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This quiz consists of 5 multiple choice and 5 short answer questions through Euclid and the Infinitude of Primes.
Multiple Choice Questions
1. According to Euclid, when is a triangle a right triangle?
(a) When a triangle does not have a side which can be considered a hypotenuse.
(b) When a triangle has a side whose square is the sum of the squares of the two legs.
(c) When a triangle has three sides whose squares are equal to the area of the triangle.
(d) When a triangle can be constructed with three unequal sides.
2. What was the bases of Hippocrates's proof ?
(a) Properties of triangles and semicircles.
(b) Properties of squares and cubes.
(c) Properties of area to volume measurements.
(d) Properties of points and lines.
3. Which of the following was an important proposition given by Euclid's number theory?
(a) Any perfect number is divisible by some composite number.
(b) Any composite number is divisible by some prime number.
(c) Numbers from one to ten are only divisible by composite numbers.
(d) Any even number is divisible by 3.
4. Which words best describe how solid proofs were developed in Elements?
(a) Axiomatic framework.
(b) Programmed order.
(c) Inverted scaffold.
(d) Simple arguments.
5. What does the Pythagorean Theorem state?
(a) For any triangle the sqaured sum of the legs is equal to half the hypotenuse.
(b) For any triangle the sum of the legs squared is equal to the length of the hypotenuse.
(c) For any right triangle the diagonal side is equal to the sum of the legs.
(d) For any right triangle the square of the diagonal side is equal to the sum of the squares of the two legs.
Short Answer Questions
1. In Elements, how many postulates must be accepted as given?
2. Which of the following becomes an important definition in mathematics that was first presented in Elements?
3. What did Ferdinand Lindeman prove in 1882?
4. What did Euclid do in his 48th proposition?
5. Numbers whose divisor add up to itself, was considered which type of number according to Euclid?
This section contains 392 words
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