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. 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

2. How does one convert pi in base 10 to base 2?

Keep only the '0' and the '1' in the decimal expansion.
It is impossible because pi > 2.
Replace each digit of pi in base 10 with a 0 if it is divisible by 2 and with and 1 if it is not.
Successively multiply pi by 2 and put a '1' when it is greater than 1 and a '0' when it is smaller than 1. Repeat this step after having kept only the fractional part of the result.
Divide pi in base 10 by 5.

3. If one were to find the circumference of a circle the size of the known universe, requiring that the circumference be accurate to within the radius of one proton, how many decimal places of pi would need to be used?

2 million
39
11
48,000
300

4. What is the volume of a sphere (3-dimensional, not a hypersphere) [r = radius]?

6(pi*r)^3
(4/3)(pi)(r^3)
([2/3]*pi*r)^3
2*pi*r
4*pi*(r^2)

5. 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)

eve@eveandersson.com