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
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total possible outcomes of 5 coin flips
Now, the number of ways you can choose r objects from five objects, for different r, is given by the 6th row of Pascal's triangle, which is
Thus the total number of outcomes is 1+5+10+10+5+1 = 32. And, 5C4 = 5. So the probability that Pascal will be ahead 9 to 6 is 5/32 = 0.15625. That is, we expect that this will happen 15.625 percent of the time.
to Probability: Summary and Problems
to a Proof of the Pythagorean Theorem
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