Suppose I draw a 'random' chord on the unit circle. What is the probability that the length of the chord exceeds the side length of an inscribed equilateral triangle?
Obviously there are many answers, but how many ways can you think of picking a chord 'uniformly' to give different probabilities?
Suppose I draw a 'random' chord on the unit circle. What is the probability that the length of the chord exceeds the side length of an inscribed equilateral triangle?
Obviously there are many answers, but how many ways can you think of picking a chord 'uniformly' to give different probabilities?
Lets see... at very small chord length, the side would be greater until some point where they become equal. Then side would be smaller until there is a straight line across the circle, or side = 0. This all seems familiar to the golden days of Mr. Calls plain and solid geometry proofs. I don't remember much of those days, truth told.
Probabilites? hmmm. Here is the part where I usually just play pin the tail on the donkey. <grimace> I have no clue as to the math of it.
intuitively, i think that the area inscribed up to equality of side to chord is probably the ratio of half of circles total area * pi?
Easy one
29 Feb '04 23:17
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