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

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Quiz Answer Key and Fun Facts

Answer:
**Continuum Hypothesis**

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.

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.

Answer:
**The Golden Ratio**

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.

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.

Answer:
**Benoit B. Mandelbrot**

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.

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.

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.

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.

Answer:
**The Four Color Theorem**

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.

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.

Answer:
**Klein Bottle**

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.

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.

Answer:
**Hypotrochoid**

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".

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".

Answer:
**Graham's Number**

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.

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.

Answer:
**Axiom of Choice**

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.

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.

Answer:
**Banach-Tarski Paradox**

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.

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.

Answer:
**Russell's 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.

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.

Answer:
**Godel's Incompleteness Theorem**

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.

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.

Answer:
**Riemann Hypothesis**

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.

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.

Answer:
**Ulam Spiral**

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.

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.

Answer:
**Fields Medal**

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.

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.

This quiz was reviewed by FunTrivia editor rossian before going online.

Any errors found in FunTrivia content are routinely corrected through our feedback system.

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