Name: _________________________ | Period: ___________________ |
This quiz consists of 5 multiple choice and 5 short answer questions through A Sampler of Euler's Number Theory.
Multiple Choice Questions
1. What was most noticeable about Euler at a young age?
(a) He was very athletic.
(b) He had an aptitude for literature.
(c) He was not very quick with arithmatic.
(d) He had a remarkable memory.
2. What was described as true about the series 1 + 1/2 + 1/6 + 1/10 + 1/15 + 1/21?
(a) It's a convergent series of cubic numbers.
(b) It's a divergent series with a sum of 2.
(c) It's a convergent series of triangular numbers.
(d) It's a divergent series squared numbers.
3. What great theorem is presented by Dunham in this chapter?
(a) An improvement on Leibniz's caluclus as presented by Jakob Bernoulli.
(b) A theorem on infinite series published by Jakob Bernoulli.
(c) A theorem on series developed by Jakob and published by Johann Bernoulli.
(d) A theorem on finite series developed by Johann Bernoulli.
4. 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 diameter.
(b) 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.
(c) 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.
(d) 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.
5. Which of Euclid's postulates troubled many of the following generations of mathematicians?
(a) Euclid's postulate on parallel lines.
(b) Euclid's postulate on creating an arc.
(c) Euclid's proof on right triangles.
(d) Euclid's postulate on right triangles.
Short Answer Questions
1. What did Archimedes manage to prove using Euclid's ideas?
2. Who wrote a treatise that supposed that cubic equations may be impossible to solve?
3. Which of the following was an important proposition given by Euclid's number theory?
4. What range of values did Archimedes determine for pi?
5. That properties of specific shapes were early Egyptians aware of?
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