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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?

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