Hostname: page-component-77c89778f8-m8s7h Total loading time: 0 Render date: 2024-07-19T22:21:50.799Z Has data issue: false hasContentIssue false
  • English
  • Français

Large Numbers

Published online by Cambridge University Press:  03 November 2016

J.E. Littlewood
Get access Rights & Permissions [Opens in a new window]

Extract

The problem how to express very large numbers is discussed in ‘The Sand-Reckoner’ of Archimedes. Grains of sand being proverbially ‘innumerable’, Archimedes develops a scheme, the equivalent of a 10 n notation, in which the ‘Universe’, a sphere reaching to the Sun and calculated to have a diameter less than 1010 stadia, would contain, if filled with sand, fewer grains than ‘1000 units of the seventh order of numbers’, which is 1051. [A myriad-myriad is 108; this is taken as the base of what we should call exponents, and Archimedes contemplates 108 ‘periods’, each containing 108 ‘orders’ of numbers ; tlle final number in the scheme is 108. 1015.] The problem of expression is bound up with the invention of a suitable notation; Archimedes does not have our ab , with its potential extension to aa a . We return to this question at the end ; the subject is not exhausted.

Type
Research Article
Information
The Mathematical Gazette , Volume 32 , Issue 300 , July 1948 , pp. 163 - 171
Copyright
Copyright © The Mathematical Association 1948

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Page 165 of note * Note that it is pairs and not ordered pairs that are relevant.

Page 166 of note * I learn from Mr. H. A. Webb that in one of Blackburne’s games a position recurred for a second time, but with a pair of rooks interchanged. Each player expected to win, otherwise (as Blackburne said) a delicate point for decision would have arisen.

Page 167 of note * We may suppose that C (in the light of A’s performance!) does not suspect the position, and resigns in the ordinary way

Page 169 of note * See Math. Ann. 109 (1934), 661-667 ; Bull. Anzer Math. Soc. 1928, 84-56 ; Amer Math. Monthly, 43 (1036), 347-354.

Page 169 of note † It is acessible in a Ph.D. thesis deposited in the Cambridge University Library.

Page 169 of note ‡ See J. L. M. S., 8 (1933), 277-283.