# How to find the closed form of 10.3500574150076 with software/algorithm?

The number $10.3500574150076$ is a numeric approximation of $\log(2)^2+\pi^2$. It has a relatively simple form. But I have tried Maple's identify, ISC+, wolframalpha, and none of these could find a closed form of it. Is there anyway to find its closed form with algorithm/software?

My impression is that these software do a good job in detecting integer relationship between well-known constants, i.e., the form of like $3 \cdot \log(2)+1/2 \cdot \pi$. But they have trouble with detecting linear combinations of products like $\log(2)^2+\pi^2$ or $\pi\log(2)+\pi^2$.

• what is preventing me from writing my own custom software that always answers "it is $\log(2)^2+\pi^2$" ? – mercio Jun 5 '17 at 11:17
• WA do return some possible close form for the number. e.g. root of $68 x^3 - 745 x^2 + 483 x - 586$ near $x = 10.3501 \approx 10.35005741500756709898446$. – achille hui Jun 5 '17 at 11:38
• Related question at Mathematica.SE: Can Mathematica propose an exact value based on an approximate one? – Ruslan Jun 5 '17 at 14:35
• ISC, or similar programs, are search machines. They don't know anything about mathematics. They have combined known simple constants in myriad ways and now check their catalogue of numbers against your input. Of course you could set up another ISC with a tree depth that is even deeper, and maybe your number would show up then. – Christian Blatter Jun 5 '17 at 15:53
• @ablmf I see that you have created (integer-relation) tag. It might be useful to create also tag-wiki or at least tag-excerpt. It might help other users to use the tag correctly. (This is probably not a problem here, since the tag name seems to be descriptive enough.) Another reason is that the tags used on only one question are automatically deleted after certain time unless they have tag-wiki. – Martin Sleziak Jul 20 '17 at 9:37