Print

Please login or register.
1 Hour 1 Day 1 Week 1 Month Forever
Login with username, password and session length

[ToonyMan]

What's 5+9 again.

[Grek]

Well, that just means that we have to state that a^-2=t instead of a=0. That's the only one that's not continuous on its domain.

No, every single-valued function is continuous.

...you know what I mean!

[Vector]

Actually, I didn't ^_^;;

Sorry for the misunderstanding, whatever it was.

[Ochita]

What's 5+9 again.

quatorze.

[Grek]

Actually, I didn't ^_^;;

Sorry for the misunderstanding, whatever it was.

a=0 is the only one that results in rocks getting teleported around.

[Heron TSG]

Besides, making the rocks follow the curve instead of teleporting lets you do crazy stuff like avoiding obstacles via exponential functions. Trig, too, if you're trying to path through a sidewinder snake's track.

[MaximumZero]

Or make fancy bullet hell patterns.

With Vector's brainpower and math skillz, I wonder how many knives she could juggle?

[Virex]

There is a little problem with your system. Take the following spell:


theta = 0
phi = 0
da/dt = max of what you can exert.


Now consider the result of using this to launch a pebble towards a city 50 km away...
Edit: I had dr/dt while I obviously wasn't talking about speed but acceleration.

[Willfor]

That problem is not fixed via math, but through other means. Mages have a mortality rate of 76% before graduation, coupled with the fact that this is actually one of the weaker disciplines they have at their command. And most cities have at least one mage at their disposal who has been graduated for at least ten years, and those usually put considerable effort into counterspelling. This system might be a little broken, but it is not the most broken of them. Mages are to countries on that particular world as nuclear weapons are to countries on ours, and there are no anti-proliferation treaties.

Aside: I had originally been thinking mostly about trigonometry functions when I first had the concept, but any time you expose an idea to math things escalate. It's nice to be able to see what people would do with an idea. And I am learning new things through it, so it's all good in my opinion.

[Grek]

Theoretical Math Question!

The following formula (the surveyor's formula) can be used to calculate the area of any polygon:
n-1
 Σ  (x_iy_i+1 - x_i+1y_i)/2
i=0

Does a generalization of this formula to the third or higher dimensions exist? If so, what is it?

[Darvi]

D'you mean surface or the volume of 3d objects(and whatever their higher dimensional equivalents are)?

[Grek]

Volume and hyper-volume. Surface area is just a matter of treating each face as a polygon, computing it seperately and then adding it all up.

[Darvi]

Bluh, I can only tell you the formula for rotated objects.

Google isn't cooperative either.

[Christes]

Theoretical Math Question!

The following formula (the surveyor's formula) can be used to calculate the area of any polygon:
n-1
 Σ  (x_iy_i+1 - x_i+1y_i)/2
i=0

Does a generalization of this formula to the third or higher dimensions exist? If so, what is it?

Probably yes, though you're going to have to be very careful about orientations.  If such a formula exists, it probably involves orienting each face and taking lots of determinants.

[Vector]

Mathematical object.

I figured it might be good for a laugh.