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ThudnBlunder
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Testing my New Calculator
« on: Apr 7th, 2003, 3:29pm » |
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This evening, while testing my new calculator, I got 1 - epi*sqrt(163) = -262537412640768743.000000000000....
This means that [ln262537412640768743/pi]2 = 163 {an integer!!} 
What's going on here?? Shall I demand a refund?
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| « Last Edit: Apr 7th, 2003, 4:14pm by ThudnBlunder » |
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Icarus
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Re: Testing my New Calculator
« Reply #1 on: Apr 7th, 2003, 5:59pm » |
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Who Knows what evil lurks in the heart of numbers?
Ramanujan knows!
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"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
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KicksGenius
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Re: Testing my New Calculator
« Reply #2 on: Apr 8th, 2003, 3:32am » |
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Well....
I tested the first on my trusty TI 83+ and it proved true. However, for the second, I found the answer to be approx. 1518.227593. I'd suggest refunding in that case
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towr
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Re: Testing my New Calculator
« Reply #3 on: Apr 8th, 2003, 8:55am » |
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I get
262537412663781332 instead of 262537412640768743
And derive5 is usually a bit more precise than a calculator..
In any case, for the reverse you can take the last 10 or so digits as 0, and you still get 163. It is probably just rounded, and only by approximation 163.
It gives an interesting way to approximate pi(^2)..
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NickH
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Re: Testing my New Calculator
« Reply #4 on: Apr 8th, 2003, 9:12am » |
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I get epi*sqrt(163) ~ 262537412640768744, which is 744 + (26*3*5*23*29)3.
(Edited for clarity in response to wowbagger, below.)
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| « Last Edit: Apr 8th, 2003, 9:30am by NickH » |
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wowbagger
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Re: Testing my New Calculator
« Reply #5 on: Apr 8th, 2003, 9:23am » |
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on Apr 7th, 2003, 3:29pm, THUDandBLUNDER wrote:| This evening, while testing my new calculator, I got 1 - epi*sqrt(163) = -262537412640768743.000000000000.... |
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Using Maple 6, I get
-262537412640768742.999999999999250072597194...
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| « Last Edit: Apr 8th, 2003, 9:26am by wowbagger » |
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ThudnBlunder
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Re: Testing my New Calculator
« Reply #6 on: Apr 8th, 2003, 11:48am » |
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Quote:
I tested the first on my trusty TI 83+ and it proved true. However, for the second, I found the answer to be approx. 1518.227593. I'd suggest refunding in that case
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1518.227593...? Yes, I agree you should seek a refund. 
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| « Last Edit: Apr 8th, 2003, 11:59am by ThudnBlunder » |
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ThudnBlunder
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Re: Testing my New Calculator
« Reply #7 on: Apr 8th, 2003, 11:58am » |
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Quote:I get
262537412663781332 instead of 262537412640768743
And derive5 is usually a bit more precise than a calculator..
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....if used correctly. Perhaps it's time to upgrade to Maple or Mathematica.
For epi*sqrt(163) Mathematica 4.1 gives
262537412640768743.99999999999925007259719818568887935385633733699086270 75374103
782106479101186073129511813461860645041930838879497538640449057287144771 96814852
322432039116478291488642282720131178317065010452226878014448417703469694 63355707
681723887681000923706539519386506362757657888558223948114276912100830886 65110728
471062346581129818301245913283610006498266592365172617883086371078645219 55281542
...
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ThudnBlunder
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Re: Testing my New Calculator
« Reply #8 on: Apr 8th, 2003, 12:05pm » |
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Quote:I get epi*sqrt(163) ~ 262537412640768744, which is 744 + (26*3*5*23*29)3.
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I bet you use Pari GP, right?
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ThudnBlunder
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Re: Testing my New Calculator
« Reply #9 on: Apr 8th, 2003, 12:20pm » |
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Quote:Using Maple 6, I get
-262537412640768742.999999999999250072597194... |
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You are right. I should have used an integer or an expression greater than 262537412640768743 (instead of 1) in order to get the required .000000000000....
As Icarus (inevitably ) pointed out, this unusual-looking result was first discovered by the Indian mathematician, Ramanujan.
See also http://www.cacr.caltech.edu/~roy/upi/episqrtn.html
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| « Last Edit: Apr 8th, 2003, 6:07pm by ThudnBlunder » |
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towr
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Re: Testing my New Calculator
« Reply #10 on: Apr 8th, 2003, 12:41pm » |
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on Apr 8th, 2003, 11:58am, THUDandBLUNDER wrote:
....if used correctly. Perhaps it's time to upgrade to Maple or Mathematica. |
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If you're willing to pay for a licence
I'm just a poor student you know..
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NickH
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Re: Testing my New Calculator
« Reply #11 on: Apr 8th, 2003, 12:47pm » |
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Quote:| I bet you use Pari GP, right? |
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Windows calculator.
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Icarus
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Re: Testing my New Calculator
« Reply #12 on: Apr 8th, 2003, 4:41pm » |
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I had heard of this one before. Practically all that Ramanujan did is beyond me, but I did attend a conference on Theta Functions (which are deeply involved in his work) once. This result is just one of several "near integers" involving e and pi that he discovered. Some of them are considerably closer than this one (going hundreds of digits before veering away), but this one is the easiest to express.
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"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
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