|Name: _________________________||Period: ___________________|
This test consists of 5 multiple choice questions, 5 short answer questions, and 10 short essay questions.
Multiple Choice Questions
1. What was Eratosthanes most famous for?
(a) He showed that there are no even prime numbers.
(b) He developed a simple way to find prime numbers and for determining the circumference of the Earth.
(c) He developed a way to navigate using logitude and latitude.
(d) He showed that the Earth must be a sphere.
2. Which of the following is INCORRECT, and not used in Archimedes proof of his theory?
(a) Since the circumference can also be expressed as twice the radius multiplied by π, the area is 2πr²/2, or πr².
(b) 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.
(c) 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.
(d) The area of a triangle is one half the base times the height.
3. What did Dunham consider extraordinary about the Elements?
(a) How Hippocrates ordered the book.
(b) The content was totally unique.
(c) The content was not based on previous authors' work.
(d) How geometric proofs were presented.
4. What was the bases of Hippocrates's proof ?
(a) Properties of triangles and semicircles.
(b) Properties of points and lines.
(c) Properties of squares and cubes.
(d) Properties of area to volume measurements.
5. Which of the following is an example of a postulate that must be accepted in Elements?
(a) It is possible to connect any two points with a line and make a circle.
(b) It is possible to draw a straight line between an infinite number of points.
(c) It is possible to draw an arc with any three points.
(d) It is possible to draw a circle that contains no lines.
Short Answer Questions
1. Which of the following was NOT one of Gauss' discoveries?
2. When was the work of these early thinkers rediscovered again in history?
3. What did Plato use his inspiration from Euclid for?
4. Which of the following was one of Euclid's great theorems?
5. After Hippocrates, what shape did the Greeks attempt to square without success?
Short Essay Questions
1. Describe how Cardano eventually publishes the solution to cubic equations.
2. Describe Euclid's definition of prime numbers and the relationship he stated as existing between prime and composite numbers.
3. Who was Heron, and what is known about him today?
4. Explain what Neils Abel proved.
5. How many definitions were in Euclid's book? List some of the definitions he included.
6. Who was Luca Pacioli, and what controversy was sparked over his writings?
7. Explain what Archimedes went on to study after the circle, and what was Dunham's opinion of this work.
8. Explain why Archimedes finding a number value for pi was considered a great achievement according to Dunham.
9. Describe the ancient city Alexandria and name a few of its third century geniuses.
10. Explain when the knowledge of ancient scholars was rediscovered.
This section contains 965 words
(approx. 4 pages at 300 words per page)