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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 can be constructed with three unequal sides.
(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 does not have a side which can be considered a hypotenuse.

2. Which shapes as described by Euclid, inspired the Greek philosopher Plato?
(a) Manifolds.
(b) Regular polyhedrons.
(c) Triangles.
(d) Spheres and cones.

3. What did Dunham consider as Archimedes's "masterpiece"?
(a) Archimedes' work on determining angular measurements.
(b) Archimedes' work on volume to surface area ratios.
(c) Archimedes' work on shperes, cones, and cylinders.
(d) Archimedes' work on determining a number value for pi.

4. Who was the first of ancient philosophers to consider why geometric properties existed?
(a) Thales.
(b) Hippocrates.
(c) Pythagoras.
(d) Aristotle.

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

Short Answer Questions

1. What was Eratosthanes most famous for?

2. What did Gauss set out to prove?

3. What were the proofs in Elements based on?

4. What did Plato use his inspiration from Euclid for?

5. Who was the author of the book Elements?

(see the answer key)

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