Journey Through Genius: The Great Theorems of Mathematics Test | Mid-Book Test - Easy

William Dunham (mathematician)
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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?

(see the answer keys)

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