Recognizing numbers

Questions
1

Python’s sympy has a function called nsimplify that can do this:

>>> from sympy import *
>>> nsimplify(4.242640687119286)
3*sqrt(2)
>>> nsimplify(pi, tolerance=1e-7)
exp(141/895 + sqrt(780631)/895)

It finds closed form approximations to numbers. This looks like a lot of fun (and is potentially useful).
Original source: Recognizing numbers with SymPy nsimplify

So, can Mathematica do this?

Cheers,
Mike

2

Built in function

RootApproximant[4.242640687119286]
Out = 3*Sqrt[2]

works, and so does the Wolfram|Alpha query with quite a few results:

http://www.wolframalpha.com/input/?i=4.242640687119286

637×487 22.7 KB

Recent post at Wolfram Blog From Close to Perfect—A Triangle Problem just discussed this very issue.

Hope that helps.

3

Very nice. Thank you.

4

BTW the same function was used to recover some of the Ramanujan lost equations, as discussed in this latest Wolfram Blog**: After 100 Years, Ramanujan Gap Filled** . Below is the image from his “lost notebook” showing some incomplete equations. Click on the link or the image to read the full blog.

5

Hello Mike,

One of the very first posts on Mathematica.SE was on a similar topic:

http://mathematica.stackexchange.com/questions/16/can-mathematica-propose-an-exact-value-based-on-an-approximate-one

Be sure to look at all answers (not just highly voted ones), and follow the links. I asked a similar question on MathGroup a few years ago which also has interesting answers:

https://groups.google.com/d/msg/comp.soft-sys.math.mathematica/vq-MBdu51RI/lvNoiwHUPv8J

It was inspired by Maple’s identify() function.

6

Thanks for the replies everyone :slight_smile: