Exercise Set 1.1
1. The word geometry comes from which Greek word and what is the breakdown of that word and its
meaning?
2. From which action is the word geometry derived?
3. What is the Pythagorean triple? Give three examples.
4. Who was the first person that tried to use deductive reasoning in mathematics rather than trial and
error to prove mathematics statements? Also, include the theorem in his name.
5. Name the four subjects into which Pythagoreans divided mathematics.
6. Name the subjects in the trivium.
7. What subjects comprise the Artes Liberals (Liberal Arts)?
8. What is the earliest known example of the Golden Ratio in architecture?
9. Who is known to have coined the words "mathematics" and "philosophy"?
10. What is π? What was the value of π for Babylonians, ancient Chinese, Egyptians, and Romans?
11. Who was the great ancient Greek mathematician who completed a textbook in Geometry? Also, name
the textbook, the number of volumes, and the place where he worked.
12. To what does the Platonic school refer?
13. What are the five axioms of Euclid’s geometry?
14. Name the mathematicians who discovered non-Euclidean geometry independently in the nineteenth
century. This discovery resulted from which part of Euclid’s geometry?
15. The following figure presents the method that Euclid used in his geometry book, Elements, in order
to prove the Pythagorean Theorem (see Figure 1.1.6). Write a short essay and explain this method in
order to convince someone that the Pythagorean Theorem is true (You need to start from the top left and
show that the gray area in all the steps is the same.)
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Figure 1.1.8
16. The following figure presents a method to prove the Pythagorean Theorem. The method is adapted
from the Chou pei suan ching book (see Figure 1.1.3). Write a short essay and explain this method in
order to convince someone that the Pythagorean Theorem is true.
a
c
c
a
b
b
Figure 1.1.9
17. The following figure presents a method to prove the Pythagorean Theorem based on a figure by
Hindu mathematician Bhaskara (1114-1185). His drawing came with a word, “Behold”. Write a short
essay and explain this method in order to convince someone that the Pythagorean Theorem is true.
2
c
b
a
c
a
b
Figure 1.1.10
18. The following figure presents another method for determining the area of a circle with radius
r. Consider that you know the circumference of a circle is equal to2 r and the area of a rectangle
is equal to its width times its length. Write a short essay and explain this method in order to convince
someone that the area of a circle is equal to r2.
Figure 1.1.11
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