이곳은 개발을 위한 베타 사이트 입니다.기여내역은 언제든 초기화될 수 있으며, 예기치 못한 오류가 발생할 수 있습니다.문서의 임의 삭제는 제재 대상으로, 문서를 삭제하려면 삭제 토론을 진행해야 합니다. 문서 보기문서 삭제토론 Exponential Idle (문단 편집) ====# Euler's Formula #==== > You're a student hired by a professor at a famous university. Since your work has received a bit of attention from your colleagues in the past, you decide to go into a subject not yet covered by your professor, which has interested you since day 1 of deciding to study mathematics - Complex numbers. > You hope that with your research on this subject, you can finally get the breakthrough you always wanted in the scientific world. > > This theory explored the world of complex numbers, their arrangement and their place in the Universe of Mathematics. The theory, named after the famous mathematician Leonhard Euler, explores the relationship between exponential and trigonometric functions. > Your task is to use this formula, and with the help of the Pythagorean theorem, to calculate the distances of [math(\cos(t))] and [math(i\sin(t))] from the origin and grow them as large as possible using many different methods and approaches! > A theory with interesting grow and decay rates, unusual properties, and (We hope) an interesting story! > > ---- > > 당신은 유명한 대학의 교수가 고용한 학생입니다. 당신의 작업이 과거에 동기들로부터 약간의 관심을 받아서, 아직 교수님이 다루지 않은 주제로 들어가기로 결정했습니다. 그것은 수학을 공부하기로 결심한 첫날부터 당신의 관심을 끌었던, [[복소수]]입니다. > 당신은 이 주제에 대한 연구를 통해 과학계에서 항상 원했던 돌파구를 마침내 얻을 수 있기를 바랍니다. > > [[오일러 공식|이 이론]]은 복소수의 세계, 그들의 배열, 그리고 수학계에서의 위치를 탐구했습니다. 유명한 수학자 [[레온하르트 오일러]]의 이름을 딴 이 이론은 [[지수함수]]와 [[삼각함수]] 사이의 관계를 탐구합니다. > 당신의 임무는 [[피타고라스 정리]]의 도움을 받아 원점으로부터 [math(\cos(t))]와 [math(i\sin(t))]의 거리를 계산하고 여러 가지 방법과 접근법을 사용하여 가능한 한 크게 성장시키는 것입니다! > 흥미로운 성장률과 붕괴율, 특이한 성질, 그리고 흥미로운 (그랬으면 하는) 이야기를 담은 이론입니다! 주어진 식은 다음과 같다. * [math(\dot{\rho}=\sqrt{tq^2})] [math(G(t)=g_r+g_i)] [math(g_r=\cos(t),\ g_i=i\sin(t))] [math(\dot{q}=q_1q_2)] [math(\tau_{11}=\max\rho^{0.4})] Euler's Formula의 기본 변수는 [math(\dot{t})], [math(q_1)], [math(q_2)]이고, 이정표 업그레이드를 통해 [math(b_1)], [math(b_2)], [math(c_1)], [math(c_2)], (?)를 해금할 수 있다. 혼돈 이론과 유사하게, [math(G)]로 표현되는 점의 운동을 바탕으로 ρ를 성장시키는 이론이다. 그러나 운동 방정식이 정해져 있고 이를 관측하기만 하는 혼돈 이론과는 다르게, Euler's Formula에서는 운동 방정식을 수정해나가며 점의 속도를 키울 수 있다. Euler's Formula의 이정표는 다음과 같다. 아래 주어진 순서대로만 해금할 수 있다. * 실수부 [math(\mathrm{R})] 추가 (1e10ρ) 식이 다음과 같이 수정되며, 화폐 [math(\mathrm{R})]과 변수 [math(b_1)], [math(b_2)]가 해금된다. [math(\dot{\rho}=\sqrt{tq^2+\mathrm{R}^2})] [math(g_r=b_1b_2\cos(t))] [math(\dot{\mathrm{R}}=(g_r)^2)] * 허수부 [math(\mathrm{I})] 추가 (1e20ρ) 식이 다음과 같이 수정되며, 화폐 [math(\mathrm{I})]와 변수 [math(c_1)], [math(c_2)]가 해금된다. [math(\dot{\rho}=\sqrt{tq^2+\mathrm{R}^2+\mathrm{I}^2})] [math(g_i=ic_1c_2\sin(t))] [math(\dot{\mathrm{I}}=-(g_i)^2)] * [math(a_1)]항 추가 (1e30ρ) 이 이론에는 총 11개의 스토리 챕터가 있다. {{{#!folding [ 목록 펼치기 · 접기 ] * 1번째 챕터 {{{#!folding [ 펼치기 · 접기 ] 해금 조건 : 최초 실행 > '''Circular Reasoning''' > You approach your professor with a problem you found. > You say, "Professor, all other experts in our fiel keep saying that this cannot be used to further our research. > However, I think I can get something out of it!" > You hand him the paper with the theory: > [math(e^{ix}=\cos(x)+i\sin(x))] > He looks at you and says: > "This is Euler's Formula. Are you sure that you can get results out of something that has imaginary numbers?" > "Yes! I believe I can!", you reply to him with anticipation. > He gives you the green light to work on the project. }}} * 2번째 챕터 {{{#!folding [ 펼치기 · 접기 ] 해금 조건 : 1e7ρ > '''Anticipation''' > As you start your research, you realize that > it is much harder than you anticipated. > You start experimenting with this formula. > However, you cannot figure out how to integrate the graph into your equation yet. > Your motivation is higher than ever though, > and you can't wait to progress further with this. }}} * 3번째 챕터 {{{#!folding [ 펼치기 · 접기 ] 해금 조건 : 실수부 [math(\mathrm{R})] 추가 > '''A Breakthrough''' > After several months of work on this as a side project, > you finally figure it out: > You know how to modify the equation. > You try to modify the cosine value > and give it a new name: 'R'. > You start experimenting with 'R' > and try to figure out what happens > when you modify it. }}} * 4번째 챕터 {{{#!folding [ 펼치기 · 접기 ] 해금 조건 : 허수부 [math(\mathrm{I})] 추가 > '''Complex Progress''' > Interesting. > You see that the modification did something to the partical. > It's not affecting ρ but its doing something. > You decide that doing the same to the complex component is a good idea. > 'i' is going to be interesting to deal with... > You name it 'I' and continue your calculations. }}} * 5번째 챕터 {{{#!folding [ 펼치기 · 접기 ] 해금 조건 : a_base first milestone > '''A Different Approach''' > Several weeks have passed since you have added 'I' as a component to your research. > However, you observe the growth slow down considerably and worry that your research is all for nothing. > You ask your colleagues what you should do. > One of them says: "Add a variable to multiply the theory with. > Maybe that will help with your progress." > You create a small little variable called: 'a1'. }}} * 6번째 챕터 {{{#!folding [ 펼치기 · 접기 ] 해금 조건 : a_base last milestone > '''Explosion''' > It worked! > Your multipliers are doing a great job pushing the theory. > But what if you could go even further? > After all, you have observed the theory for a long time now. > You decide to create a variable called 'a3'. It will have exponential growth. > Is this enough, for the theory to reach its limit? > It nevertheless helps you immensely in your progress. }}} * 7번째 챕터 {{{#!folding [ 펼치기 · 접기 ] 해금 조건 : a_exponent last milestone > '''Exponential Ideas''' > "Of course! > It's a relationship between exponential functions and trigonometry! > Why shouldn't I add an exponent? > Surely, using this, this theory can be pushed to its limit!", > you think to yourself. > You decide to add an exponent to your multipliers. }}} * 8번째 챕터 {{{#!folding [ 펼치기 · 접기 ] 해금 조건 : a_exp and a_base max milestone > '''The End?''' > Summer break has finally arrived. > Maybe it's time for you to quit. > You have pushed this theory to its limit, you think to yourself > that there's nothing more you can do. > You have tried everything you can think of. > It's time to let go. > > > > Or is it...? }}} * 9번째 챕터 {{{#!folding [ 펼치기 · 접기 ] 해금 조건 : 1e100τ > '''A New Beginning''' > Your summer break was beautiful. > You had a great time with your friends. > However, that constant thought of the theory can't get out of your head. > Since the start of summer break, it has plagued you. > "This cannot be the end.", you think. > There has to be something more! No way its limit is so low!" > > You look over the theory again and notice something. > After all this work, how come you never changed the bases of 'b' and 'c'? > You gain motivation and start work on the theory again. }}} * 10번째 챕터 {{{#!folding [ 펼치기 · 접기 ] 해금 조건 : 1e120τ > '''Frustration''' > You wake up in a sudden panic. > You had a nightmare, of a huge 'i' falling on you. > Another night in your lab. > This has been the 3rd time this week. > Your theory is growing incredibly slow. > You cannot figure out why. > The past weeks have been filled of you > trying to grow this theory as large as you possibly can. > > More or less successful. > > Suddenly, you realize that you forgot to change the base of 'c'. > You think, about how 'a3' is connected to 'c'. > Can this be the step to push the theory to its limit? }}} * 11번째 챕터 (엔딩) {{{#!folding [ 펼치기 · 접기 ] 해금 조건 : tau = e150 > '''????''' > You finally did it. > You have proven that the theory is able to be pushed to its limit. > You are proud of yourself. > Your publications get a massive amount of attention. > One day, your professor reaches out to you: > "You have shown a lot of dedication, > far more than I have ever seen from any student I've ever lectured. > I am retiring this semester. The same as you graduate in. > I got a small job offering for you. > }}}}}}저장 버튼을 클릭하면 당신이 기여한 내용을 CC-BY-NC-SA 2.0 KR으로 배포하고,기여한 문서에 대한 하이퍼링크나 URL을 이용하여 저작자 표시를 하는 것으로 충분하다는 데 동의하는 것입니다.이 동의는 철회할 수 없습니다.캡챠저장미리보기