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Pi Trivia
History of Mathematics and Pi
Pi in Classical Calculus
Famous Numbers
Famous Quotes as Math Problems
100
What famous scientist and mathematician who revolutionized our thinking was born on March 14th (Pi Day)?
What is Albert Einstein
100
What proof marked the end of the quest for the ”Squaring the Circle” problem, which has obsessed the humanity since 1800 BC?
What is Lindemann’s proof that π is transcendental in 1882
100
Euler, to whom we owe most standard mathematical symbols for, also discovered the connection between trigonometric functions and exponential functions. What is the Euler’s famous formula that connects e , π and i ?
What is e^(πi)+1= 0
100
What is the thousand’s digit of the geometrical proportion known as the Golden Ratio or the “divine proportion” or as ɸ?
What is 8 ɸ=1.6180….
100
In Lewis Carol’s book “Alice’s Adventures in Wonderland ”, the first multiplication fact in Alice’s multiplication table “four times five is twelve” makes sense in what numerical base? “I’ll try if I know all the things I used to know. Let me see: four times five is twelve, and four times six is thirteen, and four times seven is - oh dear! I shall never get to twenty at that rate” ( “Alice’s Adventures in Wonderland”)
What is 18
200
Pi was featured as a key plot element during an episode of what popular science fiction show? (The very savvy Vulcan science officer used the calculation of pi to crash the computer.)
What is Star Trek
200
Archimedes of 3rd century B.C., the father of physics and science, calculated π by inscribing a polygon of 96 sides in a circle and then circumscribing a polygon of 96 sides to the same circle and comparing their perimeters. His calculation of π was accurate to how many decimals?
What is 2 decimals. He proved that 3.1408<π<3.1428
200
In what century was the ratio of circumference to the diameter first denoted as π while translating some of Newton’s works?
What is In the 18th century. William Jones used it first in 1717 while translating Newton’s works, and Euler used it in his publications starting with 1737, after which it became standard notation.
200
A perfect number is defined as the number that equals to the sum of all the smaller numbers that divide into it. What is the second perfect number?
What is 28
200
In the treaty “The Liber Abaci” by Leonardo of Pisa also known as Fibonacci, appears the following famous problem: A man whose end was approaching summoned his sons and said: ‘Divide my money as I shall prescribe.” To the eldest son he said: “ You are to have 1 bezant (coin) and the seventh of what is left” To the second son he said: “Take 2 bezants and the seventh of what remains” To the third son: “ You are to take 3 bezants and a seventh of what is left” Thus he gave each son 1 bezant more than the previous son and a seventh of what remained, and to the last son all what was left. After following their father’s instructions with care, the sons found that they had shared their inheritance equally. How many sons were there and how large was the inheritance?
What is 6 sons and 36 bezants
300
What book of the Bible includes an allusion to π? "And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it about.”
What is I Kings or II Chronicles
300
Ferdinand Lindemann proved in 1882 the transcendence of π. What does it mean that π is transcendental?
What is It cannot be expressed as the solution of a polynomial with rational coefficients (is not algebraic), or equivalently, it cannot be constructed according to the Greek rules by only using a straightedge and a compass.
300
Category: Pi in Classical Calculus Pascal’s formula for π π=2 (2∙2∙4∙4∙6∙6…)/(3∙3∙5∙5∙7∙7…) can be derived from Wallis’ integration formula of sin^n (x) on the interval [0,π/2]. Using Wallis’ formula, what is the exact value of area under the curve sin^2 (x) in the interval [0,π/2] ?
What is π/4
300
What is the third Mersenne prime?
What is 31 2^5-1=31 because for n=1 and n=4 the formula gives non-primes
300
Fibonacci’s riddle: “A certain man puts a pair of rabbits in a place surrounded by a wall. How many pairs of rabbits can be produced in a year if every month a pair begets a new pair which from the second month becomes also productive?”
What is 377 which is the 12th number of the Fibonacci sequence: 1, 2, 5, 8, 15, 21, 34, 55, 89, 144, 233, 377
400
Ludolph Van Ceulen (1540 - 1610) spent most of his life working pi out to 35 decimal places. In what country is π sometimes referred as the Ludolphian constant ?
What is Germany
400
What is the name of the librarian of 3rd century BC Alexandria, who calculated the circumference of the earth within 5% of the correct value by observing the difference in zenith distance of the sun at two places separated by a known distance?
What is ERATHOSTENES
400
Scotsman James Gregory ( 1638-1675) is considered the “ grandfather” of calculus. Among many things that Gregory discovered is the formula for the area under the curve 1/(x^2+1). Find the value of the area under this curve in the interval (0,1).
What is π/4
400
Which of the following numbers is equal to √(1+√(1+√(1+√(1+⋯)) ) ) e , π , ϕ , or √2 ?
What is ϕ
400
This “riddle” from Greek Anthology gives a short summary of the life of Diophantus from Alexandria. ’God gave him his boyhood one-sixth of his life; One twelfth more as youth while whiskers grew rife; And then yet one-seventh before marriage begun; In five years there came a bouncing new son. Alas, the dear child of master and sage after attaining half the measure of his father's life chill fate took him. After consoling his fate by the science of numbers for four years, his life ended.' How old was Diophantus when he died?
What is 84
500
How many π digits does NASA need for calculations involving the Space Integrated Global Positioning System?
What is 16
500
Buffon’s needle problem based on an idea of Pierre Laplace (approx. 1800) A needle of length equal precisely to the spacing between multiple parallel lines drawn on a piece of paper is thrown completely at random onto the paper. What is the probability that the needle will land in such a way that it will intersect one of the parallel lines?
What is 2/π
500
The following formula for π discovered by Leibniz : π=4(1-1/3+1/5-1/7+⋯) Gives the first accurate decimal when the number of terms is greater than or equal to what number?
What is 19
500
What is the name of this famous constant? ∑10^(-k!) =0.110001000000000000100…
What is Liouville Constant, which was the first provable transcendental number.
500
Augustus De Morgan who considerably expanded the branch of logic in the nineteenth century, once said: "I was x years old in the year x^2". In what year was De Morgan born?
What is 1806