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This quiz consists of 5 multiple choice and 5 short answer questions through A Gem from Isaac Newton.

## 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. What did Euclid state about pi in Elements?**
**(a)** The proportion of area to circumference is never equal. **(b)** There is a constant relationship between the area of a circle and the square of its diameter. **(c)** The proportion of diameter to area is never equal. **(d)** There is no relationship between the area of a circle and its circumference.

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

**4. Which of the following was NOT one of the things Dunham claimed was ingenious about Euclid's proof of the Pythagorean theorem?**
**(a)** Euclid stated that the diagonal hypotenuse of a right triangle is equal to the sums of the squares of the two legs. **(b)** Euclid used his own axioms and propositions to show relationships, **(c)** Euclid constructed squares on the sides of right triangles. **(d)** Euclid used propositions about similar angles and parallel lines.

**5. Which of the following best describes Archimedes as discussed by Dunham?**
**(a)** Creative but stubborn. **(b)** Loud and arrogant. **(c)** Absent-minded genius. **(d)** Mild-mannered researcher.

## Short Answer Questions

**1.** To how many decimal places did Newton determine the number for pi?

**2.** What is true about prime numbers?

**3.** Who wrote a treatise that supposed that cubic equations may be impossible to solve?

**4.** Numbers whose divisor add up to itself, was considered which type of number according to Euclid?

**5.** Exactly what limit is reached at a quartic equation?

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