# Archimedes&apos; Cattle Problem

Archimedes' Cattle Problem Archimedes' Cattle Problem Han Vardi A PROBLEM which Archimedes devised in epigrams, and which he communicated to students of such matters at Alexandria in a letter to Eratosthenes of Cyrene. If thou art diligent and wise, 0 stranger, compute the number of cattle of the Sun, who once upon a time grazed on the fields of the Thrinacian isle of Sicily, divided into four herds of different colours, one milk white, another glossy black, the third yellow and the last dappled. In each herd were bulls, mighty in number according to these proportions: Understand, stranger, that the white bulls were equal to a half and a third of the black together with the whole of the yellow, while the black were equal to the fourth part of the dappled and a fifth, together with, once more, the whole of the yellow. Observe further that the remaining bulls, the dappled, were equal to a sixth part of the white and a seventh, together with all the yellow. These were the proportions of the cows: The white were precisely equal to the third part and a fourth of the whole herd of the black; while the black were equal to the http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The American Mathematical Monthly Taylor & Francis

# Archimedes&apos; Cattle Problem

, Volume 105 (4): 15 – Apr 1, 1998

## Archimedes&apos; Cattle Problem

, Volume 105 (4): 15 – Apr 1, 1998

### Abstract

Archimedes' Cattle Problem Han Vardi A PROBLEM which Archimedes devised in epigrams, and which he communicated to students of such matters at Alexandria in a letter to Eratosthenes of Cyrene. If thou art diligent and wise, 0 stranger, compute the number of cattle of the Sun, who once upon a time grazed on the fields of the Thrinacian isle of Sicily, divided into four herds of different colours, one milk white, another glossy black, the third yellow and the last dappled. In each herd were bulls, mighty in number according to these proportions: Understand, stranger, that the white bulls were equal to a half and a third of the black together with the whole of the yellow, while the black were equal to the fourth part of the dappled and a fifth, together with, once more, the whole of the yellow. Observe further that the remaining bulls, the dappled, were equal to a sixth part of the white and a seventh, together with all the yellow. These were the proportions of the cows: The white were precisely equal to the third part and a fourth of the whole herd of the black; while the black were equal to the

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# References (36)

Publisher
Taylor & Francis
Copyright
Copyright Taylor & Francis
ISSN
1930-0972
eISSN
0002-9890
DOI
10.1080/00029890.1998.12004887
Publisher site
See Article on Publisher Site

### Abstract

Archimedes' Cattle Problem Han Vardi A PROBLEM which Archimedes devised in epigrams, and which he communicated to students of such matters at Alexandria in a letter to Eratosthenes of Cyrene. If thou art diligent and wise, 0 stranger, compute the number of cattle of the Sun, who once upon a time grazed on the fields of the Thrinacian isle of Sicily, divided into four herds of different colours, one milk white, another glossy black, the third yellow and the last dappled. In each herd were bulls, mighty in number according to these proportions: Understand, stranger, that the white bulls were equal to a half and a third of the black together with the whole of the yellow, while the black were equal to the fourth part of the dappled and a fifth, together with, once more, the whole of the yellow. Observe further that the remaining bulls, the dappled, were equal to a sixth part of the white and a seventh, together with all the yellow. These were the proportions of the cows: The white were precisely equal to the third part and a fourth of the whole herd of the black; while the black were equal to the

### Journal

The American Mathematical MonthlyTaylor & Francis

Published: Apr 1, 1998

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