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I know that there are two ways of solving problems in math: Analytically and Numerically.

When discussions like functions this distinction is clear to me. E.g. an analytical way to find the roots of a quadric function would be to use the quadratic formula while a numerical way to find the roots would be just trying so many numbers until you get the root ot using newtons method.

But what about problems of field other than analysis? For example when finding the length of an edge in a triangle we can do it exactly by e.g. using the phythagoran theorem or use approximations like drawing the triangle on paper. Would saying "I used the phythagoran to solve for this edge length analytically" be correct terminoligy wise?

If not what would be the word for it?

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  • I don't think these terms are always used precisely. I, personally, say that I have solved something numerically to specifically mean that I used an iterative method to approximate a solution. That is meant to distinguish between a solution which is expressed as a value of familiar functions. – lulu Jul 13 '22 at 18:28
  • We sometimes also talk about solving algebraically. – Thomas Andrews Jul 13 '22 at 18:32
  • This is a very limited way of thinking about math, though. There are lots of different types of problems in mathematics. There are lots of different types of answers. In discrete math, it often doesn't make sense to talk about "analytical" answers. For the existence or non-existence of certain type of finite combinatorial objects, the equivalent of "numeric" would be some exhaustive enumeration, I suppose. But there is also a distinction between constructive and non-constructive solutions. – Thomas Andrews Jul 13 '22 at 18:47
  • In any event, the distinction between "analytic" and "numeric" is a false dichotomy. – Thomas Andrews Jul 13 '22 at 18:49

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