1.
Who, in 1706, first gave the Greek letter “pi” its current mathematical definition?
Correct Answer
B. William Jones
Explanation
William Jones is credited with giving the Greek letter "pi" its current mathematical definition. He introduced the symbol in 1706 to represent the ratio of a circle's circumference to its diameter, a fundamental constant in mathematics. Albert Einstein, Attila the Hun, Archimedes, and Napoleon Bonaparte are not associated with giving "pi" its mathematical definition.
2.
Pi is transcendental. What does this mean, in mathematics?
Correct Answer
C. It cannot be expressed as an integer, or as a root or quotient of integers
Explanation
The statement "Pi is transcendental" means that the number pi cannot be expressed as an integer or as a root or quotient of integers. In other words, it is not a rational number. Transcendental numbers are a special type of irrational numbers that cannot be the solution to any polynomial equation with integer coefficients. Pi is one of the most famous examples of a transcendental number.
3.
What is the earliest known reference to pi in history?
Correct Answer
C. An Egyptian papyrus scroll, written approx. 1650 BC by Ahmes the Scribe
Explanation
The earliest known reference to pi in history is an Egyptian papyrus scroll, written approximately 1650 BC by Ahmes the Scribe. This papyrus, known as the Rhind Mathematical Papyrus, contains mathematical problems and solutions, including an approximation of pi. It shows that the ancient Egyptians had a basic understanding of the concept of pi and used it in their calculations. This predates other known references to pi, such as those found in the Bible or Euclid's Elements.
4.
People tried for centuries to “square the circle”. What were they trying to do?
Correct Answer
D. Use a straightedge and compass to construct a square exactly equal in area to a given circle
5.
Some people became mentally deranged when trying to “square the circle”. What was this illness named?
Correct Answer
B. Morbus Cyclometricus
Explanation
Morbus Cyclometricus is the correct answer because it refers to the illness that some people developed when attempting to "square the circle." This term suggests that individuals became mentally deranged or obsessed with finding a solution to the mathematical problem of squaring the circle, which is impossible. The name Morbus Cyclometricus captures the idea of a condition related to circular calculations or geometry, reflecting the nature of the illness.
6.
Are pi’s digits periodic? In other words, do the digits ever repeat themselves in any pattern?
Correct Answer
B. No. Every periodic number is rational, but pi is irrational
Explanation
The explanation for the correct answer is that every periodic number is rational, meaning it can be expressed as a fraction. However, pi is known to be an irrational number, which means it cannot be expressed as a fraction and its decimal representation goes on infinitely without repeating in any pattern. Therefore, the digits of pi do not repeat themselves in any pattern, making the statement "No. Every periodic number is rational, but pi is irrational" the correct answer.
7.
Pi is an irrational number. What does that really mean?
Correct Answer
C. It is a real number, but can’t be expressed as a ratio of two integers
Explanation
An irrational number is a real number that cannot be expressed as a ratio of two integers. In other words, the decimal representation of an irrational number goes on forever without repeating and cannot be written as a fraction. Pi is a famous example of an irrational number, as its decimal representation (3.14159...) goes on infinitely without a pattern or repetition. Therefore, the correct answer states that pi is a real number but cannot be expressed as a ratio of two integers.
8.
Among the digits of pi currently known, the concentration of each of the digits 0-9 are pretty close to equal. However, in the first 30 places of pi’s decimal expansion, which digit is completely missing?
Correct Answer
C. 0
Explanation
In the first 30 places of pi's decimal expansion, the digit 0 is completely missing. This means that among the first 30 digits of pi, there is no occurrence of the digit 0.
9.
What is the “formal” definition of pi?
Correct Answer
E. The ratio of a circle’s circumference to its diameter
Explanation
The correct answer is "the ratio of a circle’s circumference to its diameter." Pi is a mathematical constant that represents the relationship between a circle's circumference and its diameter. It is an irrational number, approximately equal to 3.1415926. The other options provided, such as the surface area of a sphere, the radius of a circle, and a delicious dessert, are not accurate definitions of pi.
10.
Imagine if you wrapped a rope tightly around the earth at the equator. How much longer would you have to make the rope if you wanted it to be exactly one foot above the surface all the way around?
Correct Answer
A. 2 ∏ feet
Explanation
If you wrap a rope tightly around the Earth at the equator, the rope would already be exactly one foot above the surface all the way around. Therefore, you wouldn't have to make the rope any longer.