		It is pleasant to realize that some sangaku were the works of ordinary mathematics devotees, carried away by the beauty of geometry.
	www2.gol.com /users/coynerhm/0598rothman.html (2721 words)

	Bates College \| Abstracts: Grants for the Study of Asia, 2004-2005
		The study of sangaku is a part of the study of wasan, traditional Japanese mathematics.
		Sangaku, votive mathematical tablets, were a popular means for promoting mathematics during the Edo period in Japan when the country was almost completely closed off from the Western world.
		Because sangaku lies within the study of wasan, the traditional Japanese mathematics, most of its literature is in Japanese; in fact, the first book in English on sangaku was published in 1989.
	www.bates.edu /abstracts-study-asia-grants-04-05.xml (2044 words)

	Shirley Strum Kenny Student Arts Festival (Site not responding. Last check: 2007-11-02)
		Sangaku is a Japanese tradition of celebrating geometrical beauty, popular during the Edo period (1603-1867) by members of all social classes.
		The traditional sangaku, a shaped wooden tablet on which a geometric problem or theorem is written with colorful paint was displayed in a temple or shrine as an offering, as a puzzle for others to think over and understand, and as a way for the creator to show off the geometric discovery.
		The assembly and creation of the modern day sangaku is led by Dr. George Hart, Computer Science Department.
	www.sunysb.edu /sb/artsfest/calendar.shtml (356 words)

	www.myspace.com/jedicelt
		The bulk of this is made up of Hiphop and Reggae which have been a part of my life since I was a knee high to a...
		After choosing not to be affiliated to the dojo, he left and fought his professional debut in 2003.
		Sangaku has fought in Demolition, D.O.G (cage fight), RISE, and Shootboxing and currently trains under UFC, Pride, and Pancrase fighter Kosaka Tsuyoshi at A-Square (Team Alliance).
	www.myspace.com /jedicelt (1028 words)

	Some sangaku
		Two sangaku found in two different shrines in the city of Fukuoka one is still very nice, the other is almost deleted
		Old sangaku in the museum of the Yasui shrine in Kyoto
		Two small sangaku recently dedicated to the yasui shrine in Kyoto.
	www.sangaku.info /sangaku_all.en.html (125 words)

	The Japanese Case Mod
		Well, not only is this his first ever computer mod, but it's his first computer he's built from scratch.
		Here he is in his own words as he describes the design and development of "Sangaku," a Japanese case mod...
		"Sangaku" (which in Japanese translates to "mathematics tablet") is the synthesis of my passion for furniture making and my fascination with computers, and this is my first try at modding a computer.
	www.extremetech.com /article2/0,1697,1899276,00.asp (687 words)

	Newsletter 44, November 2000: History and Culture in Mathematics Education (Site not responding. Last check: 2007-11-02)
		Spelling out in more detail how this may be achieved will be a useful service to teachers.
		Sangaku is one of Japanís indigenous mathematical customs from the Edo period.
		Sangaku appeared to be a fruitful medium for working with students, who studied constructing and solving problems through the making of Sangaku.
	www.hpm-americas.org /nl44/nl44art1.html (1568 words)

	Early Japanese Music
		So, if you were to somehow transport yourself back to an educated, ancient Japanese experience of music, you would hear distinct cultures in your music rather than hear distinct uses of the music, which is how modern musicologists and audiences hear ancient Japanese music.
		The musical life of the T'ang court was extremely varied and multicultural; a formal set of rules, called the "Ten Styles of Music" governed the hierarchy and use of Chinese and foreign musical styles in court.
		When, however, the music consisted of popular music from T'ang China, this music was classified as To-sangaku, or "unofficial T'ang music." Sangaku was the most active and exciting of the early musics—interspersed between songs were acrobatics and energetic pantomimes.
	www.wsu.edu:8080 /~dee/ANCJAPAN/MUSIC.HTM (2387 words)

	Encyclopedia
		Bugaku may now be seen only at ceremonies.
		A type of acrobatic entertainment known as sangaku, transmitted similarly to Japan from the Asian continent and popular in the 8th century, also influenced Japanese drama.
		Typical acts included tightrope walking, juggling, and sword swallowing.
	www.historychannel.com /encyclopedia/article.jsp?link=FWNE.fw..ja010300.a (1693 words)

	Sangaku Problems (Site not responding. Last check: 2007-11-02)
		During Japan's period of national seclusion (1639–1854) there arose a tradition known as sangaku, Japanese temple geometry.
		Under the roofs of their religious shrines and temples, sangaku devotees would hang brightly colored tablets engraved with solutions to geometry problems [1].
		Many sangaku problems are quite difficult; I have selected these as they can be solved armed solely with the mere knowledge of the Pythagorean Theorem and the Quadratic Formula.
	www.paginar.net /matias/articles/sangaku/sangaku.html (408 words)

	Ethnomathematics Digital Library (EDL) (Site not responding. Last check: 2007-11-02)
		This website describes sangaku from Japan, the tablets of solved math problems that were hung in temples.
		The sangaku and the problems inscribed on them represent the best record of wasan, or traditional mathematics, in Japan.
		They show a wide variety of problems and were probably created by many different kinds of people.
	www.ethnomath.org /search/browseResources.asp?type=subject&id=315 (151 words)

	Ivars Peterson's MathTrek -Temple Circles
		Scholars and others would inscribe geometric problems on wooden tablets, then hang the tablets under the eaves of Shinto shrines and Buddhist temples as offerings.
		Such a tablet is called a sangaku, which means "mathematical tablet" in Japanese.
		Additional information about sangaku and geometrical theorems can be found at http://iae.tdec.drexel.edu/Computer/CAD/CAD_3/CAD_3.html.
	www.maa.org /mathland/mathtrek_4_23_01.html (644 words)

	A Modern-Day Sangaku (Site not responding. Last check: 2007-11-02)
		On monday, April 24, 2006, I asked students, faculty, and staff to help me create a modern-day sangaku in Stony Brook University's Wang center.
		This is a celebration of the beauty of geometry, in the form of a large geometric sculpture.
		This is a display by devotees colorfully celebrating the beauty of geometry in a peaceful temple-like setting.
	www.georgehart.com /sangaku (392 words)

	Sangaku - Related mathematics (Site not responding. Last check: 2007-11-02)
		When looking at the original sangaku carefully, one can raise many interesting questions, some of which may turn out to relate this geometrical puzzle to other, often difficult and famous problems, also from other fields of mathematics.
		The sangaku shows a way of 'packing' 5 identical discs in a square without overlap.
		What happens if one changes the simulation to reflect reality better, namely by letting all lilies grow which are not colliding, and delaying only the growth of the colliding ones?
	wwwhome.cs.utwente.nl /~zsofi/sangaku/SanRel.html (335 words)

	The Math Forum - Math Library - Euclidean/Plane Geom. (Site not responding. Last check: 2007-11-02)
		Click on the map of Japan to see photographs of sangaku -- Euclidean geometry theorems rendered as colored drawings on wooden tablets, and hung in shrines or temples -- dating to the Edo period (1603-1867).
		Read PDF or PS downloads of a tutorial on the inversion method for solving Sangaku, or of the article "Japanese Temple Geometry," which first...more>>
		An article with background history and a new analysis: A unique 3rd Dynasty (~2600 B.C.) Egyptian artefact thought to be an architect's drawing has heen re-evaluated by the author and the geometry reveals surprising results.
	mathforum.org /library/topics/euclidean_g?keyid=3136706&start_at=801&num_to_see=50 (2027 words)

	Newegg.com - Case Mod Contest - Winner - October 2005
		I did, however, have substantial experience in furniture design/making and my old roommate was a computer nerd so he pushed me to combine the two, to form this project.
		My furniture related projects right before Project: “Sangaku” (which in Japanese translates to “mathematics tablet”) were related to the Japanese shoji screens and I have just been in a Japanese design mood for a while so it was natural that this case would have a Japanese feel.
		I also wanted it to have efficient air cooling since water cooling was not exactly in the budget yet.
	promotions.newegg.com /casemod/contestants/1205/winner/index.htm (484 words)

	[No title] (Site not responding. Last check: 2007-11-02)
		Geographical Location Chubu Sangaku is situated in north-central Honshu island in the Gifu, Nagano, Niigata and Toyama Prefectures.
		The park boundary starts 10km inland from the coast and follows the Hida mountain range down to Mount Norikura, 20-30km west of Matsumoto.
		Chubu Sangaku National Park Headquarters Office, Environmental Agency, Shimashima, Azumi Village, Nagano Prefecture, Japan.
	www.unep-wcmc.org /sites/pa/1305v.htm (828 words)

	Japanese Temple Geometry
		Of the world's countless customs and traditions, perhaps none is as elegant, nor as beautiful, as the tradition of sangaku, Japanese temple geometry.
		From 1639 to 1854, Japan lived in strict, self-imposed isolation from the West.
		These sangaku, a word that literally means mathematical tablet, may have been acts of homage - a thanks to a guiding spirit - or they may have been brazen challenges to other worshipers: Solve this one if you can!
	www.sciamdigital.com /index.cfm?fa=Products.ViewIssuePreview&ARTICLEID_CHAR=61587AF0-2B35-221B-68B928807970149A (169 words)

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