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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 most useful about finding the square of a shape, before Hippocrates?**
**(a)** It was useful in finding the area of oddly shaped pieces of land. **(b)** It was useful in finding the area of circles. **(c)** It was useful in determining the distance between two points. **(d)** It was useful in creating simple elevation maps,

**2. Where was the modern number system developed?**
**(a)** In ancient Rome. **(b)** In the West. **(c)** In the East. **(d)** In ancient Alexanderia.

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

**4. After Hippocrates, what shape did the Greeks attempt to square without success?**
**(a)** Circle. **(b)** Hemisphere. **(c)** Parallelogram. **(d)** Pentagon.

**5. Which of the following best describes Cardano's character?**
**(a)** Arrogant. **(b)** Eccentric. **(c)** Religious. **(d)** Flirtacious.

**6. What did Dunham consider extraordinary about the Elements?**
**(a)** The content was totally unique. **(b)** How Hippocrates ordered the book. **(c)** The content was not based on previous authors' work. **(d)** How geometric proofs were presented.

**7. What was Hippocrates famous for?**
**(a)** His ability to construct circles without a compass. **(b)** His theorem on the quadrature of the lune. **(c)** His proof on right triangles. **(d)** His proof defining gravity.

**8. What does the Pythagorean Theorem state?**
**(a)** For any right triangle the diagonal side is equal to the sum of the legs. **(b)** For any triangle the sqaured sum of the legs is equal to half the hypotenuse. **(c)** For any right triangle the square of the diagonal side is equal to the sum of the squares of the two legs. **(d)** For any triangle the sum of the legs squared is equal to the length of the hypotenuse.

**9. Which of the following is INCORRECT, and not used in Archimedes proof of his theory?**
**(a)** Since the diameter of a circle is equal to the hypotenuse of the right triangle, the area of the triangle in his proof is 1/2 the radius times the circumference. **(b)** The area of a triangle is one half the base times the height. **(c)** Since the circumference can also be expressed as twice the radius multiplied by π, the area is 2πr²/2, or πr². **(d)** Since the base of the triangle is equal to the circumference and the height is the radius, the area of the triangle in his proof is 1/2 the radius times the circumference.

**10. As described by Archimedes, what is always true about he diameter of the circle?**
**(a)** It's never proportional to its circumference. **(b)** It's equal to pi. **(c)** It's equal to the square of the radius. **(d)** It's always proportional to its circumference.

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

**12. As described by Dunham, what did Archimedes demonstrate first in his proof on pi?**
**(a)** Area of a circle is equal to that of a right triangle that has one leg equal to the circle's radius and the other leg equal to the circle's circumference. **(b)** Area of a circle is equal to that of a right triangle that has one leg equal to the circle's radius and the other leg equal to the circle's diameter. **(c)** Area of a circle is equal to that of a right triangle that has one leg equal to the circle's diameter and the other leg equal to the circle's circumference. **(d)** Area of a circle is equal to that of a right triangle that has one leg equal to the circle's hypotenuse and the other leg equal to the circle's circumference.

**13. Which of the following can not be solved using algebra?**
**(a)** Quintic equation. **(b)** Quadratic equation. **(c)** Geometric equation. **(d)** Triangulation.

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

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

## Short Answer Questions

**1.** Besides being a mathematician, what else other work was Archimedes famous for?

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

**3.** Which of Euclid's postulates troubled many of the following generations of mathematicians?

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

**5.** Which of the following is false about the modern implications of Euclid's number theory?

This section contains 942 words(approx. 4 pages at 300 words per page) |