Table of Contents:
The Bridges of Konigsberg
· Euler's Solution
· Solution, problem 1
· Solution, problem 2
· Solution, problem 4
· Solution, problem 5
The Value of Pi
· A Chronological Table of Values
· Squaring the Circle
Prime Numbers
· Finding Prime Numbers
Famous Paradoxes
· Zeno's Paradox
· Cantor's Infinities
· Cantor's Infinities, Page 2
The Problem of Points
· Pascal's Generalization
· Summary and Problems
· Solution, Problem 1
· Solution, Problem 2
Proof of the Pythagorean Theorem
| Historians estimate that by 2000 B.C. humans had noticed that the ratio of circumference to diameter was the same for all circles. This discovery hinged on the idea of proportion - in this case humans noticed that if you double the distance "across" a circle, then you double the distance "around" it. In today's algebraic notation this implied the formula |
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where Pi was constant. (It wasn't until 1706 that this notation, using the Greek letter
seen in the above equation - often written Pi and pronounced like the English 'pie' - was
introduced by William Jones).
The significance of this discovery is clear: Circles are everywhere - in the sun, the moon, the pupils of our eyes, the most basic religious rituals and the earliest man-made structures. Achieving a greater mathematical understanding of Pi would lead to scientific and technological advances that would further the development of civilization, as well as creating some very interesting problems in pure mathematics. But one problem remained - what is the numerical value of Pi?
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