The Big Pi Quizz "Pi, wait a minute, I think I know..."

Here is the creme of the questions offered on this site. Be warned, they are difficult, in my opinion, the people who can make no mistakes can be counted on one hand in France! Those questions are therefore more for people practised in maths, maybe those knowing quite well the theme of Pi. Because otherwise, I dread to imagine the score.... But don't be discouraged, the answers "I don't know" score one point! All together there are 50 of them. Since we can not always start from zero and avoid classic questions, I confirm it loud and proud: yes, there are a few question taken from the famous Pi trivia game by Eve Andersson, but luckily not many.... But like all true believers, all fans of Pi must need to have made a perilinage on this page at least once! I don't think there are any errors, but all contestation and propositions of questions are welcomed. The scoring is the same as for the short quiz: 3 points for a correct answer, 1 point for "I don't know" (let us admit our ignorance, sometimes... ) and 0 for a wrong answer.... But this time, send me your score: there's a form at the bottom, because if someone gets 150 points, well then.... I don't know what I'll do, but I bow down in any case! Off, we go :

1. : The probability that two integers pulled out at random are coprime is

2. : What is the oldest document known relating to the existance of Pi?

3. : The famous comparison by Archimedes corresponds to how many construction of a polygon with how many sides?

4. : The integral on R of the bell curve by Gauss (exp(-x^{2})) is equal to

5. : And who discovered first the value of this integral?

6. : Simon Plouffe, the famous Canadian mathematician who discoverd the BBP formula allowing to calculate the n-th digit of Pi in base 2, was already famous in 1975 in the Guiness record book. What for?

7. : What is the actual record of number of decimals calculated? (ouch, this question will be quickly obsolete, so let us indicate the date as: 20th September 1999)

9. : In 1997 Fabrice Bellard found a formula that accelerated the calculation of the n-th digit of Pi compared to the BBP formula. By how much?

10. : This dear Fabrice Bellard did not appear out of nowhere. Do you know from which French School he comes from ?

11. : Simon Plouffe owns a second internet site a lot less advertised than the one at www.lacim.uqam.ca/plouffe. It must be said that it radically changed the serious image that we could have of a mathematician (which is not true anyway). What can be found on there?

12. : How are the first few digits of Pi written in binary?

13. : The squaring of a circle is a problem known since the antiquities and numerous are those who tried to solve the problem at all costs. In the 18th century, the Science Academy had enough of the excess of stupid answers that they would recieve and decided to refuse any new proposition. But we had already given a name to this mental obsession. What was it called?

14. : Even though we studied carefully the statisctical spread of the decimals of Pi, we have still not yet found a single interesting pattern. However, some strange things happened, for example the sequence 999999 appears early on. At what possition does it appears?

15. : William Shanks spend many years of his life calculation 707 decimals of Pi, published in 1874. Unfortunatly for him, we noticed nearly a century latter that a few were wrong which forced the Palais de la Decouverte to redo their room dedicated to Pi. Nevertheless how many decimals did he get correct?

16. : (Hard) Pi as we know it belongs to the Euclidian universe. But, in the non-euclidian universe of Nikolaï Lobatchevski, Pi also appears in the formula for the circumference of a circle. What was this formula (k is a constant depending on the space, r radius)

17. : (An easy one to counter-balance !) What is the volume of a sphere with diameter d?

19. : Even though that the result was prooved by Euler, a number of mathematicians looked at the value of Zeta(2)=sum(1/n^{2})=^{2}/6 to found an even easier proof. The one considered as the most elementary, even though long, is thanks to a grec amateur mathematician who send it to the American Mathematical Monthly in 1973. What was his name ?

20. : After the 707 decimals calculated by Shanks, it seemed difficult to go any further in the calculation by hand of the decimals of Pi. With the apparition of computer after the second world war, we finnaly had a tool that allowed us to avoid all this ingrat work. In 1949, for the first time, we gave this work to ENIAC (Electronic Numerical Intergrator and Computer). How many decimals did it calculated (in 70h)?

21. : We often conjecture that Pi is normal in base 10, but that was never proved. What does that mean by the way?

22. : Another important concept, the universal number. We don't know if Pi is one. What pratical consequence could this have if the hypothesis were checked?

23. : Which French mathematician from the beginning of the 20th century invented the concept of normality?

24. : Which Japanese mathematician left an indirect method to calculate Pi with the serie expansion of the length of an arc, and at the same time calculated 4 decimals of Pi?

25. : A contempary mathematician and who participated to the research of Pi owned a number plate whose number was P 314159. Nowday it's in hexadecimal, who was it?

26. : By the way in hexadecimal, what is Pi?

27. : Pi has a Friends of Pi Club which is very active and organised. In which country did it come to be?

29. : Who said "Computer, Calculate the last decimal of Pi!"

30. : What is the name for the method that allows us to approximate Pi by counting the ratio of number of points, taken at random, inside a circle with those inside a square circonscribed?

31. : For the taupins, what is the value of Pi ?

32. :According to the famous biologist Buffon, if you throw a needle of length a on a floor made of floorboard evenly spaced of length b, what is the probability that the needle cut one of the floorboard?

33. : At what possition do we see the number 0 appear for the first time in the decimals of Pi?

34. : Still in statistics, do you know how many 7 appears in the first 400 decimals (and this seems a strange anomalie)?

35. : Pi can be found everywhere in the scientifical world, for example in physics, with oscillations. Take a pendulum of length h, what is the period of its mouvement for small oscillation (with g being the gravitational constant)?

36. : What was the arctan formula found by John Machin ?

37. : Knowing that the circumference of the Earth is 40 000 Km and that we pulled a rope around the Earth at altitude 0 (sea level), how much extra length would we need to add is we lift the rope 1m above sea level?

39. : What was the approximation of Pi that the egyptians calculated?

40. : What was called the grec mathematician who managed to square cresents in the 5th century B.C. while trying to square a circle?

41. : In which region did we discover for the first time the approximation 355/113 ?

42. : What did Descartes method of isoperimeters consist of?

43. : Who found the first infinite product converging to Pi ?

44. : Wallis asked one of his friends to reshape the serie by Madhava/Gregory/Leibniz. He managed to find an expression of Pi in continu fractions. Was it

45. : James Gregory (1638-1675), who discovered the limited expansion of arctan, did another profession than mathematician. Which one?

46. : With the appearance of computers there was a continuous improvement of the explotation of arctan formulae until the end of the 70s. However, now the method of programation are still slow. They uses algorithm that are:

47. : The BBP formulae allows to calculate the n-th digit without knowning the previous one, but it doesn't work just for Pi. We have found BBP formulae for other constant except:

49. : Brent, the co-discoverer of the Bren/Salamin formula in 1976 is a great austalian specialist in algorithm. Where does he work?

50. : After discovering the BBP formula, a young student from cecm extremly gifted organised the pihex project, with the charge of going further and further in the position of the digit of Pi calculated by putting at his disposition all of the other computers in the world. Who was he?

Fabrice Bellard Colin Percival S.C. Woon Karl Bright I don't know..!

Phew!