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) Alexandria.
(b) Olympia.
(c) Athens.
(d) Rome.

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

3. What did Hippocrates do that advanced mathematical methods?
(a) He proved that mathematics can be applied in a unlogical order.
(b) He demonstrated that geometry does not have to be based on previous knowledge.
(c) He created a new ways to disprove theories.
(d) He built theorems based on sequencially more complex proofs.

4. Exactly what limit is reached at a quartic equation?
(a) The limit of the Pythagorean Theorem.
(b) The limit of the decompressed cubic method.
(c) The limit of algebra.
(d) The limit of logical geometric proofs.

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

6. As described by Archimedes, what is always true about he diameter of the circle?
(a) It's equal to pi.
(b) It's always proportional to its circumference.
(c) It's never proportional to its circumference.
(d) It's equal to the square of the radius.

7. "Straight lines in the same plane that will never meet if extended forever" is a definition of what?
(a) 180 degree angle.
(b) Parallel lines.
(c) Circle.
(d) Intersection.

8. What was Eratosthanes most famous for?
(a) He showed that there are no even prime numbers.
(b) He showed that the Earth must be a sphere.
(c) He developed a way to navigate using logitude and latitude.
(d) He developed a simple way to find prime numbers and for determining the circumference of the Earth.

9. What do we know in modern times about Heron?
(a) We know he was an influencial scholar, but we don't know who his students were.
(b) We know he lived in Rome.
(c) We know he was a teacher and philosopher but much of his work has been lost.
(d) We know very little, but much of his work survives.

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

11. That properties of specific shapes were early Egyptians aware of?
(a) Pi and the diameter of a circle.
(b) Parallelograms.
(c) Right triangles.
(d) Irregular solids.

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

13. Who's method did Tartaglia's challenger use in the contest to solve cubic equations?
(a) del Ferro's method.
(b) Fontana's method.
(c) Pacioli's method.
(d) Cardano's method.

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

15. Which of the following is an example of a perfect number?
(a) 1.
(b) 20.
(c) 10.
(d) 6.

Short Answer Questions

1. How many sides did the pentadecagon have, as presented by Euclid?

2. Which of the following best describes Cardano's character?

3. What instruments did the Greeks use to square a shape?

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

5. In general, what did Euclid's number theory describe?

(see the answer keys)

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