The Pi Trivia Game

by Eve Andersson

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Finally this is your chance to pay tribute to the magnificent transcendental number that we have all grown to love! Here are 25 questions (given to you 5 at a time), picked randomly from my pi question database. Get ready for the thrill of your lifetime, the ultimate challenge, The Pi Trivia Game!

1. Simon Plouffe has recently derived an algorithm for calculating pi in hexadecimal. Remarkably, this formula allows one to calculate the nth decimal of pi without calculating the previous digits. Incidentally, Plouffe was listed in the 1975 Guinness Book of World Records. For which of the following accomplishments was he listed?
calculating 3 trillion digits of pi with a Cray supercomputer
walking 1002 miles with a jar of pickles balanced on his head
reciting 4096 digits of pi from memory
baking the world's largest pie, so perfectly round that its circumference divided by its diameter gave pi to an accuracy of over 300 decimal places
world chess champion

2. Consider the following series of natural numbers, constructed by taking successively larger strings of digits from the beginning of the decimal expansion of the number pi:
3, 31, 314, 3141, 31415, 314159, 3141592, etc.
Out of the first 1000 numbers in this series, how many are primes? (for example, the first two numbers, 3 and 31, are both primes)
48
34
4
21
58

3. One way to approximate the value of pi is to have a computer pick two random numbers, x and y, each between -1 and 1. If it does so N times, and if, for M of those times x^2 + y^2 < 1, then pi is approximately equal to 4*M/N (presumably becoming more accurate as N increases). This method of approximation is an example of:
the Windelius algorithm
squaring the circle
the Monte Carlo method
guessing
calculation of an infinite series

4. If you pick any two integers at random, what is that probability that they will be relatively prime? ("relatively prime" means that the two numbers share no divisors except 1)
pi/2
pi/3
1/pi
6/(pi^2)
pi^2/9

5. What rapidly converging formula for calculation of pi was found by Machin in 1706?
pi/4 = 1 - 1/3 + 1/5 - 1/7 + ...
pi/4 = 4 * arctan (1/5) - arctan (1/239)
e^(i*pi) = -1
pi = 3 (close enough)
pi = 4 * arctan 1
eve@eveandersson.com