Shotgun (for the mathematically-minded)

REJECTED

2008-02-15 08:30:53

interesting

Paradox

2008-02-15 08:45:02

Kinda bored tonite huh Grape? LOL

Cynips

2008-02-15 10:50:37

Well, the REAL question is if, in old bug-ridden HL2DM, "the shot can be seen as a circular "slice" in space with points randomly distributed in it, representing the pellets in the shot"?

Cynips

2008-02-15 14:32:27

But won't it be exactly proportionate to an inverse square, no matter what the distribution of pellets is? Since it's the area of the target that decreases, not the projectiles you shoot.

cyber_clash

2008-02-15 21:03:38

I dub this another WTF are they talking about? thread

Keeper

2008-02-15 21:46:27

provided that B falls wholly within the circular area A containing the pellets.

As the effectiveness of the gun can be taken to be the proportion of pellets hitting the target, this demonstrates the inverse-square relationship between effectiveness and distance.

The smaller the object and/or the greater the distance away, this goes towards 0. So I think the generalization of it being inversely proportional is flawed.
I also concur with the point Cynips made, except it's the effective area of the target that decreases.

the_big_cheese

2008-02-15 23:40:34

This is assuming that B is perpendicular to the barrel of the gun? Would it still apply if the target was angled?

Keeper

2008-02-15 23:48:26

No, B would be the effective area that can be "seen" by the area of the circle. You would change the total effective area based on angle, so it should hold true for all shots.

{Rx}Crowbar Ninja DJ Z3R0

2008-02-16 00:58:14

Math.
@___@;;;
:evil: :evil: :evil: :evil: :evil: :evil: :evil: :evil: :evil: :evil: :evil:

:evil:

My head hurts.

ninjins

2008-02-16 02:10:23

Damn.

Cynips

2008-02-16 02:34:03

Grape wrote:So the inverse-square relationship no longer holds if you consider arbitrary distributions. Only for the uniform distribution f(x) = 1 / A does it hold.

Ok, now I'm with you. It's over 20 years since I had any kind of math like that, so bear with me.

Paradox

2008-02-16 03:26:37

I cant deal with even looking at it in any detail. Did too much of that kind of thing for my Master's degree. It was statistics, but a lot of math nonetheless.