1. Ahmes focus in this website is on some of the theories on how ahmes, the scribe of the papyrus, calculated the fraction table. http://www.math.sfu.ca/History_of_Math/Egypt/Ahmes/frametop.html

2. The Rhind/Ahmes Papyrus - Mathematics And The Liberal ArtsThe Rhind/Ahmes Papyru A quotation by ahmes. Accurate reckoning the entrance into knowledge of all existing things and all obscure secrets. http://math.truman.edu/~thammond/history/RhindPapyrus.html

The Rhind/Ahmes Papyrus - Mathematics and the Liberal Arts To expand search, see Ancient Egypt . Laterally related topics: The Egyptian Pyramids and The Moscow Mathematical Papyrus 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 Biggs, N. L. The roots of combinatorics. Historia Math.

3. Gazalé, M.: Number: From Ahmes To Cantor. a topic from HistoriaMatematica Discussion Group HM Any views on 'Number from ahmes to Cantor'? post a message on this topic post a message on a new topic 18 Sep 2000 HM Any views on 'Number from ahmes to Cantor'?, by David Wilkins http://pup.princeton.edu/titles/6794.html

PRINCETON University Press SEARCH: Keywords Author Title More Options Power Search Search Hints E-MAIL NOTICES NEW IN PRINT E-BOOKS ... HOME PAGE Winner of the 2000 Association of American Publishers Award for Best Professional/Scholarly Book in Mathematics and Statistics One of Choice 's Outstanding Academic Books of 2000 Number: From Ahmes to Cantor Shopping Cart Table of Contents We might take numbers and counting for granted, but we shouldn't. Our number literacy rests upon centuries of human effort, punctuated here and there by strokes of genius. In his successor and companion volume to Gnomon: From Pharaohs to Fractals This abundantly illustrated book, remarkable for its coherency and simplicity, will fascinate all those who have an interest in the world of numbers. Number will be indispensable for all those who enjoy mathematical recreations and puzzles, and for those who delight in numeracy. Table of Contents Gnomon: From Pharaohs to Fractals. Subject Areas: Mathematics History of Science and Medicine, Philosophy of Science VISIT OUR MATH WEBSITE Main Selection of the Library of Science Book Club Shopping Cart: For customers in the U.S., Canada, Latin America, Asia, and Australia

4. Ahmes ahmes. Born about 1680 BC in Egypt Died about 1620 BC in Egypt. ahmes claimsnot to be the author of the work, being, he claims, only a scribe. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Ahmes.html

Ahmes Born: about 1680 BC in Egypt Died: about 1620 BC in Egypt Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Ahmes is the scribe who wrote the Rhind Papyrus (named after the Scottish Egyptologist Alexander Henry Rhind who went to Thebes for health reasons, became interested in excavating and purchased the papyrus in Egypt in 1858). @Ahmes claims not to be the author of the work, being, he claims, only a scribe. He says that the material comes from an earlier work of about 2000 BC. @The papyrus is our chief source of information on Egyptian mathematics. The Recto contains division of 2 by the odd numbers 3 to 101 in unit fractions and the numbers 1 to 9 by 10. The Verso has 87 problems on the four operations, solution of equations, progressions, volumes of granaries, the two-thirds rule etc. @The Rhind Papyrus, which came to the British Museum in 1863, is sometimes called the 'Ahmes papyrus' in honour of Ahmes. Nothing is known of Ahmes other than his own comments in the papyrus.@ The Rhind papyrus Article by: J J O'Connor and E F Robertson List of References (4 books/articles) A Quotation Mathematicians born in the same country Some pages from publications Rhind papyrus Cross-references to History Topics Egyptian papyri Squaring the circle An overview of Egyptian mathematics Other references in MacTutor Chronology: 30000BC to 500BC Other Web sites Simon Fraser University Mathematicians of the African diaspora Kevin Brown Previous (Chronologically) Next Biographies Index Previous (Alphabetically)

5. Ahmes Biography of ahmes (1680BC1620BC) ahmes is the scribe who wrote the Rhind Papyrus (named after the Scottish Egyptologist Alexander Henry Rhind who went to http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Ahmes.html

Ahmes Born: about 1680 BC in Egypt Died: about 1620 BC in Egypt Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Ahmes is the scribe who wrote the Rhind Papyrus (named after the Scottish Egyptologist Alexander Henry Rhind who went to Thebes for health reasons, became interested in excavating and purchased the papyrus in Egypt in 1858). @Ahmes claims not to be the author of the work, being, he claims, only a scribe. He says that the material comes from an earlier work of about 2000 BC. @The papyrus is our chief source of information on Egyptian mathematics. The Recto contains division of 2 by the odd numbers 3 to 101 in unit fractions and the numbers 1 to 9 by 10. The Verso has 87 problems on the four operations, solution of equations, progressions, volumes of granaries, the two-thirds rule etc. @The Rhind Papyrus, which came to the British Museum in 1863, is sometimes called the 'Ahmes papyrus' in honour of Ahmes. Nothing is known of Ahmes other than his own comments in the papyrus.@ The Rhind papyrus Article by: J J O'Connor and E F Robertson List of References (4 books/articles) A Quotation Mathematicians born in the same country Some pages from publications Rhind papyrus Cross-references to History Topics Egyptian papyri Squaring the circle An overview of Egyptian mathematics Other references in MacTutor Chronology: 30000BC to 500BC Other Web sites Simon Fraser University Mathematicians of the African diaspora Kevin Brown Previous (Chronologically) Next Biographies Index Previous (Alphabetically)

6. A Quotation By Ahmes A quotation by ahmes. Accurate reckoning the entrance into http//wwwhistory.mcs.st-andrews.ac.uk/history/Quotations/ahmes.html. http://www-gap.dcs.st-and.ac.uk/~history/Quotations/Ahmes.html

A quotation by Ahmes Accurate reckoning: the entrance into knowledge of all existing things and all obscure secrets. Quoted in A B Chase, Rhind Mathematical Papyrus (Reston Va. 1967) Main index Biographies Index History Topics Societies, honours, etc. ... Anniversaries for the year JOC/EFR February 2000 The URL of this page is: School of Mathematics and Statistics University of St Andrews, Scotland http://www-history.mcs.st-andrews.ac.uk/history/Quotations/Ahmes.html

7. History Of Mathematics @ SFU Region - - Time - - Person or Topic - ahmes, Ancient Egyptian Fractions Euclid, His Works and Influences http://www.math.sfu.ca/histmath

- Region - Time - Person or Topic Egypt 1600s BC Ahmes , Ancient Egyptian Fractions China 200s BC Remainder Problem Master Sun 100s BC Jiuzhang Suanshu Jia Xian Qin Jiushao The Ta-Yen Rule ... Counting Board Simulator Program for PC computers India Aryabhata Brahmagupta Bhaskara Europe Blaise Pascal 300s BC Euclid His Works and Influences Ada Byron King The Countess of Lovelace Emy Noether Her life and Work Alan Turing The Man and the Machine Topics Sundials Calendars History of Math Notes

8. - Great Books - ahmes and the Rhind Papyrus (1680 BC1620 BC), ahmes was the Egyptianscribe who wrote the Rhind Papyrus. The papyrus is our chief http://www.malaspina.com/site/person_57.asp

Ahmes and the Rhind Papyrus (1680 BC-1620 BC) Ahmes was the Egyptian scribe who wrote the Rhind Papyrus. The papyrus is our chief source of information on Egyptian mathematics. The papyrus is named after a young Scottish antiquary named A. Henry Rhind who purchased the papyrus at Luxor in 1858. The papyrus is said to have been found in the ruins of a small ancient building at Thebes. The scroll originally had measured 18 feet by 13 inches. The scroll was a practical handbook of Egyptian mathematics. It contains 85 problems, exhibiting the use of fractions, the solution of simple equations and progressions, and the mensuration of areas and volumes. One of the problems reads as follows [1]: "Divide 100 loaves amomg 5 men in such a way that the shares received shall be in arithmetical progression and that one seventh (1/7) of the sum of the largest three shares shall be equal to the sum of the smallest two. What is the difference of the shares?" Reference [1] Newman, James R., The World of Mathematics, Vol. 1 The Rhind Papyrus , p. 170-178, Simon and Schuster, New York, 1956 The Great Books Rhind Papyrus This web page is part of a biographical database on Great Ideas . These are living ideas that have shaped, defined and directed world culture for over 2,500 years. By definition the

9. Ahmes Launch Page Please check the other window. If another window did not appear, you needat least Netscape 3 or Internet Explorer 4 to view this website. http://www.math.sfu.ca/histmath/Egypt/Ahmes/

Please check the other window.

10. History Of Mathematics: Egypt Egypt. Mathematicians. ahmes (c. 1650 B.C.E.) http://aleph0.clarku.edu/~djoyce/mathhist/egypt.html

Egypt Mathematicians Ahmes (c. 1650 B.C.E.) See also Alexandria Resources on the web A page on Babylonian and Egyptian Mathematics at Mathematical MacTutor's History of Mathematics archive Egyptololgy Resources Bibliography Chace, A. B., L. S. Bull, H. P. Manning, and R. C. Archibald, eds. The Rhind mathematical papyrus. 2 volumes. Mathematical Association of America, Oberlin, Ohio, 1927-1929. Includes a bibliography of Egyptian and Babylonian mathematics by Archibald. Reviewed: Isis Gillings, Richard J. Mathematics in the time of the pharaohs. M.I.T. Press, Cambridge, Mass., 1972. Reprint: Dover, New York, 1982. Neugebauer, Otto. The Exact Sciences in Antiquity. Princeton University Press, Princeton, 1951. Reviewed: Isis 43 (1952), 67-73. Reprint: Brown University Press, Providence, 1957. Second edition: Harper and Row, New York, 1962. Reprint: Dover, New York, 1969. Parker, Richard Anthony The calendars of ancient Egypt. Univ of Chicago Press, Chicago, 1950. Demotic mathematical papyri. Brown Egyptological Studies, 7. Brown University Press, Providence, 1972.

11. Ahmes Translate this page ahmes (Ahmose) égyptien, vers -1650 ahmes indique que son papyrus est, en partie,une copie de résultats plus anciens (vers -2000) remontant aux Babyloniens. http://www.sciences-en-ligne.com/momo/chronomath/chrono1/Ahmes.html

AHMES (Ahmose) Ce scribe fils de la Lune A gauche : scribe égyptien, Vè dynastie, Musée des antiquités, Le Caire; à droite un extrait du papyrus Rhind ( British Museum, de Londres). la la Babyloniens . Une transcription The Rhind Mathematical Papyrus quadrature du cercle p R x . Ainsi, notre actuel nombre p p http://perso.wanadoo.fr/rolland.chaussade/ Cette approximation (dessin ci-dessous à gauche) avec 3 + 1/7... Ahmes, apparaît comme précurseur du multiplication x x x x x On part de 1 en colonne 2 On a ici 23 = 1 + 2 + 4 + 16 (les croix correspondent aux puissances de 2 choisies pour exprimer 23). Le produit x est obtenu en ajoutant les nombres en regard de la colonne 3. On a bien : x x Le processus de division X = b/a signifie b = a x X fractions unitaires On a clairement : 19 = 16 + 2 + 1 = 2 x 8 + 2 + 1, donc : x x x 7 + 3, donc : mais fausse position Papyrus de Moscou : Pour en savoir plus : http://www.math.buffalo.edu/mad/Ancient-Africa/mad_ancient_egyptpapyrus.html

12. King Ahmes II ahmes (II) (Amasis) Khnemibre (570526 BC). Horus name Semenmaat Nebty name Zaneit-sepedtawyGolden Falcon name Setepnetjeru Prenomen Khnemibre Nomen ahmes, http://www.petrie.ucl.ac.uk/digital_egypt/chronology/ahmesii.html

Homepage Timeline Maps A-Z index ... Learning Ahmes (II) (Amasis) Khnemibre (570-526 BC) King of the 26th Dynasty. The reign of the king marks the high point of the 26th Dynasty in terms of wealth and prosperity. Under Ahmes (II) Naucratis , the Greek colony in Egypt was formally founded: the city became the main trading point between Egyptians and Greeks. Herodotus and Egyptian sources relate that the king was a drinker and philanderer: this may, though, be a literary motif rather than an accurate record. Horus name: Semenmaat Nebty name: Zaneit-sepedtawy Golden Falcon name: Setepnetjeru Prenomen: Khnemibre Nomen: Ahmes Burial place: Sais (Herodotus visited it) Attestations in the Petrie Museum (click on the images to see larger pictures) UC 14504 (relief fragment) UC 38080 (shabti) Further Attestations: Buto: new temple building ( Arnold 1999 Additions at the temple at Mendes ( Arnold 1999 Isis temple at Behbeit el-Hagar ( Arnold 1999 Sais, further work at the Neith temple ( Arnold 1999 Athribis: temple of Khentikhety ( Arnold 1999 Isis temple at Memphis, described by Herodotus (

13. Ahmes Translate this page ahmes. égyptien, vers -1650. Ce scribe égyptien p = 3,125. ahmes donneune table de décomposition des fractions de la forme 2/n 2 http://www.reunion.iufm.fr/Recherche/irem/histoire/ahmes.htm

Accueil Histoire des mathématiques Philosophie des sciences Axiomatiques ... Informations - Contacts AHMES égyptien, vers -1650 Ce scribe égyptien est l’auteur du célèbre papyrus "Rhind" (du nom de l’écossais Henry Rhind qui l’acheta en 1858 à Louksor.) Actuellement conservé au British Muséum de Londres, il contient 85 problèmes relatifs à l’arithmétique, à la décomposition des fractions unitaires (dont le numérateur est 1), à l’arpentage (mesure des distances) et à la géométrie (calcul des pyramides en particulier). Ahmès indique que son papyrus est, en partie, une copie de résultats plus anciens (vers -2000) remontant aux Babyloniens. Il est écrit en écriture hiéroglyphique. Ahmès est aussi mathématicien car il semble avoir découvert le rapport liant l’aire d’un disque à son diamètre en cherchant à ramener l’aire de la circonférence à celle d’un carré équivalent. Le papyrus précise en effet une première approche de la quadrature du c ercle : la solution proposée est un carré de côté 8 d/9 où d est le diamètre du cercle. Les Egyptiens utilisèrent la base 10 (système décimal additionnel). Décomposer les fractions en fractions unitaires permettaient de résoudre les problèmes de partage à vocation commerciale ou domestique, en l'absence d'un système pratique de calcul qu'apportera, 2500 ans plus tard, la division décimale dans notre système de numération positionnel grâce, tout particulièrement à Simon Stevin en 1585.

14. Ahmes High Priest Of Letopolis ahmes. We also know that his eldest son Heriu II was born in 214, which seems moreconsistent with the earlier date of death for ahmes. Ý. 7 BM 378. Ý. http://www.geocities.com/christopherjbennett/ptolemies/hpls/aahmes.htm

[HOME] Ahmes Ahmes , same titles as Heri u II plus: prophet of the temple of Ramses in the temple of Memphis; phylarch of the five phyles of the domain of the temple of $ntj-Tnnt and of the temple of the domain of Semenmaat; prophet of Amun in the town of Ptah in the district of Mesdet; prophet of the divine statues, scribe of Ptah and of the goddes Philadelphos of each fourth phyle, who sees Serapis in aH-AXt ; master of the secrets of Rosetau, master of secrets of the domain of Ptah, of the august place, of the secrets of Heaven, Earth and the Duat, nb pHtj, prophet of the gods Adelphoi Euergetai Philopatores and Epiphaneis ; phylarch for 15 days of the fifth phyle in the temple of Memphis; who opens the gates; scribe of the Treasury of Sheb-ibed; prophet of Amun of Deniu and of the gods of Deniu; employee of the storehouse; prophet of the gods Euergetai of the temple of the domain of Semenmaat, kbH ; son of Heri u I and Tanetamun , date of birth unknown; died 4 Pharmouthi year 22 of

15. High Priests Of Letopolis: Ahmes Crosslink http://www.geocities.com/christopherjbennett/ptolemies/hpls/hpl_ahmes.htm

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16. Peripheria - Ahmes (1680-1620 Av. J.-C.) ahmes (1680-1620 av. JC). ahmes, scribe égyptienné vers 1680 av. JC en Egypte, mort vers 1620 av. JC en Egypte. http://www.peripheria.net/bios/ahmes/

intro accueil / actualités qu'est-ce que Pi ? pourquoi Pi ? histoire du nombre Pi ... les décimales de Pi récré records amusement poèmes filmographie ... logiciels compléments liens bibliographie site livre d'or contact historique du site crédits ... stats [ SPONSOR ] Ahmes (1680-1620 av. J.-C.) [retour aux mathématiciens] (plus d'images) Ahmes, scribe égyptien né vers 1680 av. J.-C. en Egypte, mort vers 1620 av. J.-C. en Egypte. Ahmes est le scribe qui écrivit le Papyrus de Rhind. Il n'en est pas l'auteur, seulement le scribe, son contenu proviendrait de travaux datant de 2000 avant Jésus Christ. Tout ce que l'on sait d'Ahmes sont ses propres commentaires sur le Papyrus de Rhind. Son papyrus est la principale source d'informations sur les mathématiques égyptiennes. Le recto contient des quotients de 2 par les nombres impairs de 3 à 101 en fractions irréductibles ainsi que les nombres de 1 à 9 par 10. Le verso contient 87 problèmes sur les 4 opérations, résolutions d'équations, progressions, volumes, etc. L'un des problèmes porte sur un cercle, et fait appel au nombre Pi, c'est de là que l'on connaît la valeur de Pi que les Egyptiens connaissaient. Il est conservé au British Museum depuis 1863, et est parfois appelé 'Papyrus d'Ahmes'. [retour aux mathématiciens] peripheria

17. Peripheria - Ahmes - Images ahmes - images. retour à ahmes Papyrus de Rhind, le Papyrusde Rhind rhind6.gif 1142 x 1425 x 2 58132 octets. retour à ahmes. http://www.peripheria.net/bios/ahmes/images.php

intro accueil / actualités qu'est-ce que Pi ? pourquoi Pi ? histoire du nombre Pi ... les décimales de Pi récré records amusement poèmes filmographie ... logiciels compléments liens bibliographie site livre d'or contact historique du site crédits ... stats [ SPONSOR ] Ahmes - images [retour à Ahmes] le Papyrus de Rhind rhind1.jpg 200 x 262 x 16M 19489 octets le Papyrus de Rhind rhind2.jpg 360 x 459 x 16M 17631 octets le Papyrus de Rhind rhind3.jpg 393 x 479 x 16M 67621 octets le Papyrus de Rhind rhind4.gif 508 x 351 x 16M 35911 octets le Papyrus de Rhind rhind5.jpg 310 x 368 x 16M 40095 octets le Papyrus de Rhind rhind6.gif 1142 x 1425 x 2 58132 octets [retour à Ahmes] peripheria

18. The Ahmes Papyrus Aritmetic The ahmes Papyrus. The ahmes was written in hieratic, andprobably originated from the Middle Kingdom 20001800 BC. It http://www.math.tamu.edu/~don.allen/history/egypt/node3.html

Next: The Moscow Papyrus Up: $FILE Previous: Counting and Aritmetic The Ahmes Papyrus The Ahmes was written in hieratic, and probably originated from the Middle Kingdom: 2000-1800 BC. It claims to be a ``thorough study of all things, insight into all that exists, knowledge of all obscure secrets." In fact, it is somewhat less. It is a collection of exercises, substantially rhetorical in form, designed primarily for students of mathematics. Included are exercises in fractions notation arithmetic algebra geometry mensuration The practical mathematical tools for construction? To illustrate the level and scope of Egyptian mathematics of this period, we select several of the problems and their solutions as found in the two papryi. For example, beer and bread problems are common in the Ahmes. Problem 72. How many loaves of "strength" 45 are equivalent to 100 loaves of strength 10? Fact: strength := Invoking the rule of three , which was well known in the ancient world, we must solve the problem: Answer loaves.

19. Counting And Aritmetic -- Basics next up previous Next The ahmes Papyrus Up $FILE Previous Basic facts about ancientCounting and Aritmetic basics. ahmes gives a table of unit fractions. http://www.math.tamu.edu/~don.allen/history/egypt/node2.html

Next: The Ahmes Papyrus Up: $FILE Previous: Basic facts about ancient Counting and Aritmetic basics The Egyptian counting system was decimal. Though nonpositional, it could deal with numbers of great scale. Yet, there is no apparent way to construct numbers arbitrarily large. (Compare that with modern systems, which is positional, which by its nature allows and economy for expressing huge numbers.) The number system was decimal with special symbols for 1, 10, 100, 1,000, 10,000, 100,000, and 1,000,000. Addition was accomplished by grouping and regrouping. Multiplication and division were essentially based on binary multiples. Fractions were ubiquitous but only unit fractions, with two exceptions, were allowed. All other fractions were required to be written as a sum of unit fractions. Geometry was limited to areas, volumes, and similarity. Curiously, though, volume measures for the fractional portions of the hekat a volume measuring about 4.8 liters, were symbolically expressed differently from others. Simple algebraic equations were solvable, even systems of equations in two dimensions could be solved.

20. Ahmes Translate this page ahmes. weitere(r) Name(n) Tätigkeit Prinz und Hohepriester von Heliopolisaus Al-Gabalain in Oberägypten. Titulatur Epoche Zeit http://www.manetho.de/person/a/ahmes.htm

Home Personen A PERSONEN Ahmes weitere(r) Name(n): Titulatur: Epoche: Zeit: Verwandtschaft: vermutlich Sohn Thutmosis III. Grab: Amenophis II. als Hohepriester von Heliopolis. Quelle: Last Update: 07.07.2001 http://www.manetho.de/

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