By the end of the month, the doubleheader Cory spent weeks to organize with the booster club finally arrived, while knowing that the D-Day for the three girls is Tuesday regarding college. But unsurprisingly, because of what the organizers believed at the time as still being possible, Geneviève and Krista are excluded from the doubleheader held at the municipal stadium on Saturday night.
"Tonight, we're assembled at the municipal stadium for the Duel of the Parishes, take two, with partial derivatives and multiple integrals on the menu, pitting our Venomous Agendas against the team of the neighboring parish for the Vans Math Contest final. But we have, as first part, special guests, from Odessa in Texas, Permian Panthers!" Cory's father announces, while the Permian team gets in position.
"Oh? Why Permian?" Ted asks, wondering what could push their mathletics team to cross Texas to enter the first part of an open-air math pageant on a Saturday night.
"Remember Permian against us at the start of the season, and that was well before Gen and Krista are suddenly in the race to the EGMO! They were routed" Ted's neighbor comments.
It's not counting on the fact that, for the first part, it's the second line that will play instead; provisionally, Imélie will be on the second line for the purposes of this doubleheader. In the visitors' locker room, the Panthers don't realize anything.
"The main reason why I accepted the fees the Venomous Agendas paid for us to come here was because I used to teach here before I moved to Odessa! They seem to have it made for academic extracurriculars!" Permian's coach then tells his mathletes.
"Coach, what do you mean, they have it made for academic extracurriculars?" Svitlana, his star player, asks with an Ukrainian accent.
"Until this year we didn't even have a functional math team! Our opponents have a girl who is somehow in the running for the EGMO! Don't let that intimidate you! Don't let the crowd intimidate you!" the coach adds some more.
"I would love to meet with her later" Svitlana adds.
"EGMO?" her teammates ask, having never heard about this competition.
"You were the one that gave us Title IX funding, so I hope the price Ector County paid for you was worth it. At the same time, you shouldn't hog all the answers; the others need some game time as well" Permian's coach warns his star mathlete.
When we arrived on American soil, my family and I, we were not prepared for all the adulation the city gave high school football, but in mathematics, I was clearly above everyone else! Permian is very anti-intellectual in comparison to middle school in Ukraine pre-war, Svitlana, Permian's star player thought, while Permian's coach imagined that they would face the big Venomous Agendas team. It would not be the reality.
"For the first part, the only VMC entrant authorized to compete is Imélie; for the second part, Gen and Krista will be benched, too" the VAs' coach gives instructions to his players.
"But why? The public wants to see them again! I'm the impresario of the team; I might agree to give playtime to lesser players, people want to watch what they cannot do themselves, hence the reason why I want our two stars to have some time on stage" Cory asks his coach.
"Cory, I am a little annoyed. Do you want to get to the same result as at the dinner should we get, as an encore, a confrontation between the public and the two of us? You know, since the dinner, and maybe even since we know each other, the public is completely powerless over partial derivatives and multiple integrals!" Gen then asks her boyfriend.
"I will go solve PDEs in open air! You did it last year, it's my turn this year!" Krista announces.
"Krista, you think it's a good idea to do this? You forced my hand last year to solve PDEs in open air, that's what brought you here! If you want to solve PDEs in open air tonight, please, no heat equation! And I won't be solving PDEs in open air tonight!" Gen pleads to her friend.
"One question, Cory: why has there not been a pep rally for the USAMO? You knew it was a meeting with history, and everyone in the parish is waiting patiently for the result!" Marcia asks.
"We never organized a pep rally for individual contests, athletic or academic. Not even the USAMO. That said, if Gen claims her dog is dead for the IMO, it is for Krista as well; they accustomed us to nearly identical mathletic performances at every turn this season" Cory answers his teammate.
"And I started from further out than Gen... neither one of us were at the USAMO last year" Krista points out.
"But I promise there will be one should either one qualifies for the EGMO"
"The kickoff for the first part is in two minutes!" Trent warns his team. "Imélie, promise me not to hog all the questions!"
The stadium does not contain the shadow of a single Permian Panthers fan; no one follows Permian mathletics to such a degree that they would be ready to travel this far away from Odessa for attending mathletic contests. But the first part of this pageant is happening with the coach of the quiz bowl team as a moderator, with the consequence that the NAQT rules are in use, with one notable exception that there are five players on each side rather than four, and unsurprisingly, Imélie is the fastest among the Venomous Agendas for this first part. The two coaches are very disappointed of their respective teams and how it transformed into a duel between the two girls: Svitlana on the one hand, for Permian, and Imélie on the other hand.
"Is that all there is to the Venomous Agendas? Is she that girl the Venomous Agendas talk about so much on social media?" Permian's coach asks his team.
"Guys, what did you expect out of a potential EGMO qualifier?" one of Permian's players asks at half-time.
As much as the Venomous Agendas could try to lure us in thinking that Imélie is the girl they present as being in the so-called race to the EGMO, something is amiss. I might be better than everyone else at Permian, I am still a long way off from that tournament; she didn't appear to be an elite mathlete to me, Svitlana, the Ukrainian refugee, thinks, while she is benched, as is Imélie; both girls scored nearly all the points of their respective teams. Nevertheless, Permian is still trailing, just not by a margin as wide as in the Math Madness regular season game nine minutes in.
But without their respective girls, the pace of gameplay slows down a little bit; the questions increase in difficulty as well. That said, the Venomous Agendas, deprived of their six best players, try to stay above water as the Panthers continue to catch up, with the infamous « second line representative » leading the charge. Questions of geometry, probability, combinatorics, questions that can destabilize people. Ultimately Permian succeeds, by a strange trick of fate, to force overtime in this hybrid game of quiz bowl but with only mathematical questions as on the Purple Comet or the AMC12.
"You see? Our team lacks depth! If we want to keep playing at the same level next year, we will need to scout more systematically!" Ted comments, sitting on the first row, behind Krista, who is sitting on the bench.
"Two hundred forty points on each side. I didn't think the coach was willing to bench so many good players to make the lesser players practice... But the opponent does the same thing" Randy comments in turn.
In quiz bowl as here, an overtime period consists of 3 questions asked after the regulation 18 minutes but without bonus. It's like the Duel of the Parishes in pre-season; here it's even harder to solve in 10 seconds! The second line representative thinks, while the demarcation is clear between regulation time and overtime.
"First overtime question: Five men and seven women stand in a line in random order. Let m and n be relatively prime positive integers so that m/n is the probability that each man stands next to a woman. Find m+n" the Venomous Agendas quiz bowl coach reads in front of the crowd. The answer was two hundred eighty-seven.
At this rate, the game that was supposed to be a first part of a mathletics pageant will be played in sudden death, i.e., after the end of the three questions of the first overtime period, with the stadium filled with cries of Venomous! Agendas! That, even though they are unable to solve them in the 10 seconds allotted. That said, the opponent is unable to solve these questions in ten seconds.
"Ninth overtime question; we are in a sudden death situation, if anyone answers correctly, we have a winner. Find n such that (4n+7)3=(2n+23)4. Bo? "Warren asks the second line's representative.
"Twenty-five" Bo answers.
"The winners of the first part: the Venomous Agendas!"
In the meantime, Zack finds himself with his girlfriend from the neighboring parish in the dressing room, while there is little time left before the main event of this pageant.
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"Tara, with you I feel I am becoming a better person outside of football. Multi-variable calculus will probably be several years away for me, if I do some eventually, but I see you do it, I feel like I no longer have anything to envy in my teammates' girlfriends. You have way more brains than I would have suspected, and not just mathematically" the strong safety tells his girlfriend.
"Thank you, you're nice, even though I know your teammates' girlfriends are even more talented than I am. It's not like boys where I go; most of them are unbelievably shallow"
"Here's for you: a can of energy drink"
Tara takes the Monster can as if it was nothing, but she does not drink its content in one go. Once the can is open, Zack leaves the dressing room and sits on the first row, just behind the visitors' bench. However, Annette seems to have rancor about the Venomous Agendas, and not just because of Krista that changed sides last year.
Among the Venomous Agendas, however, without Gen or Krista, they find themselves with a bit of anxiety, and they feel much more vulnerable without them in a team contest. But for some reason Bo is put into a playing position even though he knows he can't answer anything, or nearly so, in multi-variable calculus. Here people can focus more than in the first part of the pageant.
"Since the second part is concerned with the calculation of partial derivatives and multiple integrals, the NAQT time limits are way too strict. Then we need to use a longer delay and both teams will have an opportunity to answer. First question, for seven points: Using the following transformation: X = (V-U)/3, Y = (4V-U)/3 calculate, over the region bounded by the following points: (2,0), (5,3), (6,7) and (3,4), the following integral"
First question, for seven points: Using the following transformation: X = (V-U)/3, Y = (4V-U)/3 calculate, over the region bounded by the following points: (2,0), (5,3), (6,7) and (3,4), the following integral" [https://img.wattpad.com/0821b40a2fcf97339660dd97c4977835f933c928/68747470733a2f2f73332e616d617a6f6e6177732e636f6d2f776174747061642d6d656469612d736572766963652f53746f7279496d6167652f46745964494e5764323636744e513d3d2d313239333030383438382e313732653637663863356433373731373335393032383339333138392e706e67?s=fit&w=1280&h=1280]
But without Gen or Krista, Marcia is the locomotive pulling the Venomous Agendas in this part of the pageant. Her burst of speed leads to the following answer:
"Two hundred forty-three halves" she answers quickly.
"Seven points for the Venomous Agendas. The neighboring parish has an answer in the next ten seconds?"
"One hundred twenty-one point five" Trevor answers.
"We're tied. For four points each, calculate ∂z/∂x and ∂z/∂y for the following function..." the moderator reads while the crowd gets lost in the question, which is a question of implicit partial derivative.
For as tempting as it might be for the two girls to blurt out the answers, she knows they risk angering Trent, so they are as powerless as the crowd even though they know they can calculate these partial derivatives without complication.
The crowd, bewildered by all these calculations as complex as one another, realizes the neighboring parish has talent but what dives differs greatly from the others. Yes, they hate the Venomous Agendas, and everything they accomplished in the mathletic sphere this year, but does that lead them to play better?
After having exhausted the 20 regulation questions, where everyone tried with a relative independence to solve the partial derivatives and multiple integral problems as asked on the stadium's scoreboard, in which there is a full house, they arrive, once again, to the sudden death stage. Except that, unlike sudden death in quiz bowl overtime, each team has the opportunity, for each question, to designate an opposing player to answer it.
And they are calculating triple integrals as if it was nothing! the Permian coach thinks, realizing the extent at which the Panthers are unprepared for the VMC final! Then the EGMO or the IMO would be wet dreams for Permian...
"Concepts and Majors, your turn" the quiz bowl coach asks the opposing players.
"We pick Imélie" Tara announces their pick.
The opponent knows that Marcia is stronger than I; yet, in their minds, they imagine that girls are weaker than boys if they are unknown mathletic quantities, as is my case, Imélie thinks while her teammates consider who would be the opposing players that appears the most "takeable" to confront her.
"We pick Annette" Vontae announces the VAs' pick.
"Young ladies, we are in a sudden death situation, here's the question: Calculate"
Not hard; if we take the polar Jacobian, the integral on the scoreboard becomes, Imélie thinks, while the usage of the polar Jacobian gives: [https://img.wattpad.com/dd5d0ced4bd0f9470909c3748df9f3f2b81e4b9a/68747470733a2f2f73332e616d617a6f6e6177732e636f6d2f776174747061642d6d656469612d736572766963652f53746f7279496d6167652f714f564a567069505738797445673d3d2d313239333030383438382e313732653637666433623661393637663135313237363832383337382e706e67?s=fit&w=1280&h=1280]
Not hard; if we take the polar Jacobian, the integral on the scoreboard becomes, Imélie thinks, while the usage of the polar Jacobian gives:
In which case, in her mind, a factor of 2π gets out of the integral because it does not depend on the polar integral, transforming a double integral into a single one [https://img.wattpad.com/184ea1c3ca8b9b6952d346e33714103684b636b4/68747470733a2f2f73332e616d617a6f6e6177732e636f6d2f776174747061642d6d656469612d736572766963652f53746f7279496d6167652f634a51596a69704a5a69434e66413d3d2d313239333030383438382e313732653637666563636436386565373337383636343536363339332e706e67?s=fit&w=1280&h=1280]
In which case, in her mind, a factor of 2π gets out of the integral because it does not depend on the polar integral, transforming a double integral into a single one.
"Two pi sigma squared!" Imélie answers, without being completely sure of the second term.
"And the winner of the second part of the pageant is the Venomous Agendas!"
"Venomous! Agendas! Venomous! Agendas!" howls the crowd while Krista is about to use the board used by the moderator to show the problems on the scoreboard.
"Even though I was benched tonight, I want to share with you another wonderful mathematical object: the Laplace equation. Or"
"We suppose the solution is of the form u(x,y)=F(x)G(y), as with the heat equation that my teammate solved last year in open air [https://img.wattpad.com/01935ad85c3949951e2e7260b7105f10ae8cf132/68747470733a2f2f73332e616d617a6f6e6177732e636f6d2f776174747061642d6d656469612d736572766963652f53746f7279496d6167652f546d6754386a6f7a2d4f6a6f4b673d3d2d313239333030383438382e313732653638303238626130653436363234353432393837373939342e706e67?s=fit&w=1280&h=1280]
"We suppose the solution is of the form u(x,y)=F(x)G(y), as with the heat equation that my teammate solved last year in open air. Yet here the boundary conditions will determine the form of the solution. It has to be said, we can get to the Laplace from the heat equation in the absence of a heat source and we look for a stationary solution. Here too we will be dealing with an eigenvalue problem, which are a function of the domain size. We can then have a Fourier series on one dimension, times a hyperbolic sine or cosine... these functions being the solutions to this ordinary differential equation"
The crowd's powerlessness is such that they have no mathematical question to ask them, unlike Geneviève last year; Krista makes comments about the calculation of the hyperbolic sine and cosine, which is what happens when we try to calculate sines ... [https://img.wattpad.com/9ac13bec971e39d2d984cdea05992643ce47ba8d/68747470733a2f2f73332e616d617a6f6e6177732e636f6d2f776174747061642d6d656469612d736572766963652f53746f7279496d6167652f2d4b2d567075776e5a57786963513d3d2d313239333030383438382e313732653638303634353936386361313435343435343031333032342e706e67?s=fit&w=1280&h=1280]
The crowd's powerlessness is such that they have no mathematical question to ask them, unlike Geneviève last year; Krista makes comments about the calculation of the hyperbolic sine and cosine, which is what happens when we try to calculate sines and cosines with purely imaginary angles. Or sinh (x) = (e^x-e^-x)/2 and then cosh (x) = (e^x+e^-x)/2, having for derivatives cosh (x) and sinh (x) respectively.
"But why were you benched?" Ted asks from the first row by yelling at her.
"The coach wanted to leave the others with adequate playtime. If only one between Gen and I was playing, then we would have deprived our teammates of playtime..." Krista explains to him.
Strangely solving a PDE in open air didn't make me more satisfied on a personal level; I wonder why I wanted to do this so much other than to appear in this mathematics pageant, Krista thinks, while Gen knows so many would be a little disappointed if she didn't appear. Gen gets on stage while Krista gets off it.
"Please excuse my absence from the first two parts of this pageant, but it's for the same reasons as Krista. I accuse the parish newspaper of violating journalistic ethical standards!" Gen shouts while her face becomes basic.
"But why?" A lot of people in the crowd asks, surprised by this accusation.
"The parish newspaper put us into a compressor for months on the basis of incomplete information! The sad truth, which will surprise a lot of people here, is that our dog is dead for the IMO, for Krista as well as for me" Gen explains herself while the crowd is astonished by this declaration.
"Why incomplete?" spectators ask, surprised.
"Then the parish newspaper sold false dreams to the parish population for months! Selling dreams, yes, but a dream sold by journalistic dreams must be based on truthful and complete information! The parish newspaper imagines that, if we did well enough on the USAMO Tuesday and Wednesday last week, we would qualify for the EGMO, which, this year, is held in Georgia, and we'd play our tickets for Bath, that is, the IMO, at MOP in June. It also imagined that participating in the EGMO would qualify us automatically for the MOP while, in reality qualifying for the EGMO and the IMO is a much longer process than what the newspaper described. During season N-1 doing well on the first USAMO would make us participate to the MOP, and for season N we must enter four competitions on top of the AMC series: two TSTs, the RMM and the APMO, all counting for twenty-one points, with the USAMO of season N counting for forty-two points. The six best at the end of season N will participate at the IMO for that season"
"The newspaper did this on purpose? Or exposing all the details would lose people?" the quiz bowl coach asks.
"But what would that imply for the EGMO?" Tara asks, while the crowd barely recovers from the shock.
"Our coach did as if it was new, but in fact, it worked like this for years. The four best female non-seniors at the USAMO of the year, plus, if applicable, any other non-senior female, in the top thirty, are invited to the MOP. The potential pool of contestants for the IMO includes the top thirty among non-seniors, plus any supernumerary girl, if applicable, until we get to the count of four. It goes without saying that, if the MAA is forced to invoke the supernumerary girls clause, then the EGMO team of the following year is fixed practically a year in advance, and it also leaves no room in the event of a medical issue that would force a contestant to withdraw. One may be wondering how the EGMO reserves are made. Everyone here believed there would be hope that I would qualify for either the EGMO or the IMO"
"Adding to what Gen said, there's an overlap between the USAMO, the EGMO and the IMO for problem difficulty. We prepared for the USAMO by using the WOOT system, which attributed us old USAMO problems aswell as old EGMO and IMO problems; it took us forever and we couldn't tell where the problems came from without searching afterward" Krista continues.