Friday, January 21, 2011

Euler QQC

Quote: "It was through his work that the symbols e, π, and i (=sqrt(-1)) became common currency for all mathematicians, and it was he who linked them together in the astonishing relation e^(πi) = -1. This is merely a special case (put θ=π) of his famous formula e^(i θ) = cosθ+ i sinθ, which connects the exponential and trigonometric functions and is absolutely indispensable in higher analysis. Among his other contributions to standard mathematical notation were sin x, cos x, the use of f(x) for an unspecified function, and the use of Σ for summation....
Question: Is there anything that Euler didn't do? (other than not discover calculus)
Comment: I think that this is pretty amazing, the type of formulas and notations that he impressed upon the world of mathematics. Since we all use these notations in math class, I think Euler is a pretty relevant person. I was especially surprised by the fact that e raised to the power of i times pi equals -1, since this seems to defy the logic of an imaginary number. I don't know what the specific ramifications of this equation are, but they seem to suggest that i is a number that has a comprehensible value (other than sqrt(-1)). All this and 13 children, too! I am surprised that anybody could get anything done with 13 kids running around, even if they were very-well behaved. I was a little disappointed, however, when I read that the bridges of Konigsberg problem really was unsolvable.

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