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Name: _________________________ | Period: ___________________ |

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

## Multiple Choice Questions

**1. 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.

**2. What was known about pi, during Archimedes' time?**
**(a)** Nothing, the concept of pi was unknown. **(b)** That it could not be assigned a relationship between measurements in a circle. **(c)** That is was the relationship between the diameter and circumference of a circle. **(d)** That it was never the same number value for a given circle.

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

**4. How did Archimedes arrive at a number value for pi?**
**(a)** By proving that pi could not be a negative number. **(b)** By constructing multi-sided polygons inside and outside a circle and determining their perimeters. **(c)** By proving pi could not be equal to one. **(d)** By constructing successively smaller circles inside circles until he realized all of their ratios of diameter to area were equal.

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

**6. That properties of specific shapes were early Egyptians aware of?**
**(a)** Parallelograms. **(b)** Right triangles. **(c)** Irregular solids. **(d)** Pi and the diameter of a circle.

**7. Which was true of Euclid's number theory?**
**(a)** It was incorrect, as proved by Plato. **(b)** It has been proven too basic to be useful. **(c)** It has an impact on modern math. **(d)** It was proven to the true by Hippocrates.

**8. Who's method did Tartaglia's challenger use in the contest to solve cubic equations?**
**(a)** Pacioli's method. **(b)** del Ferro's method. **(c)** Cardano's method. **(d)** Fontana's method.

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

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

**11. Heron devised which of the following methods?**
**(a)** A way to determine the area of a triangle. **(b)** A way to determine the volume in a sphere. **(c)** A way to solve binomial equations. **(d)** A way to apply mathematics to public health.

**12. What were the proofs in Elements based on?**
**(a)** Novel notions. **(b)** Ancient greek geometry. **(c)** Lindeman's method. **(d)** Basic definitions.

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

**14. Which is one of the common notions presented in Elements?**
**(a)** "Things which are equal to the same thing are also equal to each other." **(b)** "Points with equal values can be connected with a line of equal value." **(c)** "Things with are equal have an inverse that is equal." **(d)** "The inverse of a line makes a circle."

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

## Short Answer Questions

**1.** What was Hippocrates's great advance to mathematics?

**2.** Which of the following was NOT true about Archimedes, according to Dunham?

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

**4.** What was the title of Cardano's book which contained the solution to the cubic?

**5.** Which of the following is INCORRECT, and not used in Archimedes proof of his theory?

This section contains 966 words(approx. 4 pages at 300 words per page) |