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

²/6
6/^2
2/12
3/²
I don't know..!


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

The Suse tablette from the Babylonians
The Rhind papyrus from the Egyptians
Paper on the method of Archimedes
A carved stone
I don't know..!

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

48
96
24
192
I don't know..!


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4.  : The integral on R of the bell curve by Gauss (exp(-x²)) is equal to

(2)<sup>1/2

1/2</sup>
I don't know..!


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

Leonhard Euler
Carl Gauss
Abraham de Moivre
Jean Bernoulli
I don't know..!


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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?

He calculated 2 million decimals on a Cray
He memorised 4096 decimals of
He cooked the biggest Apple Pie (3m in circumference)
By traveling 314 km on his hands
I don't know..!


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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)

206,158,430,000
206,000,000,000
68,719,470,000
6,442,450,938
I don't know..!

5 000 billionth digit
4 000 billionth digit
1 000 000 billionth digit
40 000 billionth digit
I don't know..!


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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?

16%
27%
43%
52%
I don't know..!


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

Polytechnique
Ecole Normale Supérieure d'Ulm
Ecole Centrale Paris
Ecole des Mines de Paris
I don't know..!

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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?

Some receipes for very exotic cuisine
Caricatures of political figures
A DIY manual for useless objects
The jokes made by his students
I don't know..!


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

11.1110111101111100
1.10111011010010011
101.110101000111100
11.0010010000111111
I don't know..!

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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? 

Morbus Cyclometricus
Impossibilus Quarris
Repetitionatis Decimalus
Transcendantis Morbus
I don't know..!


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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?

192
337
762
1123
I don't know..!


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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?

445
527
602
657
I don't know..!


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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)

2**r*e^k.r
*r²*e^Pi.k
2*²*k*e^r.k
*k*(e^r/k-e^-r.k)
I don't know..!


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

*d³/6
4/3**d³
*d³/8
*d³
I don't know..!

the constant such that exp(i*)=-1
the double of the unique root to the equation cos(x)=0 between 0 and 2
the real number that appears in the differention 2**e(x) of the function e(x), unique continu homorphism of the additive group R on the multiplicative group U of the complex number of absolute number 1
the perimeter of an apple divided by it's diameter
I don't know..!


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19.  : Even though that the result was prooved by Euler, a number of mathematicians looked at the value of Zeta(2)=sum(1/n²)=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 ?

Papandreou
Theodorakis
Caratheodory
Papadimitriou
I don't know..!


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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)?

2037
5432
4096
36412
I don't know..!

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

Like all normal person, has two arms
the appearance frequence of the digit 0 to 9 is 1/10
the appearance frequence of the digit 0 to 9 is 1/10, of each pair 00 to 99 is 1/100, etc...
We can find any sequence of numbers in the decimals of
I don't know..!


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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?

We could find the Bible and our own biography at a precise place in the decimals of translate in letters.
We could calculate the size of the universe
We could finally have a discusion with
We won't need to calculate it's decimal anymore because we could guess them using the previous one
I don't know..!

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

Henri Lebesgue
René Baire
Henri Poincarré
Emile Borel
I don't know..!


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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?

Li Chan
Yamamoto Kiemalgare
Seki Takakazu
Takebe Katahiro
I don't know..!


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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?

Simon Plouffe
David Bailey
Peter Borwein
David Chudnovsky
I don't know..!


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

29BC5F8...
30EA19B...
3243F6A...
34D6A96...
I don't know..!


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

France
United States of America
England
Austria
I don't know..!

He painted a big picture putting in scene the decimals of
He composed a piece by associating each decimals to a chord
He recited the decimals on top of the Eiffel tower with a megaphone
He travelled through France on foot offering pages of decimals to each people he meet
I don't know..!


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

Grégory Chudnovsky
Spock in Star Trek
Ferguson
Albert Einstein
I don't know..!


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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?

The winchester's method
The acupunctur's method
The Monte-Carlo's method
The Limousin's method
I don't know..!

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

horse/bird
cow/chicken
platypus/diplodocus
dog/cat
I don't know..!


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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?

2a/(b)
a/(b)
4a2/(b)
2b/(a)
I don't know..!

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

9
26
32
67
I don't know..!


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

7
123
63
24
I don't know..!


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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)?

h*g/
²*g/h
*h*sqrt(g)
2**sqrt(h/g)
I don't know..!


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

arctan(1/2)+arctan(1/3)
arctan(1/5)-4*arctan(1/239)
arctan(1/3)+2*arctan(1/7)
arctan(1)
I don't know..!


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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?

314 metres
6.28 Km
6.28 metres
628 Km
I don't know..!

1-0.28*10^-29
2.03101013248798454464
1+0.12*10^-14
3.14159265358...
I don't know..!


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

3+1/8
(16/9)²
3+1/7
2.3
I don't know..!


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

Hippias d'Elis
Hippocrate de Chio
Dinostrate
Euclide
I don't know.. !

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

In 5th century China with Tsu Chung-Chih
In 15th century Europe with Adrian Anthonisz
In 6th century India with Aryabhata
In 9th century Arabia with Al Khwarizmi
I don't know..!


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

Calculate the area of a n-sided polygon inscribed in a circle through recursion then let n tend to infinity
Calculate the perimeter of a n-sided polygon inscribed in a circle through recursion then let n tend to infinity
Average out the sequences of perimeters above and find a recursive relation with the new definied sequence
Calculate using recursion the diameter of a n-sided polygon with perimeter p and that are inscribed in a circle with fixed circumference p
I don't know.. (scandal !)

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

Euler
Viete
Einstein
Wallis
I don't know..!


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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

William Oughtred
Isaac Barrow
Isaac Newton
Lord Brounker
I don't know..!


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

Physicist
Biologist
Astronomer
Philosopher
I don't know..!


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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:

linear in time and memory
logarithmitic in time and linear in memory
quadratic in time and linear in memory
quadratic in time and in memory
I don't know..!


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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:

e
ln(2)
²
ln(22)
I don't know..!

On the equilibrium of plans
On the sphere and cylinder
The measure of a circle
Let's take a walk in the woods
I don't know..!


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

Camberra
Oxford
Sidney
Berkeley
I don't know....!


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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..!

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Phew!