The Grapes of Math by Alex Bellos

Author:Alex Bellos
Language: eng
Format: epub
Publisher: Simon & Schuster

It gives an approximation for the value of n!, the factorial of n, which as we saw above is the number you get when you multiply 1 × 2 × 3 × 4 × . . . × n.

The factorial is a simple procedure, just multiplying whole numbers together, so it is arresting to see, on the right side of the formula, a square root sign, a pi and an e.

When n = 10, the approximation is less than one percent off the real value of 10!, and the bigger n gets the more accurate the approximation becomes in percentage terms. Since factorials are such huge numbers (10! is 3,628,800), the formula is gobsmacking.

Something’s going on between pi and e.

Leonhard Euler uncovered another coupling between the two constants, one even more surprising and stunning than Stirling’s formula. But before we get there we need to familiarize ourselves with another vowel that he introduced to our mathematical alphabet.

Prepare to meet i.

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