[VA] SRC#002- Almost integers and other beasties

[Valentin Albillo]

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Hi all, welcome to my SRC#002 - Almost integers and other beasties.

Here I'll show an assortment of the results I can get using my HP-71B IDENTIFY program version 2.0. The original version 1.0 was extensively discussed and demonstrated with examples galore in my article Boldly Going ... Identifying Constants, published more than 10 years ago. You can download it as a PDF document using this link:

Boldly Going ... Identifying Constants

Shortly after publishing it I expanded its already substantial capabilities with important additional features such as the ability to find Minimal Polynomials and other implicit expressions, which greatly increased the recognition of arbitrary constants, and further this version 2.0 can be used creatively to find interesting, uncanny expressions never before seen, like the following ones I found and which you might enjoy seeing and checking using your trusty HP calculator:

• if x = Ln(1+\(\pi\))               then  62x\(^2\)+123x =    300.000002
• if x = Sin e                 then  11x-9x\(^2\) =      2.9999227778868800
• if x = Sin 4                 then  5x(x-4)=      17.99979999
• if x = Sin 1 + Cos 2 + Tan 3 then  6\(^3\)x-x\(^2\) =       60.9999995
• if x = \(\frac{3}{7}\sqrt[3]{\frac{261}{\pi}}\)                 then  x\(^5\)-x =         21.0000000100
• if x = 1% of Acos\(\frac{-317}{664}\)         then  \(\sqrt{10}\)-x =       3.14159265358
• if x\(^X\)= \(\pi\)                     then  (x+6)(9x-x\(^3\)) = 80.999999999
• if x = Gamma \(\pi\)               then  38x\(^2\)-3x\(^3\) =     163.00000
  

• if x is the positive root of .7x\(^2\)-6x-236 = 0, then Ln x = 3.14159265
  

Go ahead, check them, and I'd love to see any and all comments you would have on the matter, as well as your own uncanny expressions of a similar nature (Gerson, I'm looking at you ), please post your very best, original ones discovered by you (no 3rd-party ones harvested on the Internet, please) as replies in this thread.

Regards.
V.
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