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In the process of writing one of my scenes I arrived through tedious
trial and error at a particular constant with a value of 0.28867519
(plus an unknown number of additional decimals after the last place).
No matter to how many decimal places I manually determine the value, I'd
rather know for sure *where* the number came from and *what* it
represents. Is it a mathematical constant like 'e'? Is it the result of
some trigonometric expression?
My question is, in your travels in the land of mathematics, have you
seen this number before? Is it familiar to you? Have you arrived at this
value yourself in past operations, and how?
I would post the entire scene (probably the only *real* solution), but
it is fairly complex and I haven't received a lot of responses in my
previous threads.
Anyway, thanks for any assistence.
Mike
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It's likely to be the combination of two or more numbers that we may be
familiar with, but unrecognizable on its own. For instance, I might
recognize 'e', and I might recognize sqrt(3), but I wouldn't recognize e /
sqrt(3).
...assuming, of course, that no one else recognizes the number. =)
- Slime
[ http://www.slimeland.com/ ]
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Hey, that's a possible use of Wolfram alpha :-)
http://www.wolframalpha.com/input/?i=0.28867519
Seems fairly close to sqrt(3)/6, then. Not exactly but close enough.
--
Vincent
SharkD wrote:
> In the process of writing one of my scenes I arrived through tedious
> trial and error at a particular constant with a value of 0.28867519
> (plus an unknown number of additional decimals after the last place).
>
> No matter to how many decimal places I manually determine the value, I'd
> rather know for sure *where* the number came from and *what* it
> represents. Is it a mathematical constant like 'e'? Is it the result of
> some trigonometric expression?
>
> My question is, in your travels in the land of mathematics, have you
> seen this number before? Is it familiar to you? Have you arrived at this
> value yourself in past operations, and how?
>
> I would post the entire scene (probably the only *real* solution), but
> it is fairly complex and I haven't received a lot of responses in my
> previous threads.
>
> Anyway, thanks for any assistence.
>
> Mike
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SharkD wrote:
> In the process of writing one of my scenes I arrived through tedious
> trial and error at a particular constant with a value of 0.28867519
> (plus an unknown number of additional decimals after the last place).
>
> No matter to how many decimal places I manually determine the value, I'd
> rather know for sure *where* the number came from and *what* it
> represents. Is it a mathematical constant like 'e'? Is it the result of
> some trigonometric expression?
The expression for your number could be arbitrarily complex. I found at
least half a dozen simple expressions which give an answer *vaguely*
similar to the one above, but none of them are especially close to it.
To give you an example: The Fibonacci numbers. Each Fibonacci number is
the sum of the previous two numbers in the sequence. (The first two
numbers are 1 and 1.) If you divide a Fibonacci number by the one before
it, the sequence of numbers gradually approaches the number
1.618033988749894848204586834...
This number, it turns out, is equal to (1 + Sqrt(5))/2. (WTF?)
And if you think that's weird, try adding up 1/x^2 from x=1 to infinity.
The result just happens to be exactly pi^2 / 6.
The number you seek is probably a polynomial, polynomial root, or
trigonometric ratio thereof. There's a hell of a lot of potential
candidates to choose from. It's probably fundamentally impossible to
tell which one just by looking at the number itself. (Which, by the way,
you seem to have an aweful lot of digits for already...)
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Vincent Le Chevalier wrote:
> Hey, that's a possible use of Wolfram alpha :-)
>
> http://www.wolframalpha.com/input/?i=0.28867519
Heh. And to think I specifically didn't try that because I figured it
wouldn't tell me anything interesting...
So apparently your number is one nineth of the twenty vertex constant. :-P
> Seems fairly close to sqrt(3)/6, then. Not exactly but close enough.
Also 1/(2 * Sqrt(3)), cos(73°), log(4/3) and several others...
...but it's probably the root of some polynomial or something weird.
Without knowing what on earth this number is supposed to be for, it's
hard to say.
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On 11/17/2009 4:58 AM, Vincent Le Chevalier wrote:
> Hey, that's a possible use of Wolfram alpha :-)
>
> http://www.wolframalpha.com/input/?i=0.28867519
>
> Seems fairly close to sqrt(3)/6, then. Not exactly but close enough.
>
Wow! Good sleuthing! It seems Wolfram Alpha has quite a few esoteric uses.
Mike
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SharkD wrote:
> It seems Wolfram Alpha has quite a few esoteric uses.
As far as I know, *all* of Wolfram Alpha's uses are "quite esoteric". ;-)
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On 11/17/2009 5:18 AM, Invisible wrote:
>> Seems fairly close to sqrt(3)/6, then. Not exactly but close enough.
>
> Also 1/(2 * Sqrt(3)), cos(73°), log(4/3) and several others...
I'm looking for trigonometric functions in particular since I am
performing lots of vector operations.
tand(60)/6 is a good fit. I wonder if there are others.
Mike
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On 11/17/2009 7:41 AM, SharkD wrote:
> I'm looking for trigonometric functions in particular since I am
> performing lots of vector operations.
>
> tand(60)/6 is a good fit. I wonder if there are others.
>
> Mike
sind(60)/3
Mike
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On 11/17/2009 7:45 AM, SharkD wrote:
> sind(60)/3
>
> Mike
cosd(30)/3
Mike
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>> tand(60)/6 is a good fit. I wonder if there are others.
>
> sind(60)/3
Unless you can figure out *why* the value has a particular formula,
using a formula rather than a number isn't really gaining you anything.
(Although, frankly, you have a number with 8 decimal places. That's 8
orders of magnitude covered, which is already pretty accurate.)
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Invisible wrote:
> SharkD wrote:
>
>> It seems Wolfram Alpha has quite a few esoteric uses.
>
> As far as I know, *all* of Wolfram Alpha's uses are "quite esoteric". ;-)
+1
--
Darren New, San Diego CA, USA (PST)
I ordered stamps from Zazzle that read "Place Stamp Here".
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Invisible wrote:
>> Seems fairly close to sqrt(3)/6, then. Not exactly but close enough.
>
> Also 1/(2 * Sqrt(3))
You're aware that's the same thing as sqrt(3)/6, right?
> cos(73°), log(4/3)
Not unless he included way too many incorrect digits at the end.
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SharkD wrote:
> On 11/17/2009 7:45 AM, SharkD wrote:
>> sind(60)/3
>>
>> Mike
>
> cosd(30)/3
So sqrt(1/12) is it then!
As a side note, the only equation I was able to find which fit the last
digit of "9" which you included was:
2 - 1/(gamma[19/24]^2 * ln[ChampernowneNumber[10]] * zeta[3])
(formatted so you can type it into Wolfram Alpha)
Which clearly is highly unlikely to be what your number came from, so it
looks like Vincent's hypothesis is pretty surely the correct one.
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SharkD schrieb:
> On 11/17/2009 5:18 AM, Invisible wrote:
>>> Seems fairly close to sqrt(3)/6, then. Not exactly but close enough.
> I'm looking for trigonometric functions in particular since I am
> performing lots of vector operations.
>
> tand(60)/6 is a good fit. I wonder if there are others.
Note that tand(60) = sqrt(3).
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SharkD schrieb:
> On 11/17/2009 7:41 AM, SharkD wrote:
>> I'm looking for trigonometric functions in particular since I am
>> performing lots of vector operations.
>>
>> tand(60)/6 is a good fit. I wonder if there are others.
>>
>> Mike
>
> sind(60)/3
That would be the distance between the centroid of an equilateral
triangle and any of its edges.
Could that possibly be a fit?
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On 11/17/2009 10:42 PM, clipka wrote:
> SharkD schrieb:
>> On 11/17/2009 5:18 AM, Invisible wrote:
>>>> Seems fairly close to sqrt(3)/6, then. Not exactly but close enough.
>
>> I'm looking for trigonometric functions in particular since I am
>> performing lots of vector operations.
>>
>> tand(60)/6 is a good fit. I wonder if there are others.
>
> Note that tand(60) = sqrt(3).
No kidding! I *said* I was looking for _trigonometric_ functions, which
sqrt(3) isn't.
Anyway, I was able to determine where in the scene the value was coming
from, so the problem is resolved.
Mike
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0.28867519 seems perty close to Gamma/2 as well.
http://mathworld.wolfram.com/Euler-MascheroniConstant.html
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