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[malimbar04]

Yes it does make more sense mathematically. The angle of 1 pi radian is a straight line. That's the reason people invented them in the first place I think, because using degrees was a pain in the ass.

[Leafsnail]

It makes differentiating trig functions waaaaaaaaaaaay easier too.

[Willfor]

Math is most definitely not my strong suit. It never has been, but I've been getting better at it over the years. Unfortunately, I had the idea to make a magic system where certain parts require mages to either speak or heavily concentrate on functions. In battlefield conditions. Using only their minds.

So, naturally, since I can't do anything like this, I am wondering if it's humanly possible to do it. I am including some world notes, and an example. It might be better if you actually tried to do this in real life*, as I want to know how long it takes you to do it in real time. I may have to go back to the drawing board on this.

This challenge would be presented to 15 year-old:

Spoiler: Illustration (click to show/hide)

Spoiler: Challenge (click to show/hide)

You've been working with magic for 3 years already, and your teachers have been stressing math as it is deathly important for you to understand it. Stone magic was one of your first learned magics, but so far it's only been useful for releasing excess magical energy so it doesn't blast your nervous system to hell. Now you're learning to use it.

You control the x, y, z, and (to a limited degree) t of the stone via a formula of your own speaking. You must:
1. Speak a function to move it into orbiting position.
2. Speak a function that will provide an orbit for the stone.
2a. Pass the stone within a meter of magical focus that has been nailed into your wrist so that you can give it a boost of energy
3. Speak a function that will give the stone its final course.

Momentum is preserved between functions, but velocity is not. Until it passes by your magical focus it will only have as much force as if you were trying to pull it in a circle with a rope or string. The force can be altered to as much as five times the original force (with the knowledge you have anyway). You can end your magical control of the object at any time.

The point of the challenge is to hit a target that is blocked from direct attacks, and has to be hit by going around it.

The language used for magic by these mages has focused on allowing mathematical formulas to be spoken at a faster rate, but I need to know if anyone here can coherently turn math into a weapon. The example is a good start, I think, but there are a whole bunch of things I need to think about in this approach.

I am not sure if this is the right place for this, but it's technically math! And I do need help with it.

* By "in real life", I mean looking at objects and trying to figure out how you would do the same thing to them as in this example. I'm fairly certain my magic system has not penetrated reality yet, and if it did I would be so screwed. You have no idea.

[Vector]

Are we allowed to use different coordinate systems, or do we have to use cartesian?  Are we allowed to use multivalued functions?  Are we allowed to define the zero-point of the system?  Do we always know the position of the stone at a given moment?  Must we consider gravity?

I could probably do this fairly easily after a few days of practice and study, especially if I had somewhere to duck behind.

[Willfor]

Are we allowed to use different coordinate systems, or do we have to use cartesian?  Are we allowed to use multivalued functions?

The coordinates are only there for some kind of earth-standard. I'm still trying to figure out what kind of system they would use in this particular world. And yes, you're allowed to use multivalued ones as long as you can say them. Actually, the "as long as you can say it within five to ten seconds" rule* will work wonders here. You don't even have to make sense to other people, you just have to be able to understand what you mean.

Zero has to be declared at the start relative to your position and can't be changed until you don't have anything under your control. Gravity is nonexistent when you have control of the object, but comes back into play as soon as you let it go.

*Per function. Though faster is better for the purposes of not dying in the middle of it.

[Vector]

5-10 seconds is more than enough, especially if I'm allowed to just speak equations and can use wildcard variables for the opponent's position.

For example, for a spherical orbit at arm's length from my body, in spherical coordinates, in yards, I'd say:

rho = 1
phi = x
theta = x

x in R

(Sounds like "rho1 phix thetax x real," which takes about a second and a half.  If I need to set the coordinate system, I'd add "spherical" in front)

Or for a circle at height n, I'd use cylindrical coordinates:

Cylindrical
r = 1
h = n
theta = x
x in R

We say "x in R" so that the stone will keep moving forever, but we can specify an angle if we want it to stop at a particular time for throwing.

At that point, let's say it's at coordinates (x, y, z).

Then we use the parametrized equations of a line to get it to the target (x', y', z').

If we don't have to use specific, concrete coordinates, then this entire process really lends itself to a couple of seconds memorizing the "spells" in question.  If we do have to be specific, then there'd be probably 30 seconds of computation (as a lot of this is basically easy subtraction and trig problems) between spells.

[Willfor]

To be included in a locational variable in this form of magic it has to have a mass of about 250kg . So I guess spells against bigger animals would be very easy to work with, whereas spells of this sort would be quite a bit harder against smaller targets?

Though I'm sure after about one or so years of this kind of thing, a person would have a relatively good idea of what they wanted to do.

[Vector]

Well, again, it'd just be three very, very easy subtractions to launch the thing in a straight line to whatever point you guessed you wanted it at, and if you timed it correctly you'd have the stone hitting the desired orbital position at the same time as you finished the computation.

EDIT: Actually, the people doing this would probably learn very, very quickly not to stand between a mage and a heavy object, because they'd pretty much be insta-dead (since all you need is a point on the trajectory to compute the equation of the line, and there's no real reason to say "okay, stop right where that person is, dagger")

[Willfor]

I feel greatly educated. I'm glad I decided to get help with this. :3

[MaximumZero]

Thank you. You've given Vector a way to kill us all with only her razor sharp mind. I hope you're proud.

[Tellemurius]

i got geology on my side PHYSICAL OBJECTS VS. DAMN NUMBERS

[Grek]

Ok, assuming polar coordinates and an origin at my center of mass;

Let 'd' represent the distance between me and the rock, 'a' represent the horizontal angle in radians and 'b' represent the vertical angle in radians between me and the rock.

Let's also set a=0° to mean directly in front of me and b=0° to mean parallel to the ground.

To make the rock approach me and then orbit, we simply state that:

b^-2=t=d^-2=a

This makes the rock rapidly close the distance towards me, move to be at chest level from me, and orbit me at a rate of 1 orbit per 6.5ish seconds. This also, incidentally, places the rock within a meter of me.

To launch, we first state that:

a=0

to set it directly in front of us, and then

d=500t

to launch it away from us at 500m/s. If we want to make it arc, then we just state that

a=sin(t)

instead of setting it equal to 0, making it follow a sinosodial path away from us, still at over 500m/s

[Vector]

Yeah, you'd probably better assume continuous functions for this, by the way.  No teleporting rocks.

[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.

[Vector]

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.