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I want to know is there any function in Mathematica that suggests a simple irrational number combination for decimal one?

For example, if I give 0.804738 then I get (Sqrt[2] + 1)/3.

(EDIT)

Or consider 1.301290284568573 = π/(Sqrt[2] + 1).

It seems for the first example RootApproximant gives the correct answer but for the second its answer is not useful at all.

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    $\begingroup$ Have you seen RootApproximant? $\endgroup$
    – Michael E2
    Apr 10, 2021 at 2:31
  • $\begingroup$ Thank you! This works for this number. But I suggest that, for example, 0.8185261683292934 should be related to sqrt[2] with simple relation. $\endgroup$
    – Rasoul-Ghadimi
    Apr 10, 2021 at 2:36
  • $\begingroup$ I want a function that also predicts something like \pi, RootApproximant[[Pi]] is not that. $\endgroup$
    – Rasoul-Ghadimi
    Apr 10, 2021 at 3:30
  • $\begingroup$ Pi*RootApproximant[1.30129028/Pi] $\endgroup$
    – Bob Hanlon
    Apr 10, 2021 at 4:43
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    $\begingroup$ AskConstants is pretty amazing for this task. $\endgroup$
    – Roman
    Apr 10, 2021 at 6:56

2 Answers 2

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Try WolframAlpha

guess[x_]:=WolframAlpha["identify "<>ToString@x]

enter image description here

enter image description here

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    $\begingroup$ There's no need for coding here: you can get the same effect by pressing "=" twice and entering the number (or any W$\alpha$ query) directly. $\endgroup$
    – Roman
    Apr 10, 2021 at 8:12
  • $\begingroup$ Thank you. Yes, it works. $\endgroup$
    – Rasoul-Ghadimi
    Apr 11, 2021 at 1:56
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AskConstants is extremely powerful. For the second example it gives several results:

(-1 + Sqrt[2]) \[Pi]
\[Pi] Tanh[ArcCosh[3]/4]
\[Pi] Sqrt[ModularLambda[I Sqrt[2]]]
(1 + Sqrt[2]) \[Pi] Sqrt[ModularLambda[2 I]]
1/2 \[Pi] Tanh[ArcCoth[2 + Sqrt[2]] + ArcCsch[1]]

enter image description here

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  • $\begingroup$ While this package might be powerful, it is huge (!) and strangely organized. I read ` INSTALL.nb` and ` LOAD_ASKCONSTANTS.nb` twice, and still could not figure out how to install this thing. $\endgroup$
    – yarchik
    Apr 11, 2021 at 16:07

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