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From Logarithms to Euler's Formula

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Tags: logarithm

In this article, I start with the idea of logarithms , which were created to make multiplication easier. I then introduce the idea of complex numbers, which were created to define the square root of negative 1. From these, a simple geometric derivation of Euler’s famous formula can be given.

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5.57 Overall score*

39 Rank

6 Votes

5 Comments

Comments

The article did a great job of transitioning from one idea to the next, with each steps feeling natural, with explainations for why thing are. Some negatives are some parts was worded weirdly and a bit confusingly. Whilst visuals are not necessary for a math article in some of THIS article could have benefited from it.

Really nice! Short, to the point, well explained with good examples. I really liked this. Great job.

3.8

I think the logarithms explanation could have been clearer, for example by explicitly mentioning “logarithms turn multiplication (hard) into addition (easy)” at the start, or by something along the lines of “calculating 512 * 128 is hard, but calculating 2^9 * 2^7 is easy if you happen to know what 2^16 is”. Also I am not convinced by “Students of computer science might find it just as easy to multiply powers of two” - powers of ten are easy because you just append zeros.

There also seemed to be very little connection between the part about logarithm tables and the part about Euler’s formula.

The explanations were in general clear though, and the prose was good.

5.1

Useful for describing logarithms, and complex number, but the final reach to Euler’s Formula felt like a jump. Also, the imaginary number’s definition is i^2=-1, rather than sqrt(-1), since there are always 2 solutions for sqrt() and creates ambiguity (even though picking either one as ‘i’ doesn’t change the results much).

4.8

A nice, short, somewhat interactive article on logarithms. This was a pleasant read, teaching me something I had thought of, but never really explored. It ends in a nice crescendo with Euler’s formula and its connection to logarithms. While this subject is interesting, it has a relatively small target audience.