The Pi Trivia Game

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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. At which decimal of pi does the earliest occurrence of the string 999999 begin?

762
32
47528
314
9999

2. Which of the following is an arctangent formula for pi?

arctan 1
3*arctan 1/256 + 2*arctan 1/17
4/3*arctan 1
16*arctan 1/5 - 4*arctan 1/239
2*arctan 2

3. 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

4. Answer the following question (an example of pi's importance in probability), posed and solved by George Louis Leclerc, Comte de Buffon (solved also nowdays by many students in introductory statistics classes): Let a needle of length L be thrown at random onto a horizontal plane ruled with parallel lines spaced by a distance d (greater than L) from each other. What is the probability that the needle will intersect one of these lines?

pi*d^2
pi*d*L
3d/(pi*L)^2
2L/(d*pi)
e^(pi*i*d*L)

5. What 1768 proof about pi is the German mathematician Johann Lambert famous for?

Pi > e.
No pattern exists in pi's digits.
Pi is irrational.
The area of a circle is equal to pi times the square of its radius.
It's fun to recite digits of pi.

eve@eveandersson.com