Journey Through Genius: The Great Theorems of Mathematics Quiz | Eight Week Quiz C

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

2. Who was Eratosthanes?
(a) He was a teacher and philosopher.
(b) He was the chief librarian, and a mathematician.
(c) He was a mathematician, and leading doctor.
(d) He was the first to study political sciences.

3. What did Gauss set out to prove?
(a) That a circle can have less than 360 degrees.
(b) That the sum of the angles in a triangle is 180 degrees.
(c) That a right angle is always equal to 90 degrees.
(d) That Euclid's postulate on straight lines was incorrect.

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

5. What did Dunham claim about Archimedes's determination of a number value for pi?
(a) Archimedes's number was very good, considering he did not have a way to calculate square roots.
(b) Archimedes's number could have been better if he had understood Euclid's work better,
(c) Archimedes's number was perfectly correct.
(d) Archimedes's number was not very accurate, considering the technology of his time.

Short Answer Questions

1. What did Plato use his inspiration from Euclid for?

2. What did Heron's advances put into historical perspective for Dunham?

3. After working on pi, what did Archimedes continue with in his study of mathematics?

4. How did Archimedes arrive at a number value for pi?

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

(see the answer key)

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