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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. Which of the following was NOT one of the things Dunham claimed was ingenious about Euclid's proof of the Pythagorean theorem?
(a) Euclid constructed squares on the sides of right triangles.
(b) Euclid stated that the diagonal hypotenuse of a right triangle is equal to the sums of the squares of the two legs.
(c) Euclid used propositions about similar angles and parallel lines.
(d) Euclid used his own axioms and propositions to show relationships,
2. What did Hippocrates do that advanced mathematical methods?
(a) He proved that mathematics can be applied in a unlogical order.
(b) He created a new ways to disprove theories.
(c) He built theorems based on sequencially more complex proofs.
(d) He demonstrated that geometry does not have to be based on previous knowledge.
3. Which of the following is an example of a postulate that must be accepted in Elements?
(a) It is possible to draw a straight line between an infinite number of points.
(b) It is possible to draw an arc with any three points.
(c) It is possible to draw a circle that contains no lines.
(d) It is possible to connect any two points with a line and make a circle.
4. How many definitions were stated in Elements?
5. How did Lindeman prove his conclusion?
(a) Lindeman proved that square roots are irrational numbers.
(b) Lindeman proved that some numbers are constructable without the use of a compass.
(c) Lindeman proved that all numbers are constructable with a compass and ruler.
(d) Lindeman proved that some numbers are not constructable with only a compass and straight-edge.
Short Answer Questions
1. Which is one of the common notions presented in Elements?
2. Which of the following was NOT one of Gauss' discoveries?
3. Which of the following becomes an important definition in mathematics that was first presented in Elements?
4. Who was the first of ancient philosophers to consider why geometric properties existed?
5. Which words best describe how solid proofs were developed in Elements?
This section contains 419 words
(approx. 2 pages at 300 words per page)