Journey Through Genius: The Great Theorems of Mathematics Test | Mid-Book Test - Easy

William Dunham (mathematician)
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This test consists of 15 multiple choice questions and 5 short answer questions.

Multiple Choice Questions

1. Which city was the center of thinking and learning in Third century BC?
(a) Rome.
(b) Athens.
(c) Olympia.
(d) Alexandria.

2. How many definitions were stated in Elements?
(a) Twenty-three.
(b) Five.
(c) Thirty.
(d) Eighteen.

3. Who asked Tartaglia for his solution to cubic equations?
(a) Cardano.
(b) Fior,
(c) Pacioli.
(d) Fontana.

4. What did Plato use his inspiration from Euclid for?
(a) To construct his theory on the shape of the Universe.
(b) To create a new theorem of algebra.
(c) To classify geometric shapes by their complexity.
(d) To prove Euclid's number theory was incorrect.

5. Which of the following was NOT one of the basic definitions in Elements?
(a) Line.
(b) Parabola.
(c) Right angles.
(d) Straight Line.

6. In Elements, how many postulates must be accepted as given?
(a) Twelve,
(b) Twenty-two.
(c) Eighteen.
(d) Five.

7. Who was the first of ancient philosophers to consider why geometric properties existed?
(a) Pythagoras.
(b) Thales.
(c) Aristotle.
(d) Hippocrates.

8. 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 parallel lines.
(d) Euclid's postulate on creating an arc.

9. What was the bases of Hippocrates's proof ?
(a) Properties of squares and cubes.
(b) Properties of area to volume measurements.
(c) Properties of triangles and semicircles.
(d) Properties of points and lines.

10. In what time period did mathematicians find a solution to cubic equations?
(a) Seventeeth century.
(b) Fifteen century.
(c) Twentieth century.
(d) Thirteenth century.

11. 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,

12. Who was the author of the book Elements?
(a) Einstein.
(b) Hippocrates.
(c) Euclid.
(d) Lindemann.

13. What did Euclid do in his 48th proposition?
(a) Euclid proved the Pythagorean Theorem.
(b) Euclid proved the converse of the Pythagorean Theorem.
(c) Euclid demonstrated how to use the Pythagorean Theorem.
(d) Euclid demonstrated the faults of the Pythagorean Theorem.

14. Which of the following was an important proposition given by Euclid's number theory?
(a) Any even number is divisible by 3.
(b) Any composite number is divisible by some prime number.
(c) Numbers from one to ten are only divisible by composite numbers.
(d) Any perfect number is divisible by some composite number.

15. What was known about pi, during Archimedes' time?
(a) That it could not be assigned a relationship between measurements in a circle.
(b) That it was never the same number value for a given circle.
(c) Nothing, the concept of pi was unknown.
(d) That is was the relationship between the diameter and circumference of a circle.

Short Answer Questions

1. What were the proofs in Elements based on?

2. Which is a geometric concept that humans have been aware of since the dawn of agriculture?

3. What was Hippocrates famous for?

4. Which of the following best describes Archimedes as discussed by Dunham?

5. Heron devised which of the following methods?

(see the answer keys)

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