KAKURAKU vs Math Surface

KAKURAKU is an interactive educational app for experiencing probability paradoxes through hands-on simulation. The 10th installment in the SUUGAKU / BUTURAKU / DENRAKU / HARAKU / NETURAKU / KORAKU / RYURAKU series. The theme is "probability." Experience 12 famous probability paradoxes through four interactive phases. [4 Phases for Deep Understanding] 1. Intuition Quiz Answer with your gut feeling first. Most people get it wrong. 2. Simulation Run hundreds of trials and see the results with your own eyes. 3. Explanation Why does intuition fail? Mathematical explanations bring that "aha" moment. 4. Comprehension Check Test your true understanding with applied questions. [12 Probability Paradoxes] 1. The Door Trap — Monty Hall Problem (switching wins 2/3 of the time?) 2. Miracle Classroom — Birthday Paradox (50%+ chance with just 23 people?) 3. The Gold Box — Bertrand's Box (your 1/2 intuition is wrong?) 4. Reversal Statistics — Simpson's Paradox (parts and whole tell opposite stories?) 5. Envelope Dilemma — Two Envelope Problem (should you always switch?) 6. Test Trap — False Positive Problem (positive result yet only 16% infected?) 7. Sleeping Princess — Sleeping Beauty Problem (1/2 or 1/3? Still unsolved) 8. Endless Bus — Bus Waiting Paradox (average 5 min but you wait 10?) 9. Red Streak — Gambler's Fallacy (black is "due" next?) 10. Infinite Gamble — St. Petersburg Paradox (infinite expected value?) 11. Warden's Verdict — Three Prisoners Problem (does A's fate change?) 12. The Predictor's Boxes — Newcomb's Paradox (one-box or two-box?) [Features] - Interactive simulations — see it to believe it - Run single trials, 100x batches, or 1000x batches to watch probabilities converge - Live formulas and numerical values - Dark mode / Light mode - Japanese / English support - Works offline (network is used only for ad delivery) [Monetization & Ads] - This app is free to download and use - No in-app purchases, no subscriptions, no paid unlocks - A banner ad (Google AdMob) is shown at the bottom of the screen - An interstitial ad may be shown when you clear a stage - On iOS, personalized ads are only delivered after the user grants App Tracking Transparency (ATT) permission [Recommended For] - Students studying probability and statistics - Anyone curious about the gap between intuition and mathematics - Teachers looking for interactive teaching materials - Anyone who wants to truly internalize "why is it that way?"

3D surfaces, 2D curves, the complex plane, probability — all in one app. Type a formula and watch it come alive. Perfect for study, exploration, or just enjoying the beauty of math. Description: MathSurface turns equations into shapes you can hold, spin, and slice. It's a math playground for iPhone and iPad — designed for students, curious minds, and anyone who learns better by seeing. ■ Features • 3D surface plots: visualize z = f(x, y) with smooth rotation and pinch-to-zoom • 2D function plots: explicit y = f(x) or implicit 0 = F(x, y) curves • Complex plane: loci such as |z − α| = r, arithmetic operations, powers, and n-th roots of unity • Probability distributions: binomial and normal, controlled by live sliders • Surface of revolution: spin any 2D curve around the x- or y-axis (rendered with SceneKit) • Cross sections: slice any 3D surface with a plane and see the resulting curve • Compare mode: overlay two functions in the same plot • Preset gallery: paraboloid, monkey saddle, Mexican hat, lemniscate, and many more • Favorites: save your own custom expressions for instant recall ■ Who it's for • High school and university students studying calculus, analysis, or probability • Teachers looking for live visual aids • Anyone curious about how a formula actually looks • People who just enjoy beautiful math A custom Liquid Glass–style formula keyboard makes entering sin, cos, √, π, and friends quick and natural. The dark neon UI keeps the math front and center.