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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. 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 impossible to find the square of a semicircle.
(c) That the square root of the hypotenuse of a right triangle can not be found.
(d) It is possible to find the square of a circle.

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

3. How do we know about Hippocrates proofs and theorems?
(a) His books and publications.
(b) What we know is from references of later mathematicians.
(c) What is known from archived documents of his time.
(d) Mathematicians rewrote all of his proofs after his death,

4. Heron's work referred to the work of what other famous scholar?
(a) Euclid.
(b) Archimedes.
(c) Thales.
(d) Hippocrates.

5. Numbers whose divisor add up to itself, was considered which type of number according to Euclid?
(a) Nominal number.
(b) Composite number.
(c) Even number.
(d) Perfect number.

Short Answer Questions

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

2. Dunham showed that Heron's proof could also be used as which of the following?

3. Which of the following is true in modern math about twin primes?

4. That properties of specific shapes were early Egyptians aware of?

5. What was true about Hippocrates's proof?

(see the answer key)

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