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This quiz consists of 5 multiple choice and 5 short answer questions through Euclid's Proof of the Pythagorean Theorem.
Multiple Choice Questions
1. How do we know about Hippocrates proofs and theorems?
(a) What we know is from references of later mathematicians.
(b) What is known from archived documents of his time.
(c) His books and publications.
(d) Mathematicians rewrote all of his proofs after his death,
2. According to Euclid, when is a triangle a right triangle?
(a) When a triangle has three sides whose squares are equal to the area of the triangle.
(b) When a triangle can be constructed with three unequal sides.
(c) When a triangle has a side whose square is the sum of the squares of the two legs.
(d) When a triangle does not have a side which can be considered a hypotenuse.
3. What were the proofs in Elements based on?
(a) Basic definitions.
(b) Novel notions.
(c) Ancient greek geometry.
(d) Lindeman's method.
4. What did Hippocrates do that advanced mathematical methods?
(a) He created a new ways to disprove theories.
(b) He proved that mathematics can be applied in a unlogical order.
(c) He demonstrated that geometry does not have to be based on previous knowledge.
(d) He built theorems based on sequencially more complex proofs.
5. How did Lindeman prove his conclusion?
(a) Lindeman proved that square roots are irrational numbers.
(b) Lindeman proved that some numbers are not constructable with only a compass and straight-edge.
(c) Lindeman proved that all numbers are constructable with a compass and ruler.
(d) Lindeman proved that some numbers are constructable without the use of a compass.
Short Answer Questions
1. What did Dunham consider extraordinary about the Elements?
2. What is the name for determining the area of an enclosed space by constructing a square of equivalent area?
3. "Straight lines in the same plane that will never meet if extended forever" is a definition of what?
4. Which of the following is an example of a postulate that must be accepted in Elements?
5. Which of the following becomes an important definition in mathematics that was first presented in Elements?
This section contains 396 words
(approx. 2 pages at 300 words per page)