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This test consists of 15 multiple choice questions and 5 short answer questions.
Multiple Choice Questions
1. What did Euclid do in his 48th proposition?
(a) Euclid demonstrated the faults of the Pythagorean Theorem.
(b) Euclid demonstrated how to use the Pythagorean Theorem.
(c) Euclid proved the Pythagorean Theorem.
(d) Euclid proved the converse of the Pythagorean Theorem.
2. What was the bases of Hippocrates's proof ?
(a) Properties of points and lines.
(b) Properties of area to volume measurements.
(c) Properties of triangles and semicircles.
(d) Properties of squares and cubes.
3. How many sides did the pentadecagon have, as presented by Euclid?
4. What did Archimedes manage to prove using Euclid's ideas?
(a) That the square of a diameter is equal to pi.
(b) That the value of pi is proportional to the area of the circle.
(c) That the relationship of area to circumference is really the same as the relationship of radius to diameter.
(d) That the area of a circle and the square of its diameter is really the same as the relationship of diameter to circumference.
5. After working on pi, what did Archimedes continue with in his study of mathematics?
(a) He studied the relationship between ratios in triangles.
(b) He studied the relationship of sine to cosine.
(c) He studied the volume and surface area of spheres, cones, and cylinders.
(d) He studied the volume to surface area ratios of cubes.
6. How many definitions were stated in Elements?
7. Which of Euclid's postulates troubled many of the following generations of mathematicians?
(a) Euclid's proof on right triangles.
(b) Euclid's postulate on right triangles.
(c) Euclid's postulate on creating an arc.
(d) Euclid's postulate on parallel lines.
8. Who challenged Tartaglia to a contest to solve cubic equations?
(c) del Ferro.
9. Which of the following is false about the modern implications of Euclid's number theory?
(a) Euclid gave a good idea for how to construct even perfect numbers.
(b) Great mathematicians continue to puzzle over some aspects of Euclid's number theory.
(c) Euclid's recipe for constructing even perfect numbers is incorrect.
(d) Whether there are no odd perfect numbers is still not known.
10. When was the work of these early thinkers rediscovered again in history?
(a) In the Elizabethian age.
(b) In the 18th century.
(c) In the Renaissance.
(d) In the 20th century.
11. Why did Cardano take an oath to secrecy?
(a) It was the only way to get Tartaglia's solution to cubic equations.
(b) It was to the only way to win the contest with Fior,
(c) It was the only way to get his book published.
(d) It was the only way he could become a priest,
12. What else, besides a solution to cubic equations, was in Cardano's book?
(a) An alegrabic solution to quintic equations,
(b) A solution to quartic equations.
(c) A proof of the Pythagorean Theorem.
(d) A suggested method to depress all complex geometry.
13. After Hippocrates, what shape did the Greeks attempt to square without success?
14. 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.
15. What instruments did the Greeks use to square a shape?
(a) A sphere and ruler.
(b) A compass and a ruled straight-edge.
(c) A pendulum.
(d) A small grid.
Short Answer Questions
1. What was Hippocrates famous for?
2. What did the Pythagorean Theorem accomplish for mathematics?
3. Which city was the center of thinking and learning in Third century BC?
4. Which of the following is an example of a perfect number?
5. What does the Pythagorean Theorem state?
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