It was in the thirteenth century that Leonardo Fibonacci introduced the so-called Arabic numeral notation. Previously, the formalism of Roman numerals was used, which had the disadvantage of making arithmetic operations difficult. It is said that they were originally Etruscan shepherds who made notches to count the animals in their flocks. For nearly two millennia, abacuses were used to perform operations, ancestors of our multiplication tables. It is said that to carry out complex operations such as inheritances, notaries were accompanied by mathematicians who sometimes took several days to do the calculations.

However, in some cases, some operations were simple; let us take the case of multiplication by 2 from the number 67 = LXVII; each sign is written twice, which gives LL XX VV II II. With the help of simple rewriting rules, we have LL = C, VV=X and IIII=IV. This gives CXXXIV, or 134. For division, we proceed as follows, we first apply rewriting rules, especially for subtractive numbers, so that 9= IX will become VIIII. We group the numbers by two and keep only one. Thus 198 = CICVIII becomes CL XXXXVIII; and L will be changed to XXXXX, which gives C XXXXX XXXX VIII. Dividing C by 2 gives L; the 8 X’s will give XXXX or XL and VIII will become IV. The result will be LXLIV = 94. As long as we stick to multiplications or divisions with numbers less than 10, the operations will be simple, but for a division like 5637801 divided by 247, it will be necessary to build or use an abacus. However, mathematicians were looking for more practical systems. And so it was that the system introduced by Fibonacci was immediately generalized by bankers and merchants.

For thousands of years, fractions have been used below unity. Since the number 60 has many dividing properties, it was adopted and generalized as the basis of sexagesimal numeration, which is still used for hours (minutes, seconds) and angles (minutes, seconds). For the Babylonians and in the Bible (Book of Kings 1:7:23), the number π equaled 3, which gives an accuracy of about 4%, which was acceptable for the time. Then came the 22/7 fraction, probably due to Archimedes in the third century BC. And it is this value that has been used for several centuries, especially in the construction industry. However, at the beginning of the seventeenth century, the “digits after the decimal point” were invented, a notation that made calculations much easier!

To remember thirty-one digits of π, one may use these lines[1]:

“Sir, I bear a rhyme excelling 

In mystic force, and magic spelling

Celestial sprites elucidate

Or locate they who can cogitate

And so finally terminate.

Finis.”

[1] https://poetrywithmathematics.blogspot.com/2010/09/rhymes-help-to-remember-digits-of-pi.html