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         Tsu Ch'ung Chi:     more detail

1. History 430AD
tsu ch'ung chi was born in Fanyang, China in 430 AD. He was an astronomer, engineer and mathematician. In astronomy, he recommended a new calendar that he made in 463.
http://www.oxy.edu/~jquinn/home/Math490/Timeline/430AD.html
430 A.D.
Contributions from Charles and Fili Tsu Ch'ung Chi was born in Fan-yang, China in 430 AD. He was an astronomer, engineer and mathematician. In astronomy, he recommended a new calendar that he made in 463. He also found an accurate time of the solstice by measuring the length of the Sun's shadow at noon around the time of the solstice. In mathematics he found a rational approximation 355/113 = 3.14159265 to pi (3.1415927…). This is correct for six decimal places. Not much is known about his approximation because his book, written by his son is now lost. Tsu Ch'ung Chi and his father found the formula for the volume of a sphere by carrying out Liu Hui's suggestion. Author : Charles DeBoer References:
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Tsu.html

JOC/EFR December 1996 http://www.bmwf.gv.at/1bm/texts/95-2/9math.htm http://aleph0.clarku.edu/~djoyce/mathhist/china.math, Outline of the History of Chinese Mathematics
Mathematics 105, History of Mathematics, Clark University, Worcester, MA 01610, Fall 1994, D Joyce
Chinese mathematicians have contributed vastly to our current knowledge of Math. Perhaps one of the least mentioned for his work is Tsu Ch'ung Chi. A mathematician and astronomer between 430-501 AD, Chi calculated the rational approximation of 355/113 to Pi. His estimation

2. Manfred Boergens - Briefmarke Des Monats Maerz 2001
Briefmarke des Monats März 2001. tsu ch'ung chi (Zu Chong Zhi) ca.
http://www.fh-friedberg.de/users/boergens/marken/briefmarke_01_03.htm
China 1955
Scott 246
Tsu Ch'ung Chi (Zu Chong Zhi) (ca. 429 - ca. 500) St. Andrews und R. Williams in [2].
(den Mittelwert der beiden Grenzen sieht man auf der Briefmarke)
Hier ist der richtige Wert, gerundet auf 11 Nachkommastellen:
Der auf der Briefmarke abgedruckte Mittelwert ist also eine korrekte Rundung auf 8 Nachkommastellen. Wegen 355/113 = 3.14159292035... ist der von Tsu angegebene Bruch auf 6 Nachkommastellen korrekt. Und heute? Im September 1999 berechnete der Japaner Takahashi Kanada 206.158.430.000 Nachkommastellen mit einem Computer (klar!), und das Wettrennen wird sicherlich noch weitergehen.
= 805.306.368. Der Hildesheimer Mathematiker und Ingenieur Ludolph van Ceulen verbrachte die meiste Zeit seines Lebens mit n = 2 Wie hat es Tsu Ch'ung Chi gemacht? Wir wissen es nicht.
Literatur G. Bonte Yuan Zhou Shuai
MSU

R. Williams Tsu Ch'ung-Chih
MSU
J. Arndt, C. Haenel Pi - Algorithmen, Computer, Arithmetik Springer Pi through the ages A chronology of Pi zur Leitseite Mathematische Philatelie

3. Tsu
tsu ch'ung chi. a remarkable result on which it would be nice to have moredetails but tsu ch'ung chi's book, written with his son, is lost.
http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Tsu.html
Tsu Ch'ung Chi
Born: 430 in Fan-yang (now Hopeh), China
Died: 501 in China
Click the picture above
to see two larger pictures Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index
Tsu was a Chinese mathematician and astronomer. He gave the rational approximation to p which is correct to 6 decimal places. He also proved that p a remarkable result on which it would be nice to have more details but Tsu Ch'ung Chi's book, written with his son, is lost. Tsu's astronomical achievements include the making of a new calendar in 463 which never came into use. Tsu also determined the precise time of the solstice by measuring the length of the Sun's shadow at noon on days near the solstice to reduce errors caused by the fact that it is very difficult to determine the exact time of the solstice. Article by: J J O'Connor and E F Robertson Click on this link to see a list of the Glossary entries for this page List of References (3 books/articles) A Poster of Tsu Mathematicians born in the same country Cross-references to History Topics
  • Pi through the ages
  • A chronology of pi
    Other references in MacTutor Chronology: 1AD to 500 Honours awarded to Tsu
    (Click a link below for the full list of mathematicians honoured in this way) Lunar features Crater Tsu Chung-Chi Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index
    History Topics

    Societies, honours, etc.
  • 4. Tsu
    tsu ch'ung chi. Born 430 in Fanyang (now Hopeh), China
    http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Tsu.html
    Tsu Ch'ung Chi
    Born: 430 in Fan-yang (now Hopeh), China
    Died: 501 in China
    Click the picture above
    to see two larger pictures Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index
    Tsu was a Chinese mathematician and astronomer. He gave the rational approximation to p which is correct to 6 decimal places. He also proved that p a remarkable result on which it would be nice to have more details but Tsu Ch'ung Chi's book, written with his son, is lost. Tsu's astronomical achievements include the making of a new calendar in 463 which never came into use. Tsu also determined the precise time of the solstice by measuring the length of the Sun's shadow at noon on days near the solstice to reduce errors caused by the fact that it is very difficult to determine the exact time of the solstice. Article by: J J O'Connor and E F Robertson Click on this link to see a list of the Glossary entries for this page List of References (3 books/articles) A Poster of Tsu Mathematicians born in the same country Cross-references to History Topics
  • Pi through the ages
  • A chronology of pi
    Other references in MacTutor Chronology: 1AD to 500 Honours awarded to Tsu
    (Click a link below for the full list of mathematicians honoured in this way) Lunar features Crater Tsu Chung-Chi Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index
    History Topics

    Societies, honours, etc.
  • 5. Malaspina.com - Tsu Ch'ung Chi (430-501)
    Research bibliography, books and links to 1 000 other interdisciplinary entries compiled by Russell McNeil.
    http://www.mala.bc.ca/~MCNEIL/tsu.htm
    Tsu Ch'ung Chi (430-501) [MacTutor, St. Andrews]
    Great Books Biography [Malaspina]
    Tsu Ch'ung Chi Amazon Search Form]
    Used Books Search Form Alibris
    Dummies Books Amazon
    Canadian Book Orders! Chapters-Indigo
    Save on Textbooks! [Study Abroad]
    MacTutor Page on Tsu Ch'ung Chi
    Top of Page

    6. Malaspina.com - Tsu Ch'ung Chi (430-501)
    Launch Previous Entry in New Window Malaspina Science Database Launch NextEntry in New Window tsu ch'ung chi (430501) MacTutor, St. Andrews.
    http://www.malaspina.edu/~mcneil/tsu.htm
    Tsu Ch'ung Chi (430-501) [MacTutor, St. Andrews]
    Great Books Biography [Malaspina]
    Tsu Ch'ung Chi Amazon Search Form]
    Used Books Search Form Alibris
    Dummies Books Amazon
    Canadian Book Orders! Chapters-Indigo
    Save on Textbooks! [Study Abroad]
    MacTutor Page on Tsu Ch'ung Chi
    Top of Page

    7. Poster Of Tsu
    tsu ch'ung chi lived from 430 to 501 Tsu was a Chinese mathematician and astronomer. He introduced the approximation 355/113 to which is correct to 6 decimal places. Find out more at
    http://www-groups.dcs.st-and.ac.uk/history/Posters2/Tsu.html
    Tsu Ch'ung Chi lived from 430 to 501 Tsu was a Chinese mathematician and astronomer. He introduced the approximation 355/113 to which is correct to 6 decimal places. Find out more at
    http://www-history.mcs.st-andrews.ac.uk/history/
    Mathematicians/Tsu.html

    8. MA 2108's Home Page
    tsu ch'ung chi ×æ³åÖ®(430501). Links to Calculus at Other Universities;Calculus II at the University of Pennsylvania. Calculus at Harvard,
    http://www.math.nus.edu.sg/~matwujie/Spring02/
    MA 2108, Spring 2002
    Advanced Calculus II
    Lecturer: J. Wu Tutors: J. Wu Office: S14, 04-07, Faculty of Science, Lower Kent Ridge Road. e-mail: matwuj@nus.edu.sg Phone:
    Text Books:
  • William R. Parzynski and Philip W. Zipse, Introduction to mathematical analysis , International Edition 1987, McGraw-Hill Book Company Press. G. B. Thomas, Jr. and Ross L. Finney, Calculus and analytic geometry , 9th Edition, International Student Edition, Addison-Wesley Longman Inc. Press, 1996. M. Braun, Differential equations and their applications, 3rd Edition, Applied Mathematical Sciences V. 15, Springer-Verlag, 1986. Course Outline Lecture Notes Supplement to Section 3.9 Supplement to Section 3.10
  • Lectures: Monday, Thursday, 4:00-5:30 pm, LT26.
  • Everybody must attend all lectures and should arrive on time. In case you missed the class due to sick, then you should submit your MC to me. If you missed some classes without sufficient reasons, you might get negative credit to your grade from the course.
  • Tutorials:
  • Group 1: Tuesday 11-12, S13 0501
  • 9. - Great Books -
    tsu ch'ung chi (430501), Tsu was a Chinese mathematician and astronomer.He tsu ch'ung chi's book, written with his son, is lost. Tsu's
    http://www.malaspina.com/site/person_1144.asp
    Tsu Ch'ung Chi
    Tsu was a Chinese mathematician and astronomer. He gave the rational approximation 355/113 to which is correct to 6 decimals. Tsu Ch'ung Chi's book, written with his son, is lost. Tsu's astronomical achievements include the making of a new calendar in 463 which never came into use. Tsu also determined the precise time of the solstice by measuring the length of the Sun's shadow at noon on days near the solstice to reduce errors caused by the fact that it is very difficult to determine the exact time of the solstice. [Adapted from MacTutor Browse
    Research Links

    Related Science Links
    Medieval Science

    10. Mathcards.com - Mathematician Trading Cards
    tsu ch'ung chi. The images and biographical content for the "Math Cards" on this site are used with permission from the
    http://www.mathcards.com/
    Euler Laplace Cauchy Descartes Archimedes Leibniz Khayyam Liouville Lorentz Minkowski Mobius Pythagoras Ramanujan Riemann Tsu Khwarizmi Hopital Bernoulli Fibonacci Fourier Godel Picard Stokes Sturm Taylor Agnesi Cavalieri Stevin Gauss Lagrange Lobachevsky Galois Seki Cardano Weierstrass Jacobi Eisenstein Hamilton Hilbert Euclid
    Hendrik Antoon Lorentz
    The images and biographical content for the "Math Cards" on this site are used with permission from the MacTutor History of Mathematics Archive of the University of St Andrews, St Andrews, Scotland. Special thanks to Edmund Robertson , Head of the School of Mathematical and Computational Sciences at the University of St Andrews, and one of the developers of the History of Mathematics Archive

    11. - Great Books -
    Trotula of Salerno (c. 1097), Medieval Science 118. tsu ch'ung chi (430-501), MedievalScience 119. Vesalius, Andreas (1514-1564), Renaissance Science 120.
    http://www.malaspina.com/site/results_c9_page2.htm
    Search Results for: Science
    123 results found
    Pythagoras of Samos
    (c. 580 BC-c. 520 BC), Antiquity Science
    Qurrah al-Harrani, Thabit ibn
    (826-901), Medieval Science
    Razi (-al), Abu Bakr Mohammad Ibn Zakariya
    (c. 865-c. 935), Medieval Science
    Richards, Ellen Swallow
    (1842-1911), Romantic Science
    Russell, Bertrand
    (1872-1970), Modern Literature/Science
    Schrödinger, Erwin
    (1887-1961), Modern Science
    Snow, Baron Charles Percy Snow (C.P.)
    (1905-1980), Modern Literature/Science
    Somerville, Mary Fairfax
    (1780-1872), Classical Science
    Stevens, Nettie Maria
    (1861-1912), Romantic Science Strabo (c. 63 BC-3 BC), Antiquity Science Sudarkasa, Niara (1945-), Modern Science Tabari (-al), Ali Ibn Rabban (838-870), Medieval Science Thales of Miletus (c. 634 BC-c. 546 BC), Antiquity Science Theano of Kroton (c. 550 BC-), Antiquity Science Theophrastus (c. 371 BC-287 BC), Antiquity Literature/Science Torricelli, Evangelista (1608-1647), Baroque Science Trotula of Salerno (c. 1097-), Medieval Science Tsu Ch'ung Chi (430-501), Medieval Science Vesalius, Andreas

    12. History Of Mathematics: China
    tsu ch'ung chi. c.430 c.501
    http://aleph0.clarku.edu/~djoyce/mathhist/china.html
    Mathematics in China
    Table of Contents
    A brief outline of the history of Chinese mathematics
    Primary sources are Mikami's The Development of Mathematics in China and Japan and Li Yan and Du Shiran's Chinese Mathematics, a Concise History . See the bibliography below.
  • Numerical notation, arithmetical computations, counting rods
    • Traditional decimal notation one symbol for each of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 100, 1000, and 10000. Ex. 2034 would be written with symbols for 2,1000,3,10,4, meaning 2 times 1000 plus 3 times 10 plus 4. Goes back to origins of Chinese writing.
    • Calculations performed using small bamboo counting rods. The positions of the rods gave a decimal place-value system, also written for long-term records. digit was a space. Arranged left to right like Arabic numerals. Back to 400 B.C.E. or earlier.
    • Addition: the counting rods for the two numbers placed down, one number above the other. The digits added (merged) left to right with carries where needed. Subtraction similar.
  • 13. EUCLID
    tsu ch'ung chi c.430 c.501 Chinese Mathematician tsu ch'ung chi,mathematician and astronomer, who calculated the value of pi
    http://www.hyperhistory.com/online_n2/people_n2/persons3_n2/tsu.html
    TSU CH'UNG CHI
    c.430 - c.501
    Chinese Mathematician
    Tsu Ch'ung Chi, mathematician and astronomer, who calculated the value of pi to 6 decimal places, and determined the precise time of the solstice www link :
    From the University of St. Andrews, Scotland
    School of Mathematics
    Biography

    14. INDEX 5
    sojo Tocqueville L Tojo P Tolstoy * Toramana Torricelli S Toulouse * Lautrec A Trajan* Tribonian * Truman P Tsai-lung Tshu-hi tsu ch'ung chi * Tudor, Mary W
    http://www.hyperhistory.com/online_n2/History_n2/index_n2/index5.html
    To General Lifelines To Special Lifelines To A-B To C-G To H-M To N-R S-Z Title S - Si
    S
    abaka
    Sachs
    , Hans L
    Sade

    Marquis de L
    Sadi

    Saikaku
    , Ihara L
    Saladin

    Sallust

    Sand
    , George L
    Sanger
    Margaret W Santa Ana P San Martin P Sappho Sartre Satie C Saud , Ibn P Savonarola Scarlatti C Schiller Schinkel A Schoenberg C Schrodinger S Schubert C Schumann Robert C Schumann Clara W Schutz Scipio Scotus Seleucus ... Selim I P Semper A Seneca Seurat A Severus Shajahan P Shaka P Shakespeare Shankara Shapur I Shaw ... Shostakovich C Shotoku Sian-chin Sibelius C Siemens S Sigismund Sigismund III King of Poland P Siloe A Sirani Elisabetta W ibn- Sina Sinan Sivaji P Sm - Sy Smetana C Snorri Socrates Solomon Solon ... Sorol Agnes W Spartacus Spinoza Ssu-ma Chien Stael , Mdm L Stalin Stein , Gertrude W Stein , Baron P Steinbeck L Stendhal L Stephenson S Stilicho Stowe , Harriet W Strabo J. Strauss C R. Strauss C Stravinsky C Strindberg L Stuart Mary W Sui Wen-ti Sui Yang-ti Sukarno P Suleiman Sulla Sun Yat-Sen P Swift L Sylvester II X enophanes Xerxes ... apata P Zeno Zenobia Zola L Zoroaster Zworykin S T - U T abari, al- Tacitus Tagore L T'ai-tsung Talleyrand P Tannhauser T'ao Tao-yue Tasso Torquato L Tchaikovsky C Tchekhov L Tecumseh P Telemann C Tenji Terence Terpander Tertullian ... Tesla S Thales Themistocles Theodora Theodoric ... Theresia,

    15. Untitled
    Ptolemaios (asi 150 nl) odhadl císlo pí hodnotou 3.1416, tsu ch'ung chi(430 501) hodnotou 355/113, al'Khwarizmi (asi 800) hodnotou 3.1416.
    http://natura.baf.cz/natura/2001/7/20010705.html
    Z historie matematiky a fyziky (2)
    zpracovali: Jiøí Svršek, Roman Bartoš Typografické poznámky k matematickým vztahùm jsou uvedeny na konci tohoto textu. 4. Historie èísla p Ve Starém zákonì v Bibli lze nalézt zmínky, napøíklad pøi popisu velkého chrámu krále Šalamouna postaveného kolem roku 850 pø.n.l, z nichž vyplývá, že èíslo p bylo odhadováno èíslem 3. Egypané a obyvatelé Mezopotámie odhadovali èíslo p hodnotou 25/8 a (10). Na obranu Šalamounových øemeslníkù je tøeba uvést, že pøi stavbì chrámu byly používány velké kvádry kamene, pøi jejichž usazování na místo nebyla nutná velká pøesnost. Skuteènost, že pomìr délky kružnice k jejímu polomìru je konstantní, byla známa velmi dlouho. První odhady èísla p byly získány mìøením, jako v pøípadì "biblické" hodnoty 3. V egyptském papyru, který objevil A. Henry Rhind je odhad èísla p dán èíslem 4.(8/9) První teoretický výpoèet èísla pí pochází od Archiméda ze Syrakus (287 - 212 pø.n.l.). Archimédes získal odhad p Archimédes vìdìl, že èíslo pí není rovno 22/7 a netvrdil, že objevil pøesnou hodnotu. Jeho nejlepším odhadem je 3.1418, jehož chyba je asi 0.0002. Archimédes pro odhad èísla p použil metodu vepsaných a opsaných mnohoúhelníkù kružnici s jednotkovým polomìrem. Nalezl vztahy pro odhad èísla pí pomocí obvodù tìchto mnohoúhelníkù a nalezl iteraèní vztahy mezi obvody n-úhelníkù a (n+1)-úhelníkù.

    16. Chinese Astronomers
    Tsu Ch'ungChi tsu ch'ung chi (430-501) was a Chinese mathematicianand astronomer. In astronomy, he arrived at the precise time
    http://www.chinapage.com/astronomy/astronomer.html
    Chinese Astronomers
    Zhang Heng (78-139) was a Chinese astronomer, geographer, and mathematician. He constructed a celestial globe, believing that the world was round, "The sky is like a hen's egg, and is as round as a crossbow pellet; the Earth is like the yolk of the egg, lying alone at the centre. The sky is large and the Earth small." He also created a primitive, but very fanciful seismograph . His approximation of pi was the square root of 10.
    More..

    More..

    More

    Seismographs

    Zhang Sui
    A Chinese astronomer and Buddhist monk of the Tang dynasty, Zhang Sui (683-727), was the first to describe proper stellar motion, or the apparent motion of stars across the plane of the sky relative to more distant stars. In Western astronomy, Edmond Halley is credited with this discovery in 1718 for some stars from Ptolemy's catalogue.
    Tsu Ch'ung-Chi
    Tsu Ch'ung Chi (430-501) was a Chinese mathematician and astronomer. In astronomy, he arrived at the precise time of the solstice by measuring the sun's shadow at noon on days around the solstice. He gave the rational approximation 355/113 to p which is correct to 6 decimal places.

    17. Chinese Astronomers
    Cui Zhongji Tsu Ch'ungChi Cui Zhongji tsu ch'ung chi (430-501)was a Chinese mathematician and astronomer. In astronomy, he
    http://www.chinapage.org/astronomy/astronomer.html
    Chinese Astronomers
    Zhang Heng (78-139) was a Chinese astronomer, geographer, and mathematician. He constructed a celestial globe, believing that the world was round, "The sky is like a hen's egg, and is as round as a crossbow pellet; the Earth is like the yolk of the egg, lying alone at the centre. The sky is large and the Earth small." He also created a primitive, but very fanciful seismograph . His approximation of pi was the square root of 10.
    More..

    More..

    More

    Seismographs

    Zhang Sui
    A Chinese astronomer and Buddhist monk of the Tang dynasty, Zhang Sui (683-727), was the first to describe proper stellar motion, or the apparent motion of stars across the plane of the sky relative to more distant stars. In Western astronomy, Edmond Halley is credited with this discovery in 1718 for some stars from Ptolemy's catalogue.
    Cui Zhongji [Tsu Ch'ung-Chi]
    Cui Zhongji [Tsu Ch'ung Chi] (430-501) was a Chinese mathematician and astronomer. In astronomy, he arrived at the precise time of the solstice by measuring the sun's shadow at noon on days around the solstice. He gave the rational approximation 355/113 to p which is correct to 6 decimal places.

    18. History
    Ptolemy (c. 150 AD) 3.1416 tsu ch'ung chi (430501 AD) 355/113 al'Khwarizmi (c.800) 3.1416 Al'Kashi (c. 1430) 14 places Viète (1540-1603) 9 places Roomen
    http://www.wfu.edu/Academic-departments/Art/pickel-websp99/inman/history.html
    HISTORY The earliest values of pi including the 'Biblical' value of 3, were almost certainly found by measurement. In the Egyptian Rhind Papyrus, which is dated about 1650 BC, there is good evidence for 4(8/9) = 3.16 as a value for The first theoretical calculation seems to have been carried out by Archimedes of Syracuse (287-212 BC). He obtained the approximation 223/71 < 22/7. Before giving an indication of his proof, notice that very considerable sophistication involved in the use of inequalities here. Archimedes knew, what so many people to this day do not, that does not equal 22/7, and made no claim to have discovered the exact value. If we take his best estimate as the average of his two bounds we obtain 3.1418, an error of about 0.0002. People went on calculating after Archimedes: Ptolemy (c. 150 AD) 3.1416
    Tsu Ch'ung Chi (430-501 AD) 355/113
    al'Khwarizmi (c. 800) 3.1416

    19. Home/Giáo D?c-Ðào T?o/Góc HSSV/Tin H?c/
    tsu ch'ung chi. Sinh 430 ? Trung Qu?c. M?t 501. tsu ch'ung chi dã tìmra k?t qu? p = b?ng cách nào thì không m?t ai bi?t du?c.
    http://www.hssv.vnn.vn/citd/cacsodara/nam2001/T1_2001/TR20_23.html
    Home Gi¡o dục-Đ o tạo G³c HSSV Tin học/
    TỪ TƯ DUY TON HỌC ĐẾN TƯ DUY THUẬT TON Anh Lª - (Tiếp theo) Để giºp c¡c bạn trẻ r¨n luyện kỹ năng lập tr¬nh, chºng t´i xin giới thiệu b i viết của t¡c giả Anh Lª . Qua b i n y t¡c giả giºp c¡c bạn phÆ°Æ¡ng ph¡p h¬nh th nh tÆ° duy thuật to¡n trước khi bắt tay v o lập tr¬nh. ChÆ°Æ¡ng tr¬nh về bản chất chỉ l  sá»± thể hiện của tÆ° duy thuật to¡n. Đứng trước một vấn đề, một b i to¡n bạn đừng c³ bắt tay ngay v o lập tr¬nh m  h£y nghÄ© xem l m c¡ch n o để giải n³. TÆ° duy to¡n học hay thuật to¡n từ b i to¡n đơn giản C¢u hỏi. Ho¡ ra l  c¹ng một tr¬nh thay c¡c gi¡ trị ban đầu kh¡c nhau nhÆ°ng vẫn cho ra kết quả. Với c¡c gi¡ trị ban đầu của a v  b nhÆ° thế n o th¬ tr¬nh Archimedes hội tụ về số p ChÆ°a hết ngạc nhiªn!
    Tsu Ch'ung Chi Sinh : 430 ở Trung Quốc.

    20. Asian Links - China, Japan, Korea, & India
    Ancient Mathematicians China's tsu ch'ung chi. India Caves of Ajanta and Ellora- They constitute one of the most beautiful expressions of the art of the
    http://killeenroos.com/link/asia.htm
    (in cludes China Japan Korea and Southeast Asia ( Thailand Vietnam , and India back to social studies link index

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