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

Post a reply to this message

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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