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A Dictionary of Real Numbers online?

Posted 10 years ago
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I have a book, A Dictionary of Real Numbers, by Borwein and Borwein. If you're not familiar with it, it's a list of numbers that are the result of a limited number of operations on a limited number of numbers. The numbers printed are eight digits after the decimal point, truncated, not rounded. For example, if I come up with -2.403441 as the result of some calculations, I look in the book and find 40344144, and the book shows it came from 3Sqrt[2]/4-2Sqrt[3]. Of course this isn't a mathematical proof that the number I calculated is equal to 3Sqrt[2]/4-2Sqrt[3], but it does suggest a direction I might want to go if I do try to prove it.

Is there anything like this online?
POSTED BY: Howard Wilk
5 Replies
Posted 10 years ago
Thank you all. I put together all the pages (some related to others).

For trying to find some symbolic form for a number you encounter or calculate:
http://www.wolframalpha.com/
http://mrob.com/pub/ries/index.html
http://oldweb.cecm.sfu.ca/projects/ISC/
http://oldweb.cecm.sfu.ca/projects/ISC/ISCmain.html
http://isc.carma.newcastle.edu.au/

For trying to identify integer sequences:
http://oeis.org/
POSTED BY: Howard Wilk
In Mathematica you can just
RootApproximant[0.403441, 2]


And in Wolfram|Alpha type: 0.403441 closed form

POSTED BY: Sam Carrettie
I wrote an answer, but then my internet connection got interrupted and I lost it.  Instead of rewriting it, I'm just going to post the relevant links:

This is for Mathematica:

http://mathematica.stackexchange.com/questions/16/can-mathematica-propose-an-exact-value-based-on-an-approximate-one/12

These do what you asked:

http://oldweb.cecm.sfu.ca/projects/ISC/
http://isc.carma.newcastle.edu.au/

This is for integer sequences, but you'll find answers to similar questions here as well:

http://oeis.org/
POSTED BY: Szabolcs Horvát
Posted 10 years ago
Thank you. This is useful, as is the answer I got when I posted under another discussion title, http://oldweb.cecm.sfu.ca/projects/ISC/ISCmain.html
POSTED BY: Howard Wilk
Wolfram Alpha can (sometimes) guess possible closed forms. There are also other specialized sites, here is one that identifies the example correctly

http://mrob.com/pub/ries/ries.php?target=-2.4034414433579333.
POSTED BY: Ilian Gachevski
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