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The Math Contest

Well, then, this was more popular than I expected. We have fifteen people. Just one more to make it a round sixteen. Anybody?
 
You may now send out the Pokémon as well as the commands you will be using for the first round of appeals. You have 14 days to do so. Appeals with scores greater than or equal to the median will proceed onto the next round.

Appeals will be made on a half-elliptical stage elevated one metre off the ground, with radii 6 metres deep and 10 metres wide. It is made of poplar, and may not be broken. The stage is backed by a curtain. You may play with both the curtain and the lighting. You may assume that most of the audience (and certainly all of the judges) appreciate and have an adequate understanding of the theorem that you decide to represent, and math in general.

Go!
 
Do I get to fiddle with the lighting mid-appeal, or can I only set a degree of illumination to begin the appeal with?

And likewise for the curtains; do I get to, say, start with them closed up but open them up after one or two moves?
 
It's not only the degree of illumination; there's the angle, places, colours, etc. But let's say that you get to start off with one setup, and change it once during your appeal. And let's say that you have one curtain to which you can do anything anytime. There'll be multiple layers of curtains in the back, but you get one, the one in front, to fiddle with. The one in the back is solid blue.
 
so, can we do something simple to the curtain, like fractions or percentages to it? (is all math allowed for it?)
 
so, can we do something simple to the curtain, like fractions or percentages to it? (is all math allowed for it?)

Whatever you want. But don't lose sight of what a contest is about. All of this should add to your Pokémon's appeal and not draw the audience's attention away from it.
 
This might seem a tad irrelevant, but, which side of the semi-ellipsis is facing the audience: the round one, or the straight one?
 
The round one. Also, from the point of the view of the audience, the stage is wider to the left and right (10 m each) than deep (6 m).
 
Question: for mathematical theories, can we use things that are more "science" than "math"? I'm thinking of things like the laws of thermodynamics, laws of gravity, electrical resistance laws, stuff like that. They all involve math in their applications, but are somewhat easier to illustrate via reactions and interactions, rather than just being math for math's sake.
 
Roll out, Sub-Zeroes.

Alright, as some of us know -- and as I was supposed to know, given that this was in my test the day this contest was posted -- ellipses consist of the locus of all points that are located so that their distance to each focus of the ellipse, added up, will bring up the same result. And if this doesn't count as a theorem, I can also bring up this equation:

(X-Xc)²:a² + (Y-Yc):b² = 1

Where X and Y are the coordinates of a given point, Xc and Yc are the coordinates of the ellipse's center, a is the major radius and b is the minor radius. Any point that obeys this equation is located within the border of the ellipse.

So, without further ado. In one such point, Sub-Zeroes, you will set up a few Toxic Spikes. But before that, the curtains will close; ideally, the audience won't know you put these there. After this, back away and stand on one of the ellipse's focuses (which, if necessary, I could mark with crayon or something like that).

Once you're in position, the curtain will throw open. Then, you will crawl in a straight line towards the Toxic Spikes, looking completely distracted. You will "accidentally" step on them. This will be harmless, given your typing, but you will pretend to feel sharp pain. You will Screech with pain, in fact. And then, you will Agility the hell away from those, in a straight line, until you reach the ellipse focus you didn't start from. The appeal ends with you just fearfully cowering back there.

An interesting effect of the theorem here is that, regardless of where the Toxic Spikes are set up, so as long as they are located in a point at the border of the stage, Sub-Zeroes will have to cover the same amount of distance in his appeal.

Toxic Spikes ~ Screech ~ Agility
 
I'll use Milkmaid, and I will use the following theorem:

If a line is tangent to a circle, it is perpendicular to the radius drawn to the point of tangency.

To demonstrate this, Milkmaid, first use Ice Beam, but in a circular shape. After that, use Brick Break in a straight line, right through the centre of the circle. Finally, use Brick Break, again in a straight line, but this time horizontally (from the audience's perspective), at the base of the circle, thus creating an Ice Beam circle with a tangent line and a radius running through it.

Ice Beam (circle) ~ Brick Break (to form the radius) ~ Brick Break (to form the tangent)
 
Question: for mathematical theories, can we use things that are more "science" than "math"? I'm thinking of things like the laws of thermodynamics, laws of gravity, electrical resistance laws, stuff like that. They all involve math in their applications, but are somewhat easier to illustrate via reactions and interactions, rather than just being math for math's sake.

Urf. I'm going to go ahead and say no, for the moment. Sorry :(
 
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