The Math Contest
Round 1
The general lighting was turned on. There were final preparations to the curtains, the stagelights, and the stage, to cater to the co-ordinators' extensive needs. When the judges, bulbasaur, Crazy Linoone, and Byrus, were confident that everything would work out, they gave the OK for the usher to let the audience in.
This wasn't a large audience, by any standard. Absent, from both audience and co-ordinators, was the head referee, who was present at most events. Of course, this wasn't surprising, given her recent "screw the calculus homework." And of course, there was a lack of children. All of these factors reduced the audience size to just a few rows of diehard contest-goers and math nerds.
When everyone was settled in, the judges, Byrus and Crazy Linoone, filed in, bowed/curtsied, and took their seats at the front. bulbasaur, the head judge, however, stood, walked up onto the centre of the stage, and started speaking.
"Welcome, ladies and gentlemen, Pokémon of indeterminate gender, and others. Welcome, to the Math Contest.
"Five thousand years ago, the Babylonians and the Mesopotamians started manipulating numbers. They started adding them together, subtracting one from another, and later multiplying and dividing them. They applied these to physical objects and space.
"Then, the Greeks gave birth to the first school of mathematics. They proved numerous theorems, applied them to many problems, and documented their knowledge. They passed on the tradition of mathematics and mathematical rigour to their descendants. Great Greek mathematicians include Pythagoras, whose theorem is perhaps the most famous in geometry; Euclid whose textbook
Elements is used to this day, and Archimedes, who proved, using an early form of calculus, an approximation for the value of
π.
"And then, mathematics fell into a decline. For over a thousand years, no significant mathematical results were made until Fibonacci brought the numerals we use today here. And it was another few centuries before another important development, the invention of logarithms, was made.
"Algebra was invented. The Cartesian plane was made. Complex numbers were formulated. The decimal system was standardized. But important as these are, equally important is what came after: two men, arriving independently at their conclusions, invented calculus. One was accused of plagiarism, but both Newton and Leibniz are equally important to the development of this important field of mathematics.
"And then, we arrive, in the 18th century, at the Age of Rigour in mathematics. In contrast to the previous century, we see a movement to carefully define and parametrize each aspect of mathematics, reducing them to a few basic axioms. Perhaps the most well-known of these mathematicians was Leonhard Euler, master of all trades, one of the most influential mathematicians of all time.
"Afterwards, mathematics started getting abstract. Vector spaces, set theory, and differential geometry are just a few of the highly theoretical concepts invented. And yet, they are omnipresent. We live in a vector space. Einstein's general relativity depends on differential geometry. And some mathematicians believe that the entire field of mathematics boils down to a few axioms in set theory. Undoubtedly, these very abstract concepts have very concrete applications in our everyday lives.
"And so, we arrive at present day, with its sets and its differentials and its moduli. In this contest, we will celebrate all those five thousand years, in the only way we Asberians can. Enjoy."
The Omskivar and Yuno
Definition of the Jerk: The third derivative of a function f, f''', is called the jerk of f.
The Omskivar emerged from behind the curtain, followed by his Staryu, Yuno, and made his way to the co-ordinator's box. Yuno continued walking across to the vertex of the stage. It then sped up, veered, and managed to run across the curve of the stage in a surprisingly short amount of time, trailing behind it two clones in the spotlights - which, as some were quick to notice, were of different typings. After having reached the other end of the stage, under the third limelight, it spread its points wide - here, the previously oblivious noticed the difference in types - and then Swaggered about smugly. What a jerk!
Judges’ Notes:
bulbasaur: To get the jerk, you have to differentiate three times, not twice. But I like this appeal and its play on words, even if it was groan-inducing. I think that the appeal could have been improved by having only one Staryu Swaggering - however, I understand that this is impossible with Double Team. Also, you may want to note that Camouflage will produce the same kind of clone if used in the same location - in this case, it’s Normal.
7.4
Byrus: Oh god... the math puns. I love it.
8.0
Crazy Linoone: While the third-derivative-equals-jerk pun is quite overused, the “differentiate” pun is pretty nice. This appeal is more punny than math-y, though. I don’t feel like there’s enough... well, math. Seeing that this is a math contest, I would’ve liked to see something with changing slopes or something. Using Camouflage + Double Team to make differently typed clones is pretty cool though!
4.0
Totodile and Ganymede
Mean Value Theorem: If a function f is continuous on [a,b] and differentiable on (a,b), then there exists a point c in (a,b) such that f'(c)=[f(b)-f(a)]/(b-a)
Now in the co-ordinator's box was Totodile, and on the left of the stage was Ganymede, her Ralts, facing to the right. On signal, he produced a blue ball of fire; it danced around, sometimes rising, sometimes falling, but always moving to the right. After it had made its way across the stage, it started to fade, but its after-image still was there. At that moment, not a moment sooner, not a moment later, did Ganymede swirl and face the audience, produce a Swift connecting the Will'O'Wisp's starting point with its current point, fire a beam of electricity parallel to the Swift but tangent to the Will'O'Wisp, then bow, all before the image of the flame was completely gone.
Judges’ Notes:
bulbasaur: This would have been so much better had you tinkered with the lighting. The flame, the beam, the Swift - it all came together nicely and logically. Not to mention that it looked cool - but it would have been better with some lighting effects. Still, nice job.
9.6
Byrus: Nice use of projectiles there. This looked flashy and got your point across great.
8.8
Crazy Linoone: That... is actually pretty cool, even though it’s only drawing out the math equation (albeit in a shiny, flashy manner). I love how you used Will’O’Wisp’s natural movements to make a curve, and the whole appeal is shiny and flashy while still able to get the point across clearly. Simple, but I like it even though I probably shouldn’t like it so much.
8.2
ole_schooler and Ace
Theorem: There exist multiple triangles with the same angle measures.
Next up on the stage was ole_schooler, and their Herdier, Ace. She first made two illusionary copies of herself, no problem at all for a Pokémon of her speed. When she was done, it was impossible to distinguish the real McCoy from the others. Ace then made sure the distances between them were equal, and thus the angles as well, then produced a line of thunder, almost extending to the Herdier each one faced. This formed an equilateral triangle.
Then, Ace and her clones started moving back from each other, making sure to keep their thunderbolt extended to just before the next Herdier, and to keep their distances proportional. When they could recede no longer, they held their position for the audience to see, before dropping the Thunderbolt.
Judges’ Notes:
bulbasaur: Well, I can’t really find a fault with this - it does what it’s supposed to and all that, but it just... doesn’t really appeal all that much to me :/ Sorry. For some reason, I imagine that it would appeal to me more if it the Thunderbolts were not sustained or you had used some different triangle.
7.0
Byrus: I was waiting for someone to make use of double team. This one flowed very well overall, and demonstrated the theorem quite neatly.
8.5
Crazy Linoone: This is pretty cool as well. The math shows up nicely, and you get the point across clearly, too. Using one extended Thunderbolt is sort of boring though...
7.3
Grass King and Ectoplasm
Theorem: The foci of an ellipse are two special points, F1 and F2, on the ellipse's major axis, and are equidistant from the centre point. The sum of the distances from any point P on the ellipse to those two foci is constant.
As the curtain drew back, it revealed Grass King in his box and, although the eye was not immediately drawn toward this, Ectoplasm, his Haunter, near the top of the stage. Without warning, two copies of him appeared to his left and right, each exactly 8 metres to the side of the real Ectoplasm. Then, the three Haunter each fired a Shadow Ball; the two on the side fired seemingly randomly, and the one in the centre fired straight to the center of the stage closest to the audience. That one exploded in a ball of darkness before the other two seemingly bounced off of the perimetre of the stage before heading directly to the other Haunter clone. The balls of energy hit their targets simultaneously and exploded on the curtain behind.
Judges’ Notes:
bulbasaur: I loved this one and how it was made. It was creatively performed, and illustrated the property you were showing well.
9.1
Byrus: Another good use of double team, but I think this one turned out a little messy.
7.0
Crazy Linoone: Pretty cool! You got the math across nicely and ended with an explosion. The shadow balls exploding in sync is nice.
7.6
RespectTheBlade and -273 C
Alternate Exterior Angles Theorem: When two parallel lines are cut by a transversal, the resulting alternate exterior angles are congruent.
Zero the Frosslass was sent upon the stage, hovering. When she determined that the audience was alert, she created a miniature snowstorm on the stage, suiting the holiday season. Those close to the front could see that the snow was somewhat less powdery than usual; most could see that the snow was surrounded by a faint purple aura that directed it into a shape. The spaces with an absence of snow formed three lines; two parallel and one traversal.
When Zero couldn't keep making it snow anymore, she lifted up a chunk of snow that formed one exterior angle and lifted it, via Psychic, to its alternate exterior angle. Matching them up, she bowed and was led off the stage by RTB.
Judges' Notes:
bulbasaur: It felt boring, but hey, I guess it showed the theorem, although I don't think it was very original.
7.2
Byrus:Not bad, but it didn't really bring anything new to the table. Repeating the same move also detracts from the appeal a bit.
7.0
Crazy Linoone: A solid appeal, but using the snow feels kind of messy.
6.9
Superbird and Quabble
Pythagorean theorem: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
The curtains opened to reveal a winged human and a
light cyan Frillish with a matchingly-coloured flowing robe. Quabble drew a deep breath, then exhaled with a breath of ice, drawing a right triangle on the floor with corresponding squares on its two legs. He then filled the squares with water - some members of the audience could swear they heard some music - and immediately took a mental hold of the two squares of water and combined them into one. He held it to the third side - and sure enough, it matched. Letting the water slowly drop, he took a bow before Superbird led him backstage.
Judges’ Notes:
bulbasaur: Everything from the dress to the choice of moves was perfect. It not only proved the theorem, but it also illustrated some math history as well.
10.0
Byrus: A pretty intricate appeal there, but it seemed to work out well.
7.8
Crazy Linoone: Drawing out math theorems is kind of taking the easy way out, but you made it into a pretty elegant appeal that demonstrates the math clearly. I love the effects of the squares of water combining to form a bigger square--it’s pretty clever to use water in that way.
7.0
Wargle and Androgynous Porygon
Theorem: The dihedral angle of an icosidodecahedron is given by θ=arccos(-√((5+2√5)/15))
The lights shut down gradually and completely (except for a few above emergency exits). For a long while, the audience could not see anything that was going on. Then, Androgynous Porygon's form became clear - the audience stained to count the number of sides, but some made an educated guess. To their surprise, some members of the audience saw their personal possessions near Androgynous Porygon highlighting an angle, before they got returned and the lights turned back on, and only then did the audience notice the curtain.
Judges’ Notes:
bulbasaur: I didn’t feel like you did much with the theorem; admittedly, there wasn’t much to do with it. The glowing effect was cool, but it didn’t make up for the fact that this was really shallow.
2.9
Byrus: I think Porygon is probably the perfect Pokémon for a contest like this, but I was a little underwhelmed here to be honest. Also, maybe it would have been better if you switched the order of flash and sharpen, so the audience could properly see the latter.
5.5
Crazy Linoone: The math’s not too clear with this one. Yes, there’s an equation written on the curtain, but the porygon could’ve morphed into any shape possible and we’d still end up with the same appeal. Fudging with the lightening is pretty cool, but generally the audience doesn’t like having their personal possessions taken from them.
5.0
Metallica Fanboy and Sub-Zeros
Definition of an ellipse: An ellipse consists of a 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. The general formula for an ellipse is given by (X-Xc)²:a² + (Y-Yc):b² = 1.
The curtains closed over the stage - whereas the previous curtains had all been at the back of the stage, this one closed over the front of the stage. A significant amount of time passed before they were opened again, revealing a Skorupi standing on a focus of the ellipse. She started walking, daydreaming, directly towards what the audience identified as a Toxic Spikes at the edge of the stage. Several members of the audience winced at what was about to happen. Indeed, quite an unpleasant sound was made when Sub-Zeros "accidentally" walked on them. With practiced agility, she sped to the other focus of the ellipse, and huddled there, shaking fearfully.
Judges’ Notes:
bulbasaur: Hrm, while this tried to tell a story, and was artistic, I guess, I felt that it didn’t really have a relationship with the mathematical result you were trying to illustrate.
5.8
Byrus: Nice use of toxic spikes there, and I'll admit that the image of a Skorupi scampering away fearfully is very amusing. A simple enough appeal that gets your point (ahem) across well.
7.2
Crazy Linoone: (Ow Toxic Spikes ow) Very interesting! Although the math isn’t really clearly presented, the plot is entertaining. Unfortunately for you, I’m weighing math quite heavily. If this were a normal contest, I would’ve given you more points.
7.2
Windyragon and ed'Rashtekaresket
Theorem: A parabola has a minimum or a maximum value.
ed'Rashtekaresket was released at one end of the stage. With a mighty hop, he launched himself high up into the air, to the top of the stage. When he approached the top of the parabola, he panicked and flopped around, as if trying to go higher. A moment later, when he reached the vertex, he produced a line of water, and spun around so that the audience could see him. And then, he fell, right onto the other end of the stage.
Judges’ Notes:
bulbasaur: Not as creative as I would have liked it to be, but it worked.
7.2
Byrus: Simple enough, but it gets the point across well and creates a funny visual.
7.3
Crazy Linoone: Nothing much to say here, really! Overall, a good, solid appeal.
7.0
Effercon and Milkmaid
Theorem: The normal line of a point on a circle passes through the centre of the circle.
Milkmaid drew a breath, and exhaled some ice. She carefully made it into a circular shape. Then, she punched a diameter into the circle, however, she had to bend to the floor to make an indent on the thin ice. And finally, she punched a tangential imaginary line through the base of the circle.
Judges’ Notes:
bulbasaur: I’m not really seeing how Milkmaid could punch a visible tangent line through a circular Ice Beam. In all, I just don’t think it worked (or if it did, it worked very poorly).
5.3
Byrus: I think blizzard may have been a better choice here. It would have given you more ice to work with. As it is though, it worked out fairly good.
6.8
Crazy Linoone: Drawing out the math is kind of taking the easy way out. Also, using two of the same moves in a row is sort of boring, especially since Brick Break isn’t that flashy. Points for the math though.
6.2
Whirlpool and Jet
Theorem: A circle's radii are of equal length
Jet stood at the dead centre of the stage. On a cue, he flew in a fairly large circle, faster and faster, creating a vortex. He then slowed down, surveying the resulting Whirlwind with satisfaction. Floating in the middle, he shed some feathers that slowly coloured the vortex black. He flew back up, above the vortex, then dove down and emitted a blast of heat which burned the feathers up before the vortex began to die, leaving Jet in the middle.
Judges’ Notes:
bulbasaur: Creative and well-done.
10.0
Byrus: A very flashy appeal; my favourite kind. I think it may have turned out a bit messier than you intended, but it didn't undermine your intentions.
7.0
Crazy Linoone: Amazing! Bravo! You’ve perfectly integrated an awesome, stunning, and interesting appeal with clearly-demonstrated math. In fact, your appeal would’ve worked perfectly well even if this isn’t a math contest. Very nicely done! I love the color-changing vortex, and ending everything with fire is always cool.
10.0
Mai and Tuft
The Fundamental Theorem of Arithmetic: Every positive integer, except 1, can be represented as the product of one or more prime numbers.
The curtains closed, and the audience waited patiently. After all, this was the last appeal. The assembly's patience was rewarded when the curtains re-opened, with four Accelegor behind them. One could see "4" painted on their foreheads. They danced some intricate dance which some members of the audience recognized; those who did groaned. Gradually, miniature rainclouds gathered over the audience and the stage. It was only a brief while before they deposed their contents over both audience and stage alike. With the rain went the clones, and the water-based paint Mai had used to paint Tuft; the 4 was now replaced by a 2² below which had been painted with an oil-based one. And then, Tuft, drawing on a power that was unique to him, as the announcer noted, had multicoloured orbs hover around his body and give off a spooky glow. Letting the power fade, he was led to the back of the stage before the curtains closed and concluded round one of the contest.
Judges’ Notes:
bulbasaur: Lighting would have helped some with the aesthetic aspect of the appeal, but I sort of liked this.
8.5
Byrus: A very well thought out and unique appeal. You really made good use of all your options there.
9.0
Crazy Linoone: Hm, pretty interesting, actually! I’m not sure how it makes sense, but uh it looks cool and it does make sense, if you think about it. Also, shiny ending is shiny. I don’t appreciate getting wet though :|
6.7
Scores:
Whirlpool: 27.0
Totodile: 26.6
Superbird: 24.8
Mai: 24.2
Grass King: 23.7
ole_schooler: 22.8
Windyragon: 21.5
RespectTheBlade: 21.1
~~Median~~
Metallica Fanboy: 20.2
The Omskivar: 19.4
Effercon: 18.3
Wargle: 13.4
Congratulations to those who made it, good try to those who didn't. For those who did, your arena for the next appeal will be on the side of a mountain, above the tree line. There is a thick layer of hard, packed snow on the ground, with some rocks protruding from the ground, but the weather is quite warm. There is also a glacial flow to the side. You will have lots of space and it is almost flat. There are also whatever resources you need, except trees. You may maim the landscape however you want.
Also, now that you have demonstrated that you have a knowledge of pure math, you may now show applied math, such as that found in physics and parts of chemistry. It should still be math-orientated, though, and you should have a mathematical formula to go along with your appeal. You may also use props beyond what was allowed last round. You may not use the same Pokémon or the same theorem as you did last round.
You have two weeks. Go!
