2009-04-27

e: The meaning of the base of natural logarithm's definition

Base of natural logarithm appears almost everywhere in mathematics. Many of the sciences also use this number. When I came Germany, I found it on the 10 DM note. 10DM note has a portrait of Gauss. I saw why Germany's science level is high when I found a graph of normal distribution on a 10 DM note. When children got allowance from their parents, they would ask ``what is this curve? who is this?'' Then the parents would answer ``This is Karl Friedrich Gauss. A great mathematician. This curve is called normal distribution. It represents....'' I'm not sure how accurate my imagination is. I think Euro is a good idea, but I missed Gauss on a note.

Famous transcendental numbers are e and π. It is well known how the π is defined (circumference/diameter), why e's definition is
was not on my high school text book.

I found a slide of this explanation and put the link here with the author's permission. Thanks a lot.

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