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

Multiple Choice Questions

1. Who was Heron?
(a) A philosopher from Greece.
(b) A physician from the far East.
(c) A politician from Rome.
(d) A matematician from Alexanderia.

2. What did Archimedes manage to prove using Euclid's ideas?
(a) That the relationship of area to circumference is really the same as the relationship of radius to diameter.
(b) That the square of a diameter is equal to pi.
(c) That the area of a circle and the square of its diameter is really the same as the relationship of diameter to circumference.
(d) That the value of pi is proportional to the area of the circle.

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

4. Which of the following was NOT one of Gauss' discoveries?
(a) That angles in a triangles can not add up to more than 180 degrees.
(b) "Non-euclidean" geometry.
(c) That under Euclid's definition parallel lines can intersect.
(d) That there is no apparent contraction to the assumption that the sum of angles in a triangle can have fewer than 180 degrees.

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

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

7. What did Apollonius work with in mathematics?
(a) He worked on conics.
(b) He discovered the algrebraic equation.
(c) He worked on advanced algebra.
(d) He develped a way to measure the volume of a sphere.

8. Numbers whose divisor add up to itself, was considered which type of number according to Euclid?
(a) Even number.
(b) Nominal number.
(c) Perfect number.
(d) Composite number.

9. What is true about prime numbers?
(a) That for every group of prime numbers, there exists at least one more prime.
(b) Prime numbers can not exist in a finite series.
(c) Prime numbers can never be an odd number.
(d) Prime numbers are not divisible by other numbers.

10. Who was del Ferro's student?
(a) Niccolo Fontana.
(b) Luca Pacioli.
(c) Gerolamo Cardano.
(d) Antonio Fior.

11. According to Euclid, when is a triangle a right triangle?
(a) When a triangle does not have a side which can be considered a hypotenuse.
(b) When a triangle has a side whose square is the sum of the squares of the two legs.
(c) When a triangle has three sides whose squares are equal to the area of the triangle.
(d) When a triangle can be constructed with three unequal sides.

12. After Hippocrates, what shape did the Greeks attempt to square without success?
(a) Circle.
(b) Parallelogram.
(c) Pentagon.
(d) Hemisphere.

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

14. Which is a geometric concept that humans have been aware of since the dawn of agriculture?
(a) Area.
(b) Gravity.
(c) Metric system.
(d) Volume.

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

Short Answer Questions

1. What was known about pi, during Archimedes' time?

2. What did Dunham consider as Archimedes's "masterpiece"?

3. Which of the following could NOT be included as a step in Euclid's great theorem?

4. Who was the first of ancient philosophers to consider why geometric properties existed?

5. What do we know in modern times about Heron?

(see the answer keys)

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