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This quiz consists of 5 multiple choice and 5 short answer questions through Heron's Formula for Triangular Area.

Multiple Choice Questions

1. What was the same about Apollonius and Erosthanes?
(a) They were both mathematicians.
(b) They both studied the Universe.
(c) They both calculated the circumference of the earth.
(d) They were both born in the same year.

2. Which words best describe how solid proofs were developed in Elements?
(a) Inverted scaffold.
(b) Axiomatic framework.
(c) Simple arguments.
(d) Programmed order.

3. What did Ferdinand Lindeman prove in 1882?
(a) It is impossible to find the square of a semicircle.
(b) That the square of a circle can not be found with a compass and a straight-edge.
(c) It is possible to find the square of a circle.
(d) That the square root of the hypotenuse of a right triangle can not be found.

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

5. What was true about Heron's theorem as described by Dunham?
(a) It was to determine the area of a circle by measuring a right triangle inside the circle.
(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 volume of a sphere without measuring the circumference.

Short Answer Questions

1. Which of the following was an important proposition given by Euclid's number theory?

2. Who acted as the gate keepers of knowledge?

3. Who was Eratosthanes?

4. What did Euclid do in his 48th proposition?

5. What was Hippocrates's great advance to mathematics?

(see the answer key)

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