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This quiz consists of 5 multiple choice and 5 short answer questions through Heron's Formula for Triangular Area.

Multiple Choice Questions

1. According to Euclid, when is a triangle a right triangle?
(a) When a triangle has three sides whose squares are equal to the area of the triangle.
(b) When a triangle does not have a side which can be considered a hypotenuse.
(c) When a triangle has a side whose square is the sum of the squares of the two legs.
(d) When a triangle can be constructed with three unequal sides.

2. What did Plato use his inspiration from Euclid for?
(a) To prove Euclid's number theory was incorrect.
(b) To classify geometric shapes by their complexity.
(c) To create a new theorem of algebra.
(d) To construct his theory on the shape of the Universe.

3. What do we know in modern times about Heron?
(a) We know he was a teacher and philosopher but much of his work has been lost.
(b) We know he lived in Rome.
(c) We know he was an influencial scholar, but we don't know who his students were.
(d) We know very little, but much of his work survives.

4. What is the name for determining the area of an enclosed space by constructing a square of equivalent area?
(a) Square root.
(b) Triangulation.
(c) Cubation.
(d) Quadrature.

5. Which of the following is an example of a postulate that must be accepted in Elements?
(a) It is possible to draw an arc with any three points.
(b) It is possible to draw a circle that contains no lines.
(c) It is possible to draw a straight line between an infinite number of points.
(d) It is possible to connect any two points with a line and make a circle.

Short Answer Questions

1. Which of the following could NOT be included as a step in Euclid's great theorem?

2. According to Dunham, who was most able to collect knowledge from around the globe?

3. Which of the following was an important proposition given by Euclid's number theory?

4. Which is one of the common notions presented in Elements?

5. What was true about Heron's theorem as described by Dunham?

(see the answer key)

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