I am reminded of those prodigies who spent years of their lives calculating digits of the decimal expansion of - a task that is now a mere warm-up exercise for computer software. I cannot help wandering which of my labors will appear equally quaint and pathetic to some future reader who ransacks libraries for old volumes like this one.
In geometry his greatest achievement was an accurate value of ?. His rule is stated as: dn^2+(2a-d)n=2s, which implies the approximation 3.1416 which is correct to the last decimal place.
Not to be overlooked is the fact that in the [Babylonian] sexagesimal notation of integers the "principle of position" was employed. Thus in 1.4 (=64)... The introduction of this principle at so early a date is the more remarkable, because in the decimal notation it was not introduced till about the fifth or sixth century after Christ.
It is true that even across the Himalayan barrier India has sent to us such questionable gifts as grammar and logic, philosophy and fables, hypnotism and chess, and above all our numerals and our decimal system. But these are not the essence of her spirit; they are trifles compared to what we may learn from her in the future.
The sexagesimal system was used also in fractions. Thus, in the Babylonian inscriptions, 1/2 and 1/3 are designated by 30 and 20, the reader being expected, in his mind, to supply the word "sixtieths." The Greek geometer Hypsicles and the Alexandrian astronomer Ptolemæus borrowed the sexagesimal notation of fractions from the Babylonians and introduced it into Greece. From that time sexagesimal fractions held almost full sway in astronomical and mathematical calculations until the sixteenth century, when they finally yielded their place to the decimal fractions.