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Boris Gourévitch
The world of Pi - V2.57
modif. 13/04/2013

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The Small Pi Quiz
"Pi, What's this thing?"

Here are 20 question that I have chosen. A few are trivial (so to allow some to have at least one point?) and all together, they're are not hard, well I hope... I tried to please both math and non-math people. However for the first lot, I advise them to take the big quiz which is worth it's click with 50 brand new and harder questions.
I don't think there's any errors, but all correction are welcomed!
The scoring: 3 points per correct question, 1 point for the answer 'I don't know' (knowing your ignorence is a good thing...) and 0 for incorrect.... Every time, mark the right answer!

1.  : One geometrical definiton of the constant Pi in a circle is

    the ratio of the circumference on the radius
    the ratio of the circumference on the diameter
    the product of the radius and the diameter
    the are of a british cake, the Apple Pie
    I don't know..!

2.  : Roughly at what period was the discovery of a constant that we now call Pi ?

    first civilisation (egyptian, babylonian)
    ancient greece and romans
    middle ages
    I don't know...!

3.  : The famous comparion by Archimedes is: (No calculators allowed!)

    3+1/7 < Pi < 3+10/71
    3+1/8 < Pi < 3+1/7
    3+14/100 < Pi < 3+15/100
    3+10/71 < Pi < 3+1/7
    I don't know...!

4.  : How did Archimedes die (Around 212 B.C.)?

    killed by a roman soldiers when syracuse was taken
    of old age
    he fell in the sea while defending his town against the romans
    of a long exotic illness
    I don't know..!

5.  : What was Archimedes' famous method to approximate Pi?

    fins a square of the same area of a circle and deduce an approximation for Pi
    calculate the perimeters of n-sided polygons inscibed and circumscibed in a circle and make n tend to infinity
    calculate the diameter of a circle fixing it's circumference at 1
    bake pies and calculate it's circumference
    I don't know....!

6.  : What numerical system did the chinese, so talented in the approximation of Pi, since the antiquity?

    Base 16
    Base 10
    Base 60 (like the egyptians)
    Base 2
    I don't know...!

7.  : In the middle ages, who was one of the first to intoduce in Europe base 10 as a calculation reference and found an approximation of Pi ?

    I don't know..!

8.  : A man stayed famous in Germany as he spend his life calculating 35 decimals of Pi, published in 1615. Was it:
    William Shanks
    John Machin
    Ludolph van Ceulen
    I don't know..!

9.  : A revolution in the calculation of the decimals was due to the introduction of the arctan formulae in 1706. To who do we have to thank for this brilliant discovery?

    John Machin
    James Grégory
    I don't know..!

10.  : Euler discovered many formulae on Pi and was gifted with an extraordinart memory. He's scientifical production completly clear and remarquable comprise of a total of:
    50 books of 250 pages (or 164 pages per year on average)
    50 books of 500 pages (or 328 pages per year on average)
    70 books of 700 pages (or 644 pages per year on average)
    75 books of 800 pages (or 789 pages per year on average)
    I don't know...!

11.  : The transcendance of Pi is linked to the famous ancient problem. Is it:

    The trissection of an angle
    the square egg
    the squaring of a circle
    the duplication of a cube
    I don't know..!

12.  : And what does the transcendance of Pi signify?

    Pi is not the root of a polynomial with integers coefficients
    Pi can not be written in the form a/b with integers a and b
    When a mathematician research Pi, he transcend their importance.
    Pi and e are algebraicly independant
    I don't know..!

13.  : In 1897, a law project of a wierd american decided that in the constitute of an anerucab state the exact value for Pi, which varied from Pi=3.1604 to Pi=4. Which state was it?

    I don't know..!

14.  : In 1844, a prodigy human calculator beats the records of know decimals of Pi under the alias Strassnitsky. Was it

    William Shanks
    John Wrench
    Zacharias Dahse
    Nikolaï Lobatchevski
    I don't know..!

15.  : What value of Pi does the Bible offer?

    I don't know...!

16.  : An Indian genius emerge from his class at the biginning of the 20th century. Self-educated and gifted with a fabulous intuition, was it

    I don't know..!

17.  : What was the name of the English mathematician that went to meet this Indian genius and invite him to work with him from 1914 to 1919?

    James West
    I don't know..!

18.  : What was the likely cause of Ramanujan death when he came back to India in 1920 aged 33?
    He did too many maths
    He was taken in an indian revoltion for independance
    He died due to malaria
    He fell to a serious lack of vitamines since he was vegetarian
    I don't know..!

19.  : New algorithm to calculate Pi were introduced in the 70s and 80s by Brent, Salamin, Garvan, and the Borwein brothers. The exceptional speed of convergence of the first of them for example, the one of Brent/Salamin, doubles the number of exact decimals at each iteration. We call this a ..... convergence:

    I don't know..!

20.  : Who designed for the first time the constant for the letter Pi in 1706?

    John Machin
    William Jones
    James Grégory
    I don't know (scandal !)

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