Go into the windows calculator and enter this:
((-1/2)!)^2
It had two surprises for me. First, I had thought factorial was only defined for nonnegative integers while the number itself is the second surprise.
ID:190372
 Jan 30 2003, 8:32 pm
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Jan 30 2003, 8:36 pm
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Hanns
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I speak for myself when I say, "What the hell do you mean by that?!"
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English wrote:
factorial ??? | |
Ah, go to the view menu then change it from standard to scientific mode.
You can enter it by typing it in this order: -1/2 enter n! (this key uses factorial on the current number) x^2 (squares the current number) If someone isn't familiar with factorial or the resulting number then this wouldn't really have any interest for them. It's kind of a math geek thing :p | |
English wrote:
Go into the windows calculator and enter this: Well the factorial operator was probably defined by some quikly diverging series or some other equation that uses trig functions. This is probably why the factorial is defined for a negative fractional amount and why you get PI as a result. | |
Heh, that is pretty interesting...
You're right, though... The Factorial of a negative fraction should be undefined...lol I'm no math whiz, so I'm going with Theodis's explanation as to why it works, and why you get that particular result...lol | |
The factorial function is only defined over the natural numbers, but there is a related function known as the gamma function that's defined over all real numbers. Gamma corresponds very closely with factorials... in fact, for any natural number n, n!=gamma(n+1). Since they're so closely related, a lot of calculators use gamma to find non-natural factorials, although they're not strictly "factorials".
If you're curious as to why the number you got was pi, take a look at how the gamma function is defined. This site: http://www.rskey.org/gamma.htm is really good and has some nice information on it and how to compute it. -AbyssDragon | |
Very interesting! I wish matrices made more sense to me. The good part, though, is that if they ever do, I will then have enough knowledge to become Master of the Universe! :)
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Matrices are fairly simple, although thats probably becuase I just finished second year high school math(We use a stupid integrated math book where I live, and things get real mixed around), give it a few years, ill have forgotten all about them.
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Just out of curiosity, were you just typing random stuff into the calculator? That's pretty bored... :P
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