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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 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 a circle that contains no lines.
(c) It is possible to connect any two points with a line and make a circle.
(d) It is possible to draw an arc with any three points.
2. What did the Pythagorean Theorem accomplish for mathematics?
(a) The concept of constructing useful mathematics.
(b) The concept of providing a logical proof.
(c) The ability to find square roots.
(d) The ability to measure angles.
3. In Elements, how many postulates must be accepted as given?
4. What did Euclid do in his 48th proposition?
(a) Euclid proved the converse of the Pythagorean Theorem.
(b) Euclid demonstrated how to use the Pythagorean Theorem.
(c) Euclid demonstrated the faults of the Pythagorean Theorem.
(d) Euclid proved the Pythagorean Theorem.
5. How did Lindeman prove his conclusion?
(a) Lindeman proved that some numbers are not constructable with only a compass and straight-edge.
(b) Lindeman proved that some numbers are constructable without the use of a compass.
(c) Lindeman proved that square roots are irrational numbers.
(d) Lindeman proved that all numbers are constructable with a compass and ruler.
Short Answer Questions
1. What instruments did the Greeks use to square a shape?
2. Which words best describe how solid proofs were developed in Elements?
3. What did Ferdinand Lindeman prove in 1882?
4. What did Hippocrates do that advanced mathematical methods?
5. Which of the following becomes an important definition in mathematics that was first presented in Elements?
This section contains 375 words
(approx. 2 pages at 300 words per page)