Geschichte tsu Ch ung chi (430-510),der Archimedes Arbeit vermutlich nicht kannte, eine wichtige Verbesserung p http://www.eag.aa.schule-bw.de/PROJEKTE/MUW/PI/gesch.htm
Honenfs Establishment Of A Chinese Lineage thirteenth century) established the T ient ai lineage in his Fo-tsu-t ung-chi. Thefirst begins with Bodhiruci and follows to Hui-ch ung, Tao-chang, T an Luan 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)
Intersecting Cylinders area is 16r 2 and the volume is 16r 3 /3. This result was known as far back as500BC by the chinese astronomer and mathematician tsu Ch ung chi who also 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)
A Brief History Of Pi Ptolemeios fann värdet 377/120 (=3,1416) och kinesen tsu Ch ungchi förbättradedetta genom att visa att pi ligger mellan 3,1415926 och 3,1415927. http://abel.math.umu.se/~frankw/pihist_sw.html
Extractions: This text might be available in English soon Decimaler genom historien 1853 publicerade William Shanks sin beräkning av pi till 707 decimaler och det var ett rekord som stod sig ända tills datorerna gjorde sitt intåg på 1940-talet. 1945 visade det sig att Shanks hade gjort ett räknefel och att hans resultat "bara" var korrekt till 527 decimaler. Back to my homepage.
Encyclopedia Mythica: Conversion Chart Ch en Cheng Ch eng chi Ch ih Chong Ch ung Chou Ch Hui Hun Hun Huo Huo, Pinyin WadeGilesJi chi Jia chia Zhuo Cho Zi Tzu Zong tsung Zou Tsou Zu tsu Zuan tsuan http://www.pantheon.org/miscellaneous/conversion_chart.html
Extractions: Links Conversion chart The names of deities and places in the Chinese mythology area are transcribed according to the pinyin system of romanization. This system was officially adopted by the People's Republic of China in 1979. The names according to the previously standard Wade-Giles system, which is still widely employed, are provided in each article. Pinyin Wade-Giles Ba Pa Bai Pai Ban Pan Bang Pang Bao Pao Bei Pei Ben Pen Beng Peng Bi Pi Bian Pien Biao Piao Bie Pieh Bin Pin Bing Ping Bo Po Bu Pu Pinyin Wade-Giles Ca Ts'a Cai Ts'ai Can Ts'an Cang Ts'ang Cao Ts'ao Ce Ts'e Cen Ts'en Ceng Ts'eng Cha Ch'a Chai Ch'ai Chan Ch'an Chang Ch'ang Chao Ch'ao Che Ch'e Chen Ch'en Cheng Ch'eng Chi Ch'ih Chong Ch'ung Chou Ch'ou Chu Ch'u Chuai Ch'uai Chuan Ch'uan Chuang Ch'uang Chui Ch'ui Chun Ch'un Chuo Ch'o Ci Tz'u Cong Ts'ung Cou Ts'ou Cu Ts'u Cuan Ts'uan Cui Ts'ui Cun Ts'un Cuo Ts'o Pinyin Wade-Giles Da Ta Dai Tai Dan Tan Dang Tang Dao Tao De Te Dei Tei Deng Teng Di Ti Dian Tien Diao Tiao Die Tieh Ding Ting Diu Tiu Dong Tung Dou Tou Du Tu Duan Tuan Dui Tui Dun Tun Duo To Pinyin Wade-Giles E E Ei Ei En En Er Erh
Yet Another Story Of Pi About 150 AD, Ptolemy of Alexandria (Egypt) gave its value as 377/120 andin about 500 AD the chinese tsu Ch ungchi gave the value as 355/113. http://www.geocities.com/CapeCanaveral/Lab/3550/pi.htm
Extractions: Undoubtedly, pi is one of the most famous and most remarkable numbers you have ever met. The number, which is the ratio of circumference of a circle to its diameter, has a long story about its value. Even nowadays supercomputers are used to try and find its decimal expansion to as many places as possible. For pi is one of those numbers that cannot be evaluated exactly as a decimal - it is in that class of numbers called irrationals. The hunt for pi began in Egypt and in Babylon about two thousand years before Christ. The Egyptians obtained the value (4/3)^4 and the Babylonians the value 3 1/8 for pi. About the same time, the Indians used the square root of 10 for pi. These approximations to pi had an error only as from the second decimal place. (4/3)^4 = 3,160493827... 3 1/8 = 3.125 root 10 = 3,16227766... pi = 3,1415926535... The next indication of the value of pi occurs in the Bible. It is found in 1 Kings chapter 7 verse 23, where using the Authorised Version, it is written "... and he made a molten sea, ten cubits from one brim to the other : it was round about ... and a line of thirty cubits did compass it round about." Thus their value of pi was approximately 3. Even though this is not as accurate as values obtained by the Egyptians, Babylonians and Indians, it was good enough for measurements needed at that time. Jewish rabbinical tradition asserts that there is a much more accurate approximation for pi hidden in the original Hebrew text of the said verse and 2 Chronicles 4:2. In English, the word 'round' is used in both verses. But in the original Hebrew, the words meaning 'round' are different. Now, in Hebrew, etters of the alphabet represent numbers. Thus the two words represent two numbers. And - wait for this - the ratio of the two numbers represents a very accurate continued fraction representation of pi! Question is, is that a coincidence or ...
A Treatise On Pi NAME, YEAR, ACCURACY. Ptolemy, (c. 150 AD), 3.1416. tsu Ch ung chi, (430501AD), 355/113. al-Khwarizmi, (c. 800 ), 3.1416. al-Kashi, (c. 1430), 14 places. http://www.geocities.com/pi_is_my_favourite_number/Pi/Pi.html
Extractions: The number has always been my favourite number because of its unparalleled aesthetic beauty. On this page, I shall provide an overview of this extraordinary number: its history, properties, and its interesting facts. History of Pi Ancient History is perhaps the most famous ratio in mathematics. It is defined as the ratio between the circumference of a circle and its diameter. Throughout the ages, mathematicians have strived to find the value of . One of the earliest reference to was recorded in the Rhind Papyrus during the Egyptian Middle Kingdom, and was written by a scribe named Ahmes around 1650 BC. Ahmes began the scroll with the words: "The Entrance Into the Knowledge of All Existing Things", and made passing remarks that he composed the scroll "in likeness to writings made of old." Towards the end of the scroll, which comprises of various mathematical problems and their solutions, the area of a circle is found using a rough sort of It is interesting to note that the number is also indrectly quoted in the Bible. There is a little-known verse that reads
The Contest Center - Pi 5, v(227/23), pi .00000 624, Rubin. 6, 355/113, pi + .00000 0266,tsu Ch ung chi 450AD. 7, v527 - v354 - 1, pi - .00000 0190, Rubin. http://www.contestcen.com/pi.htm
Extractions: This is an open-ended competition to find the best possible approximations to pi (about 3.14159 26535 89793 23846 26433). A good approximation would be an expression which matches pi to more significant digits than the number of digits contained in that expression. For example, the most common approximation to pi is 22/7 which is about 3.14286. This contains 3 digits, and matches the first 3 digits of pi, so it is a fair approximation. We will consider 4 types of approximations. The first type uses only the mathematical operations of addition, subtraction, multiplication, division, and square root. It may not use other operations such as decimal fractions, exponentiation, logarithms, or any trig functions. For example, 355/113 (approximately pi+0.00000 0266) would be a valid expression, but 2 arcsin(1) would not. These approximations can be constructed with ruler and compass.
About "Pi Through The Ages" A history of pi the Rhind papyrus (Egypt), Ptolemy, tsu Ch ung chi,al Khwarizmi, Al Kashi, Viet, Romanus, Van Ceulen, Gregory, Shanks, Lambert http://mathforum.org/library/more_info.html?id=5241
The Math Forum - Math Library - Pi Pi Through the Ages MacTutor Math History Archives A history of pi the Rhind papyrus(Egypt), Ptolemy, tsu Ch ung chi, al Khwarizmi, Al Kashi, Viet, Romanus 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.
CHRONOLOGY OF MATHEMATICIANS 390 THEON OF ALEXANDRIA. 415 DEATH OF HYPATIA. 470 tsu CH UNGchi VALUE OF PI. 476ARYABHATA. 485 DEATH OF PROCLUS. 520 ANTHEMIUS OF TRALLES AND ISIDORE OF MILETUS. http://users.adelphia.net/~mathhomeworkhelp/timeline.html
Extractions: CHRONOLOGY OF MATHEMATICIANS -1100 CHOU-PEI -585 THALES OF MILETUS: DEDUCTIVE GEOMETRY PYTHAGORAS : ARITHMETIC AND GEOMETRY -450 PARMENIDES: SPHERICAL EARTH -430 DEMOCRITUS -430 PHILOLAUS: ASTRONOMY -430 HIPPOCRATES OF CHIOS: ELEMENTS -428 ARCHYTAS -420 HIPPIAS: TRISECTRIX -360 EUDOXUS: PROPORTION AND EXHAUSTION -350 MENAECHMUS: CONIC SECTIONS -350 DINOSTRATUS: QUADRATRIX -335 EUDEMUS: HISTORY OF GEOMETRY -330 AUTOLYCUS: ON THE MOVING SPHERE -320 ARISTAEUS: CONICS EUCLID : THE ELEMENTS -260 ARISTARCHUS: HELIOCENTRIC ASTRONOMY -230 ERATOSTHENES: SIEVE -225 APOLLONIUS: CONICS -212 DEATH OF ARCHIMEDES -180 DIOCLES: CISSOID -180 NICOMEDES: CONCHOID -180 HYPSICLES: 360 DEGREE CIRCLE -150 PERSEUS: SPIRES -140 HIPPARCHUS: TRIGONOMETRY -60 GEMINUS: ON THE PARALLEL POSTULATE +75 HERON OF ALEXANDRIA 100 NICOMACHUS: ARITHMETICA 100 MENELAUS: SPHERICS 125 THEON OF SMYRNA: PLATONIC MATHEMATICS PTOLEMY : THE ALMAGEST 250 DIOPHANTUS: ARITHMETICA 320 PAPPUS: MATHEMATICAL COLLECTIONS 390 THEON OF ALEXANDRIA 415 DEATH OF HYPATIA 470 TSU CH'UNG-CHI: VALUE OF PI 476 ARYABHATA 485 DEATH OF PROCLUS 520 ANTHEMIUS OF TRALLES AND ISIDORE OF MILETUS 524 DEATH OF BOETHIUS 560 EUTOCIUS: COMMENTARIES ON ARCHIMEDES 628 BRAHMA-SPHUTA-SIDDHANTA 662 BISHOP SEBOKHT: HINDU NUMERALS 735 DEATH OF BEDE 775 HINDU WORKS TRANSLATED INTO ARABIC 830 AL-KHWARIZMI: ALGEBRA 901 DEATH OF THABIT IBN - QURRA 998 DEATH OF ABU'L - WEFA 1037 DEATH OF AVICENNA 1039 DEATH OF ALHAZEN
8th Grade Mathematics - Projects - Pi 3.1416. 480 AD tsu Ch ung chi, an astronomer in china approximatepi to be 355/113 (ie 3.14159292 accurate to 5 places.). 640 http://www.ic.sunysb.edu/Stu/gho/pi.html
Extractions: Pi: What is pi? Don't be fooled by the picture, it's not the same kind of pie you buy at the store. Pi is actually a letter of the Greek alphabet. In mathematics, pi is used to represent the ratio between the diameter of a circle and its circumference. Why is pi so special? Do we know the value of pi? 1650 BC - value of pi approximated as 3.14 in the Egyptian Rhind Papyrus. 950 BC - pi approximated as 3 as recorded in 2 Chronicles 4:2 in the Bible. 250 BC - Archimedes of Syracuse determined that the value of pi was between 223/71 and 22/7 (i.e. 3.140845 and 3.142857, respectively). 150 AD - Greek astronomer Ptolomy, approximated pi as 3.1416 480 AD - Tsu Ch'ung Chi, an astronomer in China approximate pi to be 355/113 (i.e. 3.14159292... accurate to 5 places.) 640 AD - Indian astronomer Brahmagupta, approximated pi as the square root of 10 (i.e. 3.1622776... accurate to 1 place) 800 AD - Al-Khwarizmi, a mathematician born in Baghdad, determined pi correctly to 4 places: 3.1416. 1220 AD - Fibonacci, Italian mathematician, approximated pi at 3.141818 (correct to 3 places.) 1596 AD - Van Ceulen, a German teacher of Mathematics found pi correctly to 35 places. (3.1415926535897932384626433832795029)
Tres Irracionales Famosos siglo II dC); p = 355/113 = 3,141592.., (tsu Ch ung-chi, siglo V, dC). http://www.xtec.es/~fgonzal2/curio_irrac.html
Extractions: p . A finales del siglo XIX, dio 707 decimales de p p p era irracional, p p, tales como y se llama (Dicho de otro modo, los Euler trascendentes p es trascendente. p trascendente p aparece en muchas cuestiones que nada tienen que ver con circunferencias. Por ejemplo, p p "La Asamblea General del estado de Indiana decreta que se ha descubierto que el área del círculo es igual al cuadrado que tiene el lado de longitud igual al cuadrante de la circunferencia". Es inmediato deducir de ello que p =4. La proposición se presentó y pasó la aprobación de un primer comité, poniéndose con ello en marcha un procedimiento para ser aprobada por el pleno del Senado, con lo que habría adquirido el rango de ley. Afortunadamente para "los padres de las leyes", fue retirada en el último momento, con lo que se evitó caer en un ridículo que habría adquirido el rango de histórico.
Assign115/#5B/98 The chinese mathematician Zu Chongzhi (or tsu Ch ung chi, 429500 CE) may have useda polygon with 24,576 sides (or possibly a more efficient method) to get http://newton.uor.edu/facultyfolder/beery/math115/m115_activ_est_pi.htm
Extractions: Archimedes' Estimate of Activity The formula On the Measurement of the Circle, Proposition 3. The ratio of the circumference of any circle to its diameter is less than 3 1/7 but greater than 3 10/71 (Dunham, 97; Katz, 109). p p p was the first in history that was correct to two places after the decimal point! p C is the circumference of the circle, r is its radius, and P insc and P circ are the perimeters of the inscribed and circumscribed polygons, respectively, then P insc C P circ , or P insc p r P circ , so that P insc r p P circ If we take the radius of the circle to be 1 ( r = 1), then P insc p P circ Archimedes started with inscribed and circumscribed regular hexagons. Since each of the six sides of a regular hexagon inscribed in a circle of radius 1 has length 1, then P insc = 6 in this case (see Problem 1a). Likewise, since each side of a regular hexagon circumscribed about a circle of radius 1 has length , then P circ (see Problem 1b). Hence, P insc P circ /2 yields , or Archimedes then doubled the number of sides of each polygon to 12, obtaining an inscribed regular dodecagon of perimeter P insc (see Problem 1c), and a circumscribed regular dodecagon of perimeter
Curso De Cálculo Diferencial (Continuación) Translate this page Las aproximaciones siguieron mejorándose durante siglos Ptolomeo (alrededor 150dC) 3,1416, tsu Chung chi (alrededor 430 - 501 dC) 355/113, AlKhwarizm http://cariari.ucr.ac.cr/~cimm/cap_06/cap6_6-1.html
Extractions: Regreso al Prefacio l y l con el mismo punto inicial O . Si A es un punto de l y B es un punto en l M AOB (figura 6.3). l con origen O y se gira el rayo alrededor de O dada por el rayo l l se llama lado inicial l se llama lado terminal y O se llama el q l l b (beta) se gira l en sentido contrario al giro que se hace para obtener a (alfa) pero en ambos casos se llega al mismo l g a l normal si su lado inicial es la parte positiva del eje x y el origen O es el punto (0,0). En un sistema de coordenadas rectangulares positivo y si se hace en el mismo sentido del movimiento de las manecillas del reloj se dice que es negativo En grados grados l exactamente una vuelta , llegando otra vez a l grado En radianes radianes o ) y suponga que q La medida en radianes de q se define como la longitud del arco del sector circular determinado por q (figura 6.8). p p p rad. s de un arco circular de radio r como el de la figura 6.9, esta es longitud de arco = s = r q q en radianes) p rad, Se deduce que: rad y 1 rad = y esto se usa para convertir grados a radianes y radianes a grados respectivamente. rad = rad.
Word Mapping Table For Pinyin, Wade-Giles And Yale ao Chau Che Ch e Che Chen Ch en Chen Cheng Ch eng Cheng chi Ch ih Chr Chong Ch ungChung Chou Ch Tz u Tsz Cong Ts ung tsung Cou Ts ou Tsou Cu Ts u tsu Cuan Ts http://www.m.isar.de/denner/neijia/romanisation/mapping.html
Extractions: Author David Aspinwall to neijia list 12 Oct 1994 Since there's been some confusion about pinyin lately, heres a table mapping between pinyin, Wade-Giles, and Yale romanization systems. I've modified this from an index file created by Ed Lai. Colons are meant to be umlauts. For English speakers, Yale is the most intuitive system. If you want to make a half-assed guess as to the pronounciation of a word, Yale is a good starting point. Pinyin is the standard system in China, and is used by most newspapers in the U.S. now. Wade-Giles used to be the most common system, and is still seen in many books. Sponsor Taiji Collection
Astronomers T Pre-1400 tsu Ch ung chi (430501) - astronomer and mathematician. He calculatedpi and devised at new calendar which never was used. He also http://www.pa.msu.edu/people/horvatin/Astronomers/astronomers_t_pre.htm
The EM Chiu Chang Suan Shu /EM (Nine Chapters On The tsu Ch ungchih, and then further improved by the tsu Ch ung-chih s son tsu Keng-chih Thisarticle 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.
THE HOLY BIBLE KNEW ABOUT THE CORRECT VALUE FOR PI LONG BEFORE Liu Hui, 263 AD, 3.14159. Siddhanta, 380 AD, 3.1416. tsu Ch ung chi, 480 AD,3.1415926. Aryabhata, 499 AD, 3.14156. Brahmagupta, 640 AD, 3.162277 = squarerootof 10. http://www.1john57.com/1kings723.htm
Extractions: VIETE of 1593 A.D. DID! by Don Hewey, email: donhewey@k-online.com main index NOTE : This outline will clearly illustrate the "inside" circumference of the molten sea (solid brass tub) which is the non-brimmed portion of the molten sea. The confusion over 1 Kings 7:23 is that the reader automatically assumes that the thirty cubits stated in verse 23 is the corresponding circumference of the outer uttermost brimmed edge. It is not. For a complete discussion on the outer portion of the molten sea, please refer to this link here that gives the proof. outer circumference proof . The exact physical represention as it is written in verse 23 is physically impossible as one should immediately become suspicious of. But with further examination of this outline and also the "yfiles" link, the bible not only proves PI once, but twice! Amazing. Please refer to the molten sea diagram representation half way down this page for an illustration to this problem. "1 Kings 7:[23] And he made a molten sea, ten
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.
