Fixed Mobile Control, Added Stages

First Principles/Assets/Resources/Localization/MathArticle/en.txt

@@ -1,7 +1,9 @@
+@@SECTION=intro
 <b><size=120%>Math concepts — in-game reader</size></b>
 <size=90%>The game <b>First Principles</b> takes its name from public remarks by <b>Elon Musk</b> on a <b>first-principles approach</b> to <b>business</b> and to <b>solving problems in life and work</b>—then teaches <b>calculus-first</b> ideas on the graph as a matching metaphor.</size>
 <size=90%>Use <b>Math concepts</b> while playing, or <b>Math tips & snippets</b> on Level select — same scrollable notes. Tap the dark backdrop or <b>Close</b> to dismiss.</size>
 
+@@SECTION=how_graph
 <b><size=115%>How this game teaches calculus (read the graph while you play)</size></b>
 <size=92%>
 • <b>Main curve</b> — the thick path on the Cartesian grid is \(y = f(x)\) for this stage. Your character tries to stand on platforms that follow that shape. The <b>Equation</b> label (when visible) names the rule being plotted.
@@ -17,9 +19,11 @@
 Everything below is a <b>topic glossary</b> you can skim between deaths or after finishing a graph — plus a <b>First principles thinking (business)</b> section before exam prep.
 </size>
 
+@@SECTION=s1
 <b><size=110%>1. Derivatives = slope & rate</size></b>
 The derivative \(f'(x)\) measures how steeply \(f(x)\) rises or falls. In physics it is often a <i>rate</i>: how fast position changes (velocity), how fast temperature changes along a bar, etc. In this game, the derivative helps decide where the ground exists.
 
+@@SECTION=rules
 <b><size=120%>──────── Differentiation rules — your skill tree ────────</size></b>
 <size=92%>These are the <b>combo moves</b> for turning \(f(x)\) into \(f'(x)\) without rebuilding from the limit every time. Read them like <b>perks</b> that change how your <b>main curve</b> and <b>derivative HUD</b> stay in sync.</size>
 
@@ -43,6 +47,7 @@ If \(y = f(g(x))\), then \(\displaystyle \frac{dy}{dx} = f'(g(x))\cdot g'(x)\).
 
 <size=92%>The game still draws \(f'\) with a <b>numeric sampler</b> on wild stages, but these identities explain <i>why</i> textbook curves snap into clean forms — and what AP / TMUA expects you to simplify before you sketch. Longer write-up: <b>docs/derivative-rules.md</b>.</size>
 
+@@SECTION=int_block
 <b><size=120%>──────── Integrals: definite vs indefinite — score vs loadout ────────</size></b>
 <size=92%><b>Indefinite</b> \(\displaystyle \int f(x)\,dx\) asks for an <b>antiderivative</b> — a whole <i>family</i> \(F(x)+C\) whose derivative is \(f\). Think <b>loadout class</b>: many valid builds differ by +\(C\) (same gameplay up to vertical shift in \(F\)). <b>Definite</b> \(\displaystyle \int_a^b f(x)\,dx\) is a single <b>number</b> (signed area from \(a\) to \(b\)) — like a <b>run score</b> for one fixed segment. No “+\(C\)” in the answer: endpoints pin it down.</size>
 
@@ -54,42 +59,55 @@ Rectangles (left / right / midpoint) estimate the <b>definite</b> score before y
 
 <size=92%>More detail: <b>docs/definite-indefinite-integrals.md</b>. (Graphing calculator / FTC proofs — see course notes; this is the game glossary.)</size>
 
+@@SECTION=s2
 <b><size=110%>2. Parabola (power / quadratic)</size></b>
 A quadratic \(y = a(x-h)^2+k\) is the shape of projectile motion in ideal textbook setups and many optimization problems (min/max). One smooth hump; the slope switches sign at the vertex.
 
+@@SECTION=s3
 <b><size=110%>3. Sine & cosine = waves & rotation</size></b>
 Sines and cosines describe vibrations, AC signals, sound, and anything that repeats. Cosine is sine shifted: same wave, different starting phase. Complex numbers (below) make these waves easier to solve in circuits and vibrations.
 
+@@SECTION=s4
 <b><size=110%>4. Absolute value & kinks</size></b>
 \(|x|\) bends the graph so there is a corner on the axis. The derivative jumps there in ideal math — in real programs we plot smooth samples, but the idea matters: nonsmooth points need special care in analysis and simulation.
 
+@@SECTION=s5
 <b><size=110%>5. Taylor & Maclaurin series</size></b>
 Smooth functions can be approximated near a point by polynomials with matching derivatives. Maclaurin means “expand around \(0\).” More terms usually improve the fit nearby; the full infinite sum is the series (where it converges).
 
+@@SECTION=s6
 <b><size=110%>6. Geometric series</size></b>
 Sums \(u^0+u^1+u^2+\cdots\) appear in probability, signal processing, and digital math. When \(|u|<1\) the tail shrinks and the infinite sum has a clean closed form; that is the same mood as stability and “things settle.”
 
+@@SECTION=s7
 <b><size=110%>7. Multivariable slices</size></b>
 Surfaces \(z = f(x,y)\) can be cut by fixing \(y=y_0\) — you get a 1D curve in \(x\). That is how higher-dimensional calculus is often reasoned about in engineering: fix all but one variable, take partial derivatives, gradients, directional slopes.
 
+@@SECTION=s8
 <b><size=110%>8. Integrals & area (Riemann sums)</size></b>
 The definite integral \(\displaystyle \int_a^b f(x)\,dx\) is the signed area under the curve. Riemann sums chop \([a,b]\) into thin rectangles: pick sample heights (left, right, midpoint), add \(f(x^\ast)\,\Delta x\). More rectangles → closer to the true integral.
 
+@@SECTION=s9
 <b><size=110%>9. Engineering math — modeling mindset</size></b>
 Engineering math picks tools that match the world: linear algebra for structures and networks, complex numbers / phasors for steady AC, differential equations for motion and heat, transforms (Laplace/Fourier) for signals and control. The goal is a <i>usable model</i>, then check it against reality.
 
+@@SECTION=s10
 <b><size=110%>10. Damped oscillation</size></b>
 Many systems lose energy while oscillating: \(e^{-\alpha t}\sin(\omega t)\) style decay is the cartoon of that idea — envelope shrinks, oscillation persists briefly. Mechanical damping, resistor–capacitor–inductor circuits, and control systems all share this language.
 
+@@SECTION=s11
 <b><size=110%>11. Catenary & cosh</size></b>
 A hanging cable under its own weight forms a catenary; \(\cosh\) is the hyperbolic cosine that models that ideal shape (and shows up in hyperbolic PDEs and relativity too). Different from a parabola even if both look “like arches.”
 
+@@SECTION=s12
 <b><size=110%>12. Rectified sine \(|\sin|\)</size></b>
 Full-wave rectification flips negative lobes upward — a first step in turning AC into something closer to DC for power supplies. Corners at zeros mean derivatives jump — a reminder that idealized circuits still start from calculus intuitions.
 
+@@SECTION=s13
 <b><size=110%>13. Circle \((x-h)^2 + (y-k)^2 = R^2\)</size></b>
 A circle is usually written implicitly. Solving for \(y\) gives two branches (\(\pm\sqrt{\cdot}\)). The game’s circle stage uses the <i>upper</i> semicircle so the path stays a function \(y(x)\) over one sweep. Implicit differentiation yields \(\frac{dy}{dx} = -\frac{x-h}{y-k}\); at the ends of the diameter the tangent is vertical (slope blows up).
 
+@@SECTION=aero
 <b><size=120%>──────── Aerospace engineering & aerodynamics ────────</size></b>
 <size=92%>Levels prefixed <b>Aerospace:</b> turn textbook flight‑vehicle math into paths you run. They are <i>toy models</i> for pedagogy — not CFD, flight test, or ITAR‑grade simulations.</size>
 
@@ -101,6 +119,7 @@ A circle is usually written implicitly. Solving for \(y\) gives two branches (\(
 
 <b><size=90%>See docs/engineering-math.md § Aerospace for a longer map.</size></b>
 
+@@SECTION=biz
 <b><size=120%>──────── First principles thinking (business) ────────</size></b>
 <size=92%>Startup culture often cites <b>Elon Musk</b> for reviving <b>first principles</b> at places like <b>Tesla / SpaceX</b>: stop trusting “the market always prices it this way,” and instead <b>unpack assumptions</b> until you hit bedrock facts (materials, energy, physics, true unit costs), then <b>reason upward</b> into a new design. The idea is older than any one founder — but the <i>habit</i> matches this game’s visuals.</size>
 
@@ -112,6 +131,7 @@ A circle is usually written implicitly. Solving for \(y\) gives two branches (\(
 
 <b><size=92%>This is <i>not</i> legal, tax, or investing advice — a thinking drill you can pair with real advisors and data. Full write-up:</size></b> <b>docs/first-principles-business.md</b> on GitHub Pages.
 
+@@SECTION=exam
 <b><size=120%>──────── Exam prep (separate tracks) ────────</size></b>
 
 <b><size=118%>Competition mathematics (contest lens)</size></b>

First Principles/Assets/Resources/Localization/ar.txt

@@ -12,17 +12,14 @@ ui.jump=قفز
 ui.move=تحرك
 ui.keyboard_hint_mobile=<size=90%><color=#5c6577>(لوحة المفاتيح: الأسهم / المسافة)</color></size>
 hud.stage=المرحلة
-controls.mobile=<color=#7a8399>تحرك</color>  <b><color=#ffd978>◀ ▶</color></b>  <color=#5c6577>·</color>  <color=#7a8399>قفز</color>  <b><color=#ffd978>مس</color></b>  <size=90%><color=#5c6577>(لوحة المفاتيح: الأسهم / المسافة)</color></size>
-controls.desktop=<color=#7a8399>تحرك</color>  <b><color=#ffd978>←</color></b>  <b><color=#ffd978>→</color></b>  <color=#5c6577>·</color>  <color=#7a8399>قفز</color>  <b><color=#ffd978>مسافة</color></b>
-controls.calculator=<color=#7a8399>آلة رسومية</color>  <b>اكتب f(u)</b>  ·  <b>Trans</b>  ·  <b>Scale</b>  ·  <b>قرصة</b>  ·  <b>رجوع</b>
 graph.label_fu=f(u) =
 graph.placeholder=x^2 + sin(x) · ln(x) عندما x>0 · min(x,3)...
 graph.status_enter=Enter / اضغط خارج الحقل للرسم
 graph.status_graphed=<color=#8fd9b3>تم الرسم</color>
 graph.line1=<b>وضع آلة الرسوم البيانية</b>
 graph.line2=<size=88%><color=#c4d0e8>اكتب <b>f(u)</b> أدناه (المتغير <b>x</b> في المربع = u الداخلي). ثم:</color></size>
 graph.line3=<size=92%><b>Trans</b> ← {0} · نقرتان <b>+</b> · اضغط مطولًا <b>−</b> · <b>Scale</b> تكبير باللمس / اضغط مطولًا للتصغير · <b>قرصة</b> بإصبعين</size>
-graph.line4=<size=88%><color=#a8b2d1>A={0} &nbsp;k={1} &nbsp;C={2} &nbsp;D={3} &nbsp;&nbsp;x في [{4},{5}]</color></size>
+graph.line4=<size=88%><color=#a8b2d1>A={0}  k={1}  C={2}  D={3}   x في [{4},{5}]</color></size>
 graph.param_a=A (مقياس عمودي)
 graph.param_k=k (مقياس أفقي)
 graph.param_c=C (إزاحة عمودية)
@@ -65,20 +62,28 @@ level.30=BC: طور وحركة توافقية بسيطة (طاقة)
 level.31=BC: تكعيب ونقطة انعطاف (رسم)
 level.32=BC: b^x و d/dx b^x
 level.33=دائرة: (x−h)² + (y−k)² = R²
-level.34=طيران: رفع C_L(α) خطي + انفصال
-level.35=طيران: قطب السحب (طفيلي، مُستحثّ، إجمالي)
-level.36=طيران: جو متساوي الحرارة ρ(h)
-level.37=طيران: حركة مجنحة / اهتزاز مُخمَّد
-level.38=طيران: نيوتوني Cp ~ sin²α
-level.39=طيران: Strouhal / نبرة انبعاث دوامات
-level.40=طيران: غلاف دخول غلاف جوي (تسخين ρV)
-level.41=اقتصاد: فقاعة الدوت كوم والانهيار (مؤشر توضيحي)
-level.42=اقتصاد: أزمة 2008 والتعافي (مؤشر توضيحي)
-level.43=الزعيم: شريحة هروب ماندلبروت (كسيري)
-level.44=فيزياء C: الديناميكا الحرارية (P–V أديباتي، γ من N)
-level.45=زعيم: لولب النسبة الذهبية (قطبي لوغاريتمي)
-level.46=تحويلات: فورييه — طيف sinc
-level.47=تحويلات: لابلاس — تضاؤل أسي
-level.48=زعيم: ماندلبروت — الختام (شريحة هروب كسيرية)
-level.49=زعيم: فراشة لورينز — الختام (جذاب غريب)
+level.34=فيزياء C: الديناميكا الحرارية (P–V أديباتي، γ من N)
+level.35=طيران: رفع C_L(α) خطي + انفصال
+level.36=طيران: قطب السحب (طفيلي، مُستحثّ، إجمالي)
+level.37=طيران: جو متساوي الحرارة ρ(h)
+level.38=طيران: حركة مجنحة / اهتزاز مُخمَّد
+level.39=طيران: نيوتوني Cp ~ sin²α
+level.40=طيران: Strouhal / نبرة انبعاث دوامات
+level.41=طيران: غلاف دخول غلاف جوي (تسخين ρV)
+level.42=اقتصاد: فقاعة الدوت كوم والانهيار (مؤشر توضيحي)
+level.43=اقتصاد: أزمة 2008 والتعافي (مؤشر توضيحي)
+level.44=تحويلات: فورييه — طيف sinc
+level.45=تحويلات: لابلاس — تضاؤل أسي
+level.46=زعيم: لولب النسبة الذهبية (قطبي لوغاريتمي)
+level.47=زعيم: ماندلبروت — الختام (شريحة هروب كسيرية)
+level.48=زعيم: جاذب لورينز — نظرية الفوضى (جذاب غريب)
+level.49=زعيم: ثقب أسود — بئر جاذبية (مقطع 1/r)
 level.50=فيزياء C: نابض–كتلة حركة توافقية (قانون هوك، بلا تخميد)
+level.51=Big O: O(1) — constant time
+level.52=Big O: O(log n) — logarithmic growth
+level.53=Big O: O(√n) — sublinear root growth
+level.54=Big O: O(n) — linear growth
+level.55=Big O: O(n log n) — n log n growth
+level.56=Big O: O(n²) — quadratic growth
+level.57=Big O: O(n³) — cubic growth
+level.58=Big O: O(2ⁿ) — exponential (base 2)

First Principles/Assets/Resources/Localization/cs.txt

@@ -7,10 +7,11 @@ level_select.cat.integration=Mult proměnné a integrály
 level_select.cat.engineering=Inženýrství
 level_select.cat.ap_bc=AP Calculus BC a fyzika C
 level_select.cat.aerospace=Letectví a kosmonautika
-level_select.cat.finale=Pokročilé a boss
+level_select.cat.economics=Ekonomie
 level_select.cat.transforms=Transformace
 level_select.cat.final_boss=Finální boss
 level_select.cat.spring_physics=Pružina a SHM
+level_select.cat.big_o=Notace Big O
 ui.math_tips=Tipy k matematice
 ui.back_menu=Zpět do menu
 ui.graphing_calculator_mode=Grafická kalkulačka
@@ -24,17 +25,14 @@ ui.jump=Skok
 ui.move=Pohyb
 ui.keyboard_hint_mobile=<size=90%><color=#5c6577>(klávesnice: šipky / Mezerník)</color></size>
 hud.stage=FÁZE
-controls.mobile=<color=#7a8399>Pohyb</color>  <b><color=#ffd978>◀ ▶</color></b>  <color=#5c6577>·</color>  <color=#7a8399>Skok</color>  <b><color=#ffd978>klepnutí</color></b>  <size=90%><color=#5c6577>(klávesnice: šipky / Mezerník)</color></size>
-controls.desktop=<color=#7a8399>Pohyb</color>  <b><color=#ffd978>←</color></b>  <b><color=#ffd978>→</color></b>  <color=#5c6577>·</color>  <color=#7a8399>Skok</color>  <b><color=#ffd978>Mezerník</color></b>
-controls.calculator=<color=#7a8399>Grafická kalkulačka</color>  <b>Zadejte f(u)</b>  ·  <b>Trans</b>  ·  <b>Měřítko</b>  ·  <b>Špetka</b>  ·  <b>Zpět</b>
 graph.label_fu=f(u) =
 graph.placeholder=x^2 + sin(x) · ln(x) pro x>0 · min(x,3)...
 graph.status_enter=Enter / klepněte mimo pro graf
 graph.status_graphed=<color=#8fd9b3>Vykresleno</color>
 graph.line1=<b>Režim grafické kalkulačky</b>
 graph.line2=<size=88%><color=#c4d0e8>Napište <b>f(u)</b> níže (proměnná <b>x</b> v poli = vnitřní u). Pak:</color></size>
 graph.line3=<size=92%><b>Trans</b> → {0} · dvojité klepnutí <b>+</b> · podržte <b>−</b> · <b>Měřítko</b> přiblížení / podržte oddálení · <b>špetka</b> dvěma prsty</size>
-graph.line4=<size=88%><color=#a8b2d1>A={0} &nbsp;k={1} &nbsp;C={2} &nbsp;D={3} &nbsp;&nbsp;x v [{4},{5}]</color></size>
+graph.line4=<size=88%><color=#a8b2d1>A={0}  k={1}  C={2}  D={3}   x v [{4},{5}]</color></size>
 graph.param_a=A (svislé měřítko)
 graph.param_k=k (vodorovné měřítko)
 graph.param_c=C (svislý posun)
@@ -85,20 +83,28 @@ level.30=BC: fáze a SHM (výměna energie)
 level.31=BC: kubická a inflexe (náčrt)
 level.32=BC: b^x a d/dx b^x
 level.33=Kružnice: (x−h)² + (y−k)² = R²
-level.34=Aerospace: vztlak C_L(α) lineární + vývrt
-level.35=Aerospace: polára odporu (parazitní, indukovaná, celková)
-level.36=Aerospace: isotermická atmosféra ρ(h)
-level.37=Aerospace: fugoid / tlumený režim výška–klopení
-level.38=Aerospace: Newtonovské Cp ~ sin²α
-level.39=Aerospace: Strouhal / tón von Kármána
-level.40=Aerospace: obal útlumu při vstupu (ρV teplo)
-level.41=Ekonomika: bublina dot-com a pád (stylizovaný index)
-level.42=Ekonomika: krize 2008 a oživení (stylizovaný index)
-level.43=BOSS: řez úniku Mandelbrota (fraktálová nálada)
-level.44=Fyzika C: termodynamika (adiabatické P–V, γ z N)
-level.45=BOSS: zlatá spirála (logaritmická polární)
-level.46=Transformace: Fourier — sinc (spektrum)
-level.47=Transformace: Laplace — exponenciální pokles
-level.48=BOSS: Mandelbrot — finále (fraktálový únikový řez)
-level.49=BOSS: Lorenzův motýl — finále (podivný atraktor)
-level.50=Fyzika C: pružina–hmota SHM (Hookeův zákon, bez tlumení)
+level.34=Fyzika C: termodynamika (adiabatické P–V, γ z N)
+level.35=Aerospace: vztlak C_L(α) lineární + vývrt
+level.36=Aerospace: polára odporu (parazitní, indukovaná, celková)
+level.37=Aerospace: isotermická atmosféra ρ(h)
+level.38=Aerospace: fugoid / tlumený režim výška–klopení
+level.39=Aerospace: Newtonovské Cp ~ sin²α
+level.40=Aerospace: Strouhal / tón von Kármána
+level.41=Aerospace: obal útlumu při vstupu (ρV teplo)
+level.42=Ekonomika: bublina dot-com a pád (stylizovaný index)
+level.43=Ekonomika: krize 2008 a oživení (stylizovaný index)
+level.44=Transformace: Fourier — sinc (spektrum)
+level.45=Transformace: Laplace — exponenciální pokles
+level.46=BOSS: zlatá spirála (logaritmická polární)
+level.47=BOSS: Mandelbrot — finále (fraktálový únikový řez)
+level.48=BOSS: Lorenzův atraktor — teorie chaosu (podivný atraktor)
+level.49=BOSS: černá díra — gravitační jáma (řez ∝ 1/r)
+level.50=Fyzika C: pružina–hmota SHM (Hookeův zákon, bez tlumení)
+level.51=Big O: O(1) — constant time
+level.52=Big O: O(log n) — logarithmic growth
+level.53=Big O: O(√n) — sublinear root growth
+level.54=Big O: O(n) — linear growth
+level.55=Big O: O(n log n) — n log n growth
+level.56=Big O: O(n²) — quadratic growth
+level.57=Big O: O(n³) — cubic growth
+level.58=Big O: O(2ⁿ) — exponential (base 2)