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Quiz about Pi  The Beauty of Mathematics
Quiz about Pi  The Beauty of Mathematics

Pi - The Beauty of Mathematics Quiz


Pi appears in many mathematics and physics equations that describe the Universe's fundamental principles. How well do you know this intriguing pi? Give it a try and have fun.

A multiple-choice quiz by Matthew_07. Estimated time: 5 mins.
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Author
Matthew_07
Time
5 mins
Type
Multiple Choice
Quiz #
273,859
Updated
Dec 03 21
# Qns
10
Difficulty
Tough
Avg Score
6 / 10
Plays
1397
Awards
Top 35% Quiz
- -
Question 1 of 10
1. Leonhard Euler started using pi as the notation for the constant 3.141... in the year 1737. Pi is the 16th letter in the Greek alphabet, which signifies? Hint


Question 2 of 10
2. One of the formulae to calculate the value of pi is given by pi = 4(1 - 1/3 + 1/5 - 1/7 + 1/9 -...). This formula is known as? Hint


Question 3 of 10
3. A sphere's volume can be calculated by using the formula V = (4/3) x pi x r^3 and the formula A = 4 x pi x r^2 gives the area of the sphere. What is the formula of the area of a hemispherical solid? Hint


Question 4 of 10
4. Which of the following statements is FALSE? Hint


Question 5 of 10
5. Apart from being used in calculating the areas of circles and volumes of cylinders, pi is also used in the calculations of trigonometric functions. In geometry, pi = 3.141..., but in trigonometry, 1 pi radian equals to how many degrees? Hint


Question 6 of 10
6. The value of e is 2.718... Which of the following numbers is the closest to the value of [e^(pi)] - pi? Hint


Question 7 of 10
7. There exist many mathematical formulae to calculate the value of pi. One of them was discovered by a famous mathematician from India. Who was he? Hint


Question 8 of 10
8. A very famous mathematical equation that contains pi is f(x) = 1/[sigma x surd (2 x pi)] x e^a, where a = -(mean-miu)^2/(2 x sigma^2). This equation is used in which field of mathematics? Hint


Question 9 of 10
9. A retired Japanese engineer, Akira Haraguchi has memorized pi up to 100, 000 digits. He achieved this by using a mnemonics system. Which of the following sentence is NOT a pi mnemonic? Hint


Question 10 of 10
10. The pi constant appears not only in mathematics, but also in chemistry and physics equations.



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Quiz Answer Key and Fun Facts
1. Leonhard Euler started using pi as the notation for the constant 3.141... in the year 1737. Pi is the 16th letter in the Greek alphabet, which signifies?

Answer: Perimeter

Perimeter corresponds to a circle's circumference.
2. One of the formulae to calculate the value of pi is given by pi = 4(1 - 1/3 + 1/5 - 1/7 + 1/9 -...). This formula is known as?

Answer: Leibniz formula

The Leibniz formula was named after a German mathematician, Gottfried Wilhem Leibniz, who made many great contributions in the field of calculus and topology.
3. A sphere's volume can be calculated by using the formula V = (4/3) x pi x r^3 and the formula A = 4 x pi x r^2 gives the area of the sphere. What is the formula of the area of a hemispherical solid?

Answer: 3 x pi x r^2

The area of a sphere is A = 4 x pi x r^2. So, half of it is 2 x pi x r^2. We should add another pi x r^2 to 2 x pi x r^2 to get the total area of a hemisphere, 3 x pi x r^2, since a hemisphere consists of 2 surfaces: a flat circle and a curved hemisphere itself.

The volume of a cone with a radius (of the circle at the base) of r and a height of h can be calculated using the formula V = (1/3) x pi x h x r^2.

There exists a Pizza Theorem, a mathematics joke that I found online. It says that for a pizza with a radius of z, and a thickness of a, its volume is V = pizza (pi x z x z x a). Interesting, isn't it?
4. Which of the following statements is FALSE?

Answer: Pi is the ratio of a circle's circumference to its radius.

Pi is actually the ratio of a circle's circumference to its diameter.

Pi is an irrational number and hence it cannot be written in a fraction. The fraction 22/7 is only an approximation to the real value of pi and it only matches for the first few decimal places. The value of 22/7 exceeds the real value of pi.

Since pi = 3.141..., this number is celebrated on 14 March (3-14) each year. Many other constants are also being celebrated. For example, phi (the golden ratio, 1.618...) is celebrated on 18 June. On the other hand, the Avogadro constant, 6.02 x 10^22 is celebrated on 22 June.

In 225 BC, Archimedes found the first approximation of pi, namely somewhere between 223/71 and 22/7. He found this value based on his calculation of a circle inscribed in a 96-gon (a polygon with 96 sides).

Pi is known as the Ludolph's constant, too. Ludolph van Ceulen is a German mathematician who calculated the value of pi to 35 decimal places.
5. Apart from being used in calculating the areas of circles and volumes of cylinders, pi is also used in the calculations of trigonometric functions. In geometry, pi = 3.141..., but in trigonometry, 1 pi radian equals to how many degrees?

Answer: 180

1 pi radian equals 180 degrees. Therefore, 1 radian equals (180/pi) degrees.

Trigonometry is a branch of mathematics that studies the relationship between length of triangle sides and it deals with functions such as sine, cosine and tangent.
6. The value of e is 2.718... Which of the following numbers is the closest to the value of [e^(pi)] - pi?

Answer: 20

The exact value of [e^(pi)] - pi is 19.99909998, which is very close to 20.

Without using a calculator, one can make a rough approximation of [e^(pi)] - pi, take e = pi = 3, so the approximation would be (3^3) - 3 = 24, which is close to 20.
7. There exist many mathematical formulae to calculate the value of pi. One of them was discovered by a famous mathematician from India. Who was he?

Answer: Srinivasa Ramanujan

Ramanujan was considered one of the greatest mathematicians. He was born in 1887. But sadly, he died at the age of 32 of tuberculosis.

His pi formula was extremely complicated yet so beautifully written with the combination of summation of series involving factorial, fraction and exponential operations.
8. A very famous mathematical equation that contains pi is f(x) = {1/[sigma x surd (2 x pi)]} x e^a, where a = -(mean-miu)^2/(2 x sigma^2). This equation is used in which field of mathematics?

Answer: Statistics

This function is called the probability density function. It is a bell-shaped graph. The total area bounded by the bell-shaped curve and the x-axis equals to 1, which corresponds to the maximum probability value of 1.
9. A retired Japanese engineer, Akira Haraguchi has memorized pi up to 100, 000 digits. He achieved this by using a mnemonics system. Which of the following sentence is NOT a pi mnemonic?

Answer: May I read a pie story for you?

Notice the following sentence: How (3) I (1) wish (4) I (1) could (5) calculate (9) pi (2) faster (6). The first word contains 3 letters, the second contains 1 letter, and the third one contains 4 letters, and so on.

All of these mnemonics are obtained from www.wikipedia.com .
10. The pi constant appears not only in mathematics, but also in chemistry and physics equations.

Answer: True

In chemistry, the Heisenberg Uncertainty Principle is (delta X) x (delta p) is equal or greater than h/(4 x pi), where h is the Planck constant, X is the position of an object and p is the object's momentum. This principle states that it is impossible to tell the exact location and momentum of a particle during a certain time.

Meanwhile, in physics, pi appears in many equations, such as the cosmological constant, Kepler's third law constant and Coulomb's law.
Source: Author Matthew_07

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