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This quiz consists of 5 multiple choice and 5 short answer questions through Cardano and the Solution of the Cubic.
Multiple Choice Questions
1. Which of the following best describes Archimedes as discussed by Dunham?
(a) Mild-mannered researcher.
(b) Absent-minded genius.
(c) Loud and arrogant.
(d) Creative but stubborn.
2. After working on pi, what did Archimedes continue with in his study of mathematics?
(a) He studied the volume to surface area ratios of cubes.
(b) He studied the relationship of sine to cosine.
(c) He studied the relationship between ratios in triangles.
(d) He studied the volume and surface area of spheres, cones, and cylinders.
3. Which of the following was NOT true about Archimedes, according to Dunham?
(a) He died during the fall of Syracuse.
(b) His death was described as being by the hands of a Roman invader.
(c) Archimedes died because he refused to follow orders until he completed a math problem.
(d) He died as a soldier.
4. 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 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.
(c) The area of a triangle is one half the base times the height.
(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.
5. 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.
Short Answer Questions
1. Which of the following is true in modern math about twin primes?
2. What did the Pythagorean Theorem accomplish for mathematics?
3. How did Archimedes demonstrate his theory of pi?
4. Who was Eratosthanes?
5. Who asked Tartaglia for his solution to cubic equations?
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