The Ancient Greeks and Their Restless Cattle: 2300 years of Bigints!
summary
Solves Archimedes’ Cattle Under the Sun by reducing it to Pell equations and using continued fractions to get the fundamental unit then raising a quadratic integer to a huge power to produce the minimal solution of about 206000 digits (first four digits 7766). Historical runtimes: IBM 7040 took 7h49m, Cray-1 later verified; modern code in Ruby computes and prints digits instantly on a laptop, so the implementation and result are real and reproducible.
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chapters (8)
- 0:00Archimedes and big numbers
- 1:09Sand Reckoner and Greek numerals
- 2:56Catherine’s cattle problem
- 4:01Pell equations history
- 5:05Continued fractions explained
- 6:30Amthor solves cattle problem
- 7:14206000-digit solution
- 9:02Live cattle problem computation
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