A Brief History Of Pi@Everything2.com Except for tsu Ch ungchi, about whom very little is known and who is very unlikelyto have known about Archimedes work, there was no theoretical progress http://www.everything2.com/index.pl?node_id=366822
Kao-tsu -- Encyclopædia Britannica Includes links to articles on Archimedes, Gregory, Ptolemy, tsu Ch ung chi,alKhwarizmi, and Leibniz. Tao Te ching Translations http://www.britannica.com/eb/article-9044631
Extractions: Home Browse Newsletters Store ... Subscribe Already a member? Log in Content Related to this Topic This Article's Table of Contents Kao-tsu Print this Table of Contents Shopping Price: USD $1495 Revised, updated, and still unrivaled. The Official Scrabble Players Dictionary (Hardcover) Price: USD $15.95 The Scrabble player's bible on sale! Save 30%. Merriam-Webster's Collegiate Dictionary Price: USD $19.95 Save big on America's best-selling dictionary. Discounted 38%! More Britannica products Kao-tsu Pinyin Gao Zu (temple name, or miao-hao ), personal name ( hsing-ming Liu Pang, or Liu Chi , posthumous name ( shih Kao Huang-ti founder and first emperor of the Han dynasty (206 BC AD 220), under which the Chinese imperial system assumed most of the characteristics that it was to retain until it was overthrown in 1911/12. He reigned from 206 to 195 BC BC
Astronomers T Pre-1400 tsu Ch ung chi (430501) - astronomer and mathematician. He calculated pi anddevised at new calendar which never was used. He also determined the precise http://www.pa.msu.edu/people/horvatin/Astronomers/astronomers_t_pre.htm
History Of Astronomy: Persons (T) tsu Ch ung chi (430501). Short biography and references (MacTutor Hist. Math.)Tuckerman, Frederick Goddard (1821-1873) Relation to astronomy studied http://www.astro.uni-bonn.de/~pbrosche/persons/pers_t.html
Historical Computation Of PI Table 1 3.15555 = 142/45 Liu Hui 263 5 3.14159 Siddhanta 380 3 3.1416 tsu Ch ung chi 480?7 3.1415926 Aryabhata 499 4 3.14156 Brahmagupta 640? http://www.csgnetwork.com/pitable.html
Extractions: On our site and in all of our calculators, 3.14159 is the value for PI that we use, except those that we specify as higher accuracy. Please see our Piece Of PI information. You can also calculate it yourself using our PI Calculator . Dividing the PI(e) has always been a problem but sometimes multiplying with it is also. You can do either here PI power is also available.
A Piece Of Pi About 150 AD, Ptolemy of Alexandria (Egypt) gave its value as 377/120 and inabout 500 AD the chinese tsu Ch ungchi produced the value as 355/113. http://www.csgnetwork.com/piinfo.html
Extractions: Pi, which is denoted by the Greek letter ( ), is the most famous ratio in mathematics, and is one of the most ancient numbers known to humanity. PI is approximately 3.14, by definition, the number of times that a circle's diameter will fit around the circle. PI goes on forever, and can't be calculated to perfect precision. On our site and in all of our calculators, 3.14159 is the value we use, unless otherwise specified. (You can also calculate it yourself using our PI Calculator . Dividing the PI(e) has always been a problem but sometimes multiplying with it is also. You can do either here PI power is also available.) The only exception is the expatiated calculation below. (I didn't have much to do last night and TV was terrible - the only thing on was the 8,534,565th repeat of Hawaii 50 (divided by PI), so I calculated PI to 10,000 places on my 1959, still working, easy on the eye yellow, NASA issue, Pickett slide rule . I was going to try for a million but the slide was a little dirty and I felt accuracy MIGHT be compromised... We certainly don't want to compromise PI!) The value 3.14159 was defined in 1998 by the Alabama legislature as the official state value for PI. (I'll bet you didn't know that you needed a state value for PI. Of course, they also said that PI are round and cornbread are squared... They would have been better served to say that PI was to personal taste.) This infinite calculation phenomena is known as the decimal expansion of PI. No apparent pattern emerges in the extreme succession of digits; a predestined yet unfathomable code. They do not repeat periodically, but seemingly do pop up repeating a few sequences by blind chance, (lacking any perceivable order, rule, reason, or design). In 1991, the Chudnovsky brothers in New York, using their computer
The EM Chiu Chang Suan Shu /EM (Nine Chapters On The in the chiu Chang Suan Shu, improved by Liu Hui or perhaps tsu Ch ungchih, This article discusses one of these, the chi-Chü, or piling up of http://math.truman.edu/~thammond/history/ChiuChangSuanShu.html
Extractions: Chiu Chang Suan Shu (Nine Chapters on the Mathematical Art) - Mathematics and the Liberal Arts To expand search, see China . Laterally related topics: Yang Hui The I Ching , and Chu Shih-chieh The Mathematics and the Liberal Arts pages are intended to be a resource for student research projects and for teachers interested in using the history of mathematics in their courses. Many pages focus on ethnomathematics and in the connections between mathematics and other disciplines. The notes in these pages are intended as much to evoke ideas as to indicate what the books and articles are about. They are not intended as reviews. However, some items have been reviewed in Mathematical Reviews , published by The American Mathematical Society. When the mathematical review (MR) number and reviewer are known to the author of these pages, they are given as part of the bibliographic citation. Subscribing institutions can access the more recent MR reviews online through MathSciNet Mathews, Jerold. A Neolithic oral tradition for the van der Waerden/Seidenberg origin of mathematics.
China - Mathematics And The Liberal Arts tsu Ch ungchih, and then further improved by the tsu Ch ung-chih s son This article discusses one of these, the chi-Chü, or piling up of squares . http://math.truman.edu/~thammond/history/China.html
Extractions: To refine search, see subtopics The Chiu Chang Suan Shu (Nine Chapters on the Mathematical Art) Yang Hui ... The I Ching , and Chu Shih-chieh . To expand search, see Asia . Laterally related topics: India Japan Siam Malaysia , and Vietnam The Mathematics and the Liberal Arts pages are intended to be a resource for student research projects and for teachers interested in using the history of mathematics in their courses. Many pages focus on ethnomathematics and in the connections between mathematics and other disciplines. The notes in these pages are intended as much to evoke ideas as to indicate what the books and articles are about. They are not intended as reviews. However, some items have been reviewed in Mathematical Reviews , published by The American Mathematical Society. When the mathematical review (MR) number and reviewer are known to the author of these pages, they are given as part of the bibliographic citation. Subscribing institutions can access the more recent MR reviews online through MathSciNet Andersen, Kirsti. The mathematical treatment of anamorphoses from Piero della Francesca to Niceron.
Extractions: Skip Navigation You Are Here ENC Home Curriculum Resources Search the Site More Options Don't lose access to ENC's web site! Beginning in August, goENC.com will showcase the best of ENC Online combined with useful new tools to save you time. Take action todaypurchase a school subscription through goENC.com Classroom Calendar Digital Dozen ENC Focus ... Ask ENC Explore online lesson plans, student activities, and teacher learning tools. Search Browse Resource of the Day About Curriculum Resources Read articles about inquiry, equity, and other key topics for educators and parents. Create your learning plan, read the standards, and find tips for getting grants. Series: RSE program.
Asian Links - China, Japan, Korea, & India Fitness Matters Forum for Dynamic Relaxation,T ai chi, Yoga History ofMathematics china Ancient Mathematicians china s tsu Ch ung chi http://killeenroos.com/link/asia.htm
Extractions: Art of China HomePage/Zodiac Art - many articles on Batik (intor to how to etc..), tie dying from India, facial make up in chinese operas. Products from Good Orient Ancient Contacts Between India And Greece @ The Aryan Pages Art - Cinese by dynasties Beijing - maps, Forbidden City very complete Biomedicine - History of -includes both Asian and Indian sites Boxer Rebellion China - China Special - CNN very interactive has timeline, maps, games, rulers, Quotes of Mao, 1800s in China - "The Open Door" great actual photographs plus text 50the Anniversay - predictions for the future Art of War - Sun Tzu's Ancient Chinese Dynasties - Zhou art - Five dynasties during feudal period Astrology Boxer Rebellion Calendar Classical Art ... Calligraphy - thinkquest very detailed about how to write, the shape of the letters, how to make numbers
User:Gerritholl/mathematicians - Wikipedia, The Free Encyclopedia Gabrielle du Châtelet Nikolai Chebotaryov - Pafnuty Chebyshev - Cheng Dawei -Shiing-shen Chern - Sergei Chernikov - Claude Chevalley - chi tsu Ch ung http://en.wikipedia.org/wiki/User:Gerritholl/mathematicians
Extractions: The Red Cross and other charities also need your help. User:Gerritholl edit Ernst Abbe Niels Henrik Abel Abraham bar Hiyya Max Abraham ... Antoni Zygmund Retrieved from " http://en.wikipedia.org/wiki/User:Gerritholl/mathematicians Views Personal tools Navigation Search Toolbox What links here Related changes Upload file Special pages ... Permanent link This page was last modified 01:33, 19 August 2005. All text is available under the terms of the GNU Free Documentation License (see for details).
Intersecting Cylinders This result was known as far back as 500BC by the chinese astronomer andmathematician tsu Ch ung chi who also calculated pi to 6 decimal places, http://astronomy.swin.edu.au/~pbourke/polyhedra/cylinders/
Extractions: Two perpendicular cylinders. This is known as a Steinmetz solid, the surface area is 16r and the volume is 16r /3. This result was known as far back as 500BC by the Chinese astronomer and mathematician Tsu Ch'ung Chi who also calculated pi to 6 decimal places, namely 355/113. Tetrahedron (4 cylinders)
The Math Forum - Math Library - Pi A history of pi the Rhind papyrus (Egypt), Ptolemy, tsu Ch ung chi, al Khwarizmi,Al Kashi, Viet, Romanus, Van Ceulen, Gregory, Shanks, Lambert, Euler, http://mathforum.org/library/topics/pi/
Extractions: Whether it is considered to be of historical significance, mathematical importance, or a personal goal, Pi has universal appeal. This site is an adventure in exploring the concept of Pi, with activities, projects, applications, history, an information video, and teacher resources. Activities include finding out how different mathematicians have calculated Pi; looking at a Pi hyperstack and video; participating in a Pi pizza project; doing some hands-on Pi problems; and celebrating Pi day, March 14. more>> The Pi Pages - Centre for Experimental and Constructive Mathematics (CECM) "Pi is one of the few concepts in mathematics whose mention evokes a response of recognition and interest in those not concerned professionally with the subject. It has been a part of human culture and the educated imagination for more than twenty five hundred years...." Links to many sources of information on pi: Story of the history of the computation of Pi; Current records of computation; People involved in the computation of Pi in recent years; How to Compute 1 Billion Digits of Pi, the 100 Billionth Binary Digit of Pi, Pi and the AGM, The Quest for Pi, Recognizing a Number, Experimental Pi; Pi News; Pi on the net - The New Pi, From Number to Formula, The Miraculous Pi, The Passion for Pi, A Question of Numbers; Pi Files.
Math Forum: T2T FAQ: Pi Day A history of Pi the Rhind papyrus (Egypt), Ptolemy, tsu Ch ung chi, al Khwarizmi,Al Kashi, Viet, Romanus, Van Ceulen, Gregory, Shanks, Lambert, Euler, http://mathforum.org/t2t/faq/faq.pi.html
Extractions: Teachers use this date to engage students in activities related to the history and concept of . Students are often familiar with before this day and the projects and activities associated with Pi Day are meant to enrich and deepen the students' understanding of the concept. Activities may include investigations of the value of by approximating the ratio of the circumference to the diameter of a circle. Students may also share their own Pi Projects with their classmates. Some teachers choose to end their Pi Day celebration by eating pie! If you are looking for some ways to celebrate math in your math class, or if you would like to suggest some school-wide thematic activities, you are certain to find ideas on this page to help you design a Pi Day that students will enjoy. If honoring is not enough of a reason to make this day special, keep in mind that March 14 is also
Math Games: Keen Approximations The convergents (close fractions) of p are 3, 22/7 (Archimedes), 333/106,355/113 (tsu Ch ungchi, 480 AD), 103993/33102, and so on. http://www.maa.org/editorial/mathgames/mathgames_03_15_05.html
Extractions: Search MAA Online MAA Home Ed Pegg Jr., March 15, 2005 This column generated a lot of good feedback when it appeared last month. I've been given some of the best approximations I've seen. So what is this word best that I speak of, in a mathematical sense? There are several interesting bestness lists in math: Best is different from Largest . The largest known prime for the moment is 2 - 1, but that won't last forever. Likely, it won't even be on the top ten list in 2015, if previous searches are any indication. An example of best What is the best packing for 10 circles in a unit square? De Groot proved the best result in 1990. At least four attempts at "best" before him were wrong. For approximations I wanted something similar. Looking through my thesaurus, I pulled out keenness as a good descriptive term, since approximations need to cut close. I later learned of the Uniformity Conjecture . Daniel Richardson's paper "
Roboteacherpage (tsu Ch ung chi, Charles Atlas, and Edgar Allen Poe return.) tsu Ch ung chiis humming what he thinks is an octave. The kids all look at him, http://www.montessori.evansville.net/Roboteacherpage.html
Extractions: Roboteacher 3000 (Scene opens on a classroom. The kids are throwing paper airplanes and generally misbehaving, until a few of them notice that the teacher is on his way into the room. They shush each other and return to their seats. The teacher enters.) Mr. Lamey Good morning, children. Class Good morning, Mr. Lamey! Mr. Lamey My goodness, arent we all sitting so nice and pretty today? I wish I had my camera. (He picks up a paper airplane that hes discovered on his chair.) Whats this? Im guessing that the principal has been in here again, throwing paper airplanes while you all sat watching in horror, am I right? Class Yes, Mr. Lamey. Mr. Lamey Now kids, you know Ive asked you not to throw these things in the room. What have I told you might happen? Tori Ann? Tori Ann Youll put someones eye out? Mr. Lamey Maybe not. But you will go running around like crazy to catch them, trip over your untied shoelace, knock something over, and get sent to the principals office. Shes the one with the put someones eye out obsession, not me. (Looking at his clipboard) Anyway, lets take a look and see whos here today. Tess Teasdale? Tess Here.
A History Of PI Approximations About 480 AD in china, tsu Ch ungchi gave = 355/113 (3.1415929 ) which is 7digits of accuracy. Not until the 15th century did Al-Kashi reach 16 digits. http://home.egge.net/~savory/maths7.htm
Extractions: is the ratio of the circumference of any convex curve of constant diameter to that diameter. Usually a circle is stated, but this more precise definition includes e.g. Wankel rotors, and others of that ilk with more than the Wankel's three lobes :-) In the bible's old testament, I Kings 7:23 implies that Ahmes, an egyptian scribe, wrote that the area of a circle is like a square on 8/9 of its diameter, thus giving Archimedes used a 96-sided polygon to limit to between 3 + 10/71 (3.14085...) and 3 + 10/70 (3.142857...) . Archimedes also gave the schoolchild's approximation 22/7 (3.142857...) Ptolomy worked with About 480 AD in China, Tsu Ch'ung-Chi gave = 355/113 (3.1415929...) which is 7 digits of accuracy. Not until the 15th century did Al-Kashi reach 16 digits. Ludolph van Ceulen (1540-1610) reached 20, then 32, then 35 digits. They are carved on his gravestone in the church in Leyden. In 1706 John Machin calculated 100 digits. Finally, Johann Lambertz (1728-1777) proved that is irrational (i.e. is not expressible as a fraction). His personal best approximation was 1,019,514,486,099,146 / 324,521,540,032,945. Here is a shorter
TIMELINE 5th CENTURY Page Of ULTIMATE SCIENCE FICTION WEB GUIDE 430 tsu Ch ung chi was born in Fanyang, china in 430 AD. tsu Ch ung chi andhis father found the formula for the volume of a sphere by carrying out Liu http://www.magicdragon.com/UltimateSF/timeline5.html
Extractions: Return to Ultimate SF Table of Contents May be posted electronically provided that it is transmitted unaltered, in its entirety, and without charge. We examine both works of fiction and important contemporaneous works on non-fiction which set the context for early Science Fiction and Fantasy. There are hotlinks here to authors, magazines, films, or television items elsewhere in the Ultimate Science Fiction Web Guide or beyond. Most recently updated: 20 May 2003 [from 152 to 169 kilobytes]. This web page draws heavily on FACTS as listed in " The Timetables of Science Facts were also checked against " The 1979 Hammond Almanac " [ed. Martin A. Bacheller et al., Maplewood, New Jersey, 1978], p.795. It also utilizes facts from Volume I of D.E. Smith's " History of Mathematics " [(c) 1921 by David Eugene Smith; (c) 1951 by May Luse Smith; New York: Dover, 1958]. Facts are also drawn from the 1911 Encyclopedia Brittanica , and the Wikipedia Executive Summary of the Fifth Century Mathematical/Scientific/Philosophical/Literary People of the Fifth Century Fiction About the 5th Century Non-Fiction About the 5th Century ... 5th Century Historians, on the 5th Century
Math History - Pre-historic And Ancient Times About 460, tsu Ch ung chi gives the approximation 355/113 to p which is correctto 6 decimal places. 499, Aryabhata I calculates p to be 3.1416. http://lahabra.seniorhigh.net/pages/teachers/pages/math/timeline/MpreAndAncient.
Extractions: Prehistory and Ancient Times Middle Ages Renaissance Reformation ... External Resources About 30000BC Palaeolithic peoples in central Europe and France record numbers on bones. About 25000BC Early geometric designs used. About 4000BC Babylonian and Egyptian calendars in use. About 3400BC The first symbols for numbers, simple straight lines, are used in Egypt. About 3000BC Babylonians begin to use a sexagesimal number system for recording financial transactions. It is a place-value system without a zero place value. About 3000BC Hieroglyphic numerals in use in Egypt. About 3000BC The abacus is developed in the Middle East and in areas around the Mediterranean. A somewhat different type of abacus is used in China. About 1950BC Babylonians solve quadratic equations.
Honenfs Establishment Of A Chinese Lineage century) established the T ient ai lineage in his Fo-tsu-t ung-chi. The first begins with Bodhiruci and follows to Hui-ch ung, Tao-chang, http://www.jsri.jp/English/Honen/TEACHINGS/clineage.html
Extractions: Honen's Establishment of a Chinese Lineage A common method of legitimation which East Asian Buddhist sects have used is establishing a lineage of the transmission from Shakyamuni Buddha himself down to their particular founder, and from thence to the present age. This is always established in order to invest the teachings with authority. It was during the Sung Dynasty (960-1297) that the establishment of official lineages for the various schools of Buddhism became common. The Ch'an school lineage was established at this time through Tao-yuan's Ching-te-chuan-teng-lu . Yuan-chao (1048-1116) established the nine patriarchs of the Four Part Vinaya school in his Nan-shan-lu-tsung tsu-ch'eng-t'u-lu , and Chih-p'an (circa late thirteenth century) established the T'ien-t'ai lineage in his Fo-tsu-t'ung-chi . Pure Land Buddhism was in turn influenced by these earlier examples, and Tsung-hsio (1151-1214) established the Pure Land lineage in his Le-pang-wen-lei (T. 1469, vol. 47). This lineage is as follows: Hui-yuan of Lu-shan, Shan-tao, Fa-chao, Shao-k'ang, Sheng-ch'ang, and Tsung-tse. Honen's lineage, however, differs fundamentally in that he neither recognized Hui-yuan as Shan-tao's teacher nor as a patriarch at all. In Honen's Commentary on the Jodosanbukyo (Sanbukyo shaku) , in reference to the Amida Sutra , he says: In the Pure Land school of Shan-tao, no one studied directly under him, and no one praises him. But I, through his writings, have inherited his intention and so have founded the Pure Land sect. Therefore, in the Pure Land school there is nothing one can call a lineage, nor is there any proof of the oral transmission of its teachings. Nevertheless, on the basis of the teaching of the sutras and commentaries, and on my personal experience, I have established the Pure Land sect. (SHZ. 145)
