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

William Dunham (mathematician)
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Mid-Book Test - Easy

Name: _________________________ Period: ___________________

This test consists of 15 multiple choice questions and 5 short answer questions.

Multiple Choice Questions

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

2. Which of the following best describes Cardano's character?
(a) Religious.
(b) Eccentric.
(c) Arrogant.
(d) Flirtacious.

3. After working on pi, what did Archimedes continue with in his study of mathematics?
(a) He studied the volume and surface area of spheres, cones, and cylinders.
(b) He studied the relationship of sine to cosine.
(c) He studied the relationship between ratios in triangles.
(d) He studied the volume to surface area ratios of cubes.

4. What instruments did the Greeks use to square a shape?
(a) A compass and a ruled straight-edge.
(b) A small grid.
(c) A pendulum.
(d) A sphere and ruler.

5. Which is one of the common notions presented in Elements?
(a) "Things which are equal to the same thing are also equal to each other."
(b) "Things with are equal have an inverse that is equal."
(c) "Points with equal values can be connected with a line of equal value."
(d) "The inverse of a line makes a circle."

6. Dunham showed that Heron's proof could also be used as which of the following?
(a) A proof of Euclid's number theory
(b) A proof of the Pythagorean Theorem.
(c) A proof of Hippocrates' squared areas.
(d) A proof of Archimedes' number theory.

7. What was the title of Cardano's book which contained the solution to the cubic?
(a) La Magnifica.
(b) Elements.
(c) Tarsisia.
(d) Ars Magna.

8. What name did Euclid give for numbers that could be divided by numbers other than themselves and one?
(a) Perfect numbers.
(b) Composite numbers.
(c) Discrete numbers.
(d) Even numbers.

9. Where was Archimedes born?
(a) Sicily.
(b) Olympia.
(c) Athens.
(d) Rome.

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

11. What was Euclid's definition of a prime number?
(a) Numbers which can only be divided by themselves and 1.
(b) Numbers which do not, and can not, contain a perfect number.
(c) Numbers which contain an infinite number of composite numbers.
(d) Numbers which are divisible by 2.

12. What did Dunham discuss for many pages in this chapter?
(a) Heron's religious beliefs-
(b) Heron's complicated proof.
(c) Heron's political tendancy.
(d) Heron's origins of the universe.

13. What was true about Heron's theorem as described by Dunham?
(a) It was to determine the volume of a sphere without measuring the circumference.
(b) It was to find the area of a triangle when only the length of the sides are known.
(c) It was to solve equations were only two varibles are known.
(d) It was to determine the area of a circle by measuring a right triangle inside the circle.

14. How did Lindeman prove his conclusion?
(a) Lindeman proved that square roots are irrational numbers.
(b) Lindeman proved that all numbers are constructable with a compass and ruler.
(c) Lindeman proved that some numbers are constructable without the use of a compass.
(d) Lindeman proved that some numbers are not constructable with only a compass and straight-edge.

15. As described by Dunham, what did Archimedes demonstrate first in his proof on pi?
(a) Area of a circle is equal to that of a right triangle that has one leg equal to the circle's hypotenuse and the other leg equal to the circle's circumference.
(b) Area of a circle is equal to that of a right triangle that has one leg equal to the circle's radius and the other leg equal to the circle's diameter.
(c) Area of a circle is equal to that of a right triangle that has one leg equal to the circle's radius and the other leg equal to the circle's circumference.
(d) Area of a circle is equal to that of a right triangle that has one leg equal to the circle's diameter and the other leg equal to the circle's circumference.

Short Answer Questions

1. Which of the following was NOT one of the basic definitions in Elements?

2. What allowed Cardano to justify publishing his book?

3. What were the proofs in Elements based on?

4. In Elements, how many postulates must be accepted as given?

5. What was Hippocrates famous for?

(see the answer keys)

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