  # Why Math is Interesting Trivia Quiz

### ...And in no particular order, here are some of the most interesting things about math that I could think of in fifteen questions. No calculations necessary!

A multiple-choice quiz by mitchcumstein. Estimated time: 6 mins.

Time
6 mins
Type
Multiple Choice
Quiz #
368,675
Updated
Dec 03 21
# Qns
15
Difficulty
Tough
Avg Score
8 / 15
Plays
830
This quiz has 2 formats: you can play it as a or as shown below.
Scroll down to the bottom for the answer key.
1. It has been shown that when two infinite sets are compared, one can be larger than the other. The set of real numbers is much larger than the set of integers. What theory says that there is no set larger than the set of integers and smaller than that of real numbers? Hint

Non-denumerability of the Continuum
Continuum Hypothesis
Cantor's Theorem
Axiom of Infinity

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2. What constant is closely associated with perfection and shows up in the Pantheon, Art proportions, and nature as well as the Fibonacci sequence? Hint

The Golden Ratio
Pythagoras's Constant
Pi
Euler's Constant

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3. Fractals are shapes that are self similar at any scale and repeat indefinitely. Who is considered to be the father of fractal geometry? Hint

Ignaz Semmelweis
Benoit B. Mandelbrot
Gerolamo Cardano
Alfred Wegener

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4. Where was Fermat's Last Theory written down? Hint

A napkin
Illuminated scrolls found in some jars in a cave
Etched on a desk
The margins of a different paper

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5. What was the first mathematical proof that required a computer program as part of the proof? Hint

Konigsberg Bridges Problem
Prime Number Theorem
The Four Color Theorem
The Polyhedra Formula

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6. What well known mathematical shape, truly existing in four dimensions, yields a mobius strip when a section is taken through its middle? Hint

Cross Cap
Klein Bottle
Real Projective Plane
Boy's Surface

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7. What kind of curve is made by using a Spirograph? Hint

Conchoid of Nicomedes
Hypotrochoid
Catenary Curve
Jordan Curve

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8. What is the largest number that was given a name and practically used to solve a problem? Hint

24
Graham's Number
Googolplex

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9. What statement simply says that if you have a collection of sets, there is a way to select one element from each set? Hint

Fourier Transformation
Parallel Postulate
Axiom of Choice
Zermelo-Fraenkel set theory

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10. What theorem of mathematics seems to prove that if you take a mathematically perfect sphere apart, you can arrange it in such a way that you can put two spheres back together that are the same size as the original one? Hint

ABC Conjecture
Zorns Lemma
Moonshine Theory

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11. "In a town of one barber who cuts the beards of men that don't cut their own beard, who cuts the barber's beard?". This is a generalization of which paradox? Hint

Crocodile Dilemma

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12. What theory states that all formal systems will invariably have inconsistencies? Hint

Theory of Meta-mathematics
Axiomatic Set Theory
Godel's Incompleteness Theorem
Plato's Theory of Forms

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13. Which Millennium Problem describes the distribution of prime numbers in terms of complex numbers? Hint

Sieve of Erastothenes
P vs. NP Problems
Poincar� Conjecture
Riemann Hypothesis

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14. What shape uses numbers arranged in a pattern in order to demonstrate a correlation with prime numbers? Hint

Tesseract
Sierpinski Triangle
Bucky Balls
Ulam Spiral

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15. What is the highest honor rewarded in mathematics? Hint

Nobel Prize in Mathematics
Fields Medal
Grand Poobah Award
Centennial Prize

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Quiz Answer Key and Fun Facts
1. It has been shown that when two infinite sets are compared, one can be larger than the other. The set of real numbers is much larger than the set of integers. What theory says that there is no set larger than the set of integers and smaller than that of real numbers?

The continuum hypothesis has been proven that it can not be proven true and it has been proven that it can not be proven false. Because of this, it has been determined that the solution to the continuum hypothesis is "undecidable". The size of an infinite set is called its cardinality.
2. What constant is closely associated with perfection and shows up in the Pantheon, Art proportions, and nature as well as the Fibonacci sequence?

The golden ratio, or Phi, is 1.618... It goes on forever and has no pattern, a lot like pi. It was thought to be a perfect ratio and was considered to be the ideal proportions of people's features as well as architecture. It has been demonstrated in plants, flight patterns of birds, and spirals of galaxies and many other places.

It seems to be a constant that fits well with natural occurrences as well as aesthetics.
3. Fractals are shapes that are self similar at any scale and repeat indefinitely. Who is considered to be the father of fractal geometry?

Mandelbrot coined the term fractal in 1975. These shapes can be anywhere from very simple to extremely complex (expressed complex equations only represented with the help of computers). Fractals have taken on a life of their own and can be seen anywhere from mathematical proofs to pop culture art. There have been many comparisons to mathematical fractal shapes and the seemingly fractal nature of the universe.

It is also rumored that the "B" in Benoit B. Mandelbrot's middle name stands for "Benoit B. Mandelbrot". This would be ironic because this would create an infinite fractal as well.
4. Where was Fermat's Last Theory written down?

Answer: The margins of a different paper

The theorem was discovered late after Fermat's death. It was in the margins of his copy of an ancient Greek text called "Arithmetica" by Diophantus.

It states that "X^n+Y^n=Z^n has no positive integers for any n>2" and goes on to say, "I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain." in 1637.

It was finally proven in 1995 by Andrew Wiles. It is hard to believe that Fermat had a proof, considering the vast and varied fields of mathematics Wiles used that hadn't been discovered when Fermat was alive.
5. What was the first mathematical proof that required a computer program as part of the proof?

The four color theorem was proven in 1976 by Kenneth Appel and Wolfgang Haken. Basically the four color theorem states that any general map made on a 2-dimensional surface can be colored with four colors, such that no two adjacent territories are the same color. This was generally accepted by mapmakers for quite some time as a rule of thumb. This proof has had little impact on any other mathematical issues besides as an interesting tid-bit.

It is still controversial today if computers should be allowed to be used in conjunction with a mathematical proof, the idea being that computer programs can still have bugs and miss an important aspect of the proof.
6. What well known mathematical shape, truly existing in four dimensions, yields a mobius strip when a section is taken through its middle?

A Klein Bottle is a non-orientable surface. It has no inside or outside, thus providing both infinite volume and zero volume at the same time. It can only exist in four dimensions because it intersects itself in three dimensions. Three dimensional models are often made and can be purchased in many different mediums. All incorrect answers are also non-orientable surfaces.
7. What kind of curve is made by using a Spirograph?

The hypotrochoid is closely related to the cycloid. The Pittsburgh Steelers logo contains three hypotrochoids and is the most popularly known example of it. The one used for the Steelers has a ratio of 4 to 1 and is called an "asteroid".
8. What is the largest number that was given a name and practically used to solve a problem?

Graham's number is so large that there was no practical way to represent it without taking up an obscene amount of space on a paper (or computer screen). An entirely new system of expressing numbers had to be developed to indicate the ridiculous vastness of the number.
9. What statement simply says that if you have a collection of sets, there is a way to select one element from each set?

The Axiom of Choice seems simple enough. It has been shown that it can not be derived from the rest of Zermelo-Frankel set theory and so must be introduced as an independent axiom. It gets complicated when dealing with infinite sets and produces rather unusual results that are often counter-intuitive. Because of this, many results obtained using the Axiom of Choice explicitly state its requirement.
10. What theorem of mathematics seems to prove that if you take a mathematically perfect sphere apart, you can arrange it in such a way that you can put two spheres back together that are the same size as the original one?

This can be proven but does include the Axiom of Choice as one of its instrumental tools. This seems so counter-intuitive that many people have rejected the Axiom of Choice as a consequence. There have been many similar axioms, lemmas, conjectures and theories that are similar to the Axiom of Choice.
11. "In a town of one barber who cuts the beards of men that don't cut their own beard, who cuts the barber's beard?". This is a generalization of which paradox?

Russell's paradox asks, "Does the set of all those sets that do not contain themselves contain itself?" The barber paradox is a generalization that Russell came up with to make it more accessible. All answers are self referential.

The Crocodile Dilemma says that a crocodile will let go of a man's son only if he can guess what the crocodile will do. The man replies that the crocodile will not return the son. The crocodile has reached a paradox because if the father is correct, the crocodile must return the son and if the crocodile returns the son, the father is incorrect.

The Paradox of the Court says that the law student promises to pay the teacher after he/she wins the first case. The teacher sues the student for payment before he/she has won the first case. If the teacher wins the case, then the teacher gets paid. If the teacher loses the case then the student has won his/her first case and owes the teacher the money. Both ways the teacher wins.

The Pinocchio Paradox simply has Pinocchio state, "My nose will grow". Pinocchio can only be lying or telling the truth. If he's telling the truth- his nose grows which indicates that he is lying. If he's lying- his first statement is a lie and his nose will not grow which indicates the truth (even though it is a lie) His nose can neither grow or not grow.
12. What theory states that all formal systems will invariably have inconsistencies?

One main thing that can be taken from Godel's incompleteness theory is that there can be certain cases that are unprovable within its axiomatic set, yet true.
13. Which Millennium Problem describes the distribution of prime numbers in terms of complex numbers?

The Riemann Hypothesis is considered by some to be the greatest unsolved problem in mathematics. It states that the real part of non-trivial zeros of the Riemann Zeta function is 1/2. There have been a large amount of zeros discovered that show it to be true, however there has been no proof for the generalization of it.
14. What shape uses numbers arranged in a pattern in order to demonstrate a correlation with prime numbers?

Although the Ulam Spiral seems to show a correlation with prime numbers, it is by no means perfect. Prime numbers have a large tendency to line up when arranged in the spiral, but it fails to predict where a prime number will occur. Ulam made this discovery as he was doodling during a speech.
15. What is the highest honor rewarded in mathematics?

It is surprising that there is no recognition for mathematics in the Nobel Prize categories. The fields medal is awarded every four years to 2-4 mathematicians for outstanding work. It is closely matched in prestige to the Abel prize. The Abel prize is presented from the King of Norway to one or more mathematicians every year.
Source: Author mitchcumstein

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