Lie group vs Physics Playground App

This app represents Lie algebra and Lie group. You can have some understanding for Lie algebra and Lie group.

Physics & Math, made playable. Touch a slider and watch the equation rewrite itself. Tilt a ramp and feel the friction. Aim a cannon, dial in a Lorentz factor, swing a double pendulum into chaos. Every idea has a hands-on playground that responds in real time. One app. The entire universe of physics and math - from counting blocks to category theory, from throwing a ball to the Theory of Everything. WHAT'S INSIDE • 55+ topics across Physics and Math, organized by tier - Classical, Modern, Frontier, plus Math Foundations, Intermediate, and Frontier. • A live difficulty slider that rewrites every explanation in real time for Child, Teen, Undergrad, or PhD. • Interactive playgrounds for every topic. Sliders, simulations, force diagrams, and SpriteKit physics that actually behave like physics. • Mini-games that earn you badges - predict chaos, balance crates, dial in gamma, win at quantum measurement, escape a black hole. • A concept map that shows how every idea connects to every other - drag, zoom, tap a node and dive in. • A constellation of earned badges that grows as you master the subjects. PHYSICS, FROM "WHAT IF" TO "WHY" Newton's Laws. Projectile motion. Energy & momentum. Orbits. Waves. Pendulum chaos. Thermodynamics. Fluids. Optics. Electromagnetism. Special Relativity. Spacetime. Photoelectric effect. Double-slit. Heisenberg uncertainty. Quantum tunneling. Stern-Gerlach spin. Atomic orbitals. The Standard Model. Statistical mechanics. Condensed matter. Lasers. Black holes. The Big Bang. String theory. Loop quantum gravity. Entanglement. Quantum computing. And the prize at the end - a Theory of Everything badge for mastering them all. MATH THAT BUILDS Counting → addition → subtraction → multiplication → division → fractions → decimals → percents and ratios → the number line. Then algebra, geometry, trigonometry, functions, exponents and logs, sequences, probability, and statistics. Then limits, derivatives, integrals, linear algebra, differential equations, complex analysis, topology, and category theory. HOW IT WORKS Pick a topic. Read a leveled explanation that matches your background. Scroll to the live equation strip and watch the variables update as you drag. Play with the simulator. Take on the challenge, earn the badge. Tap a related topic to follow the thread - every page links to its prerequisites and to the ideas it unlocks. BUILT FOR FOCUS • Beautiful, calm visuals on a deep-space backdrop. • Smooth 60fps animations, gentle haptics, and confetti for the wins. • No ads. No accounts. No tracking. • Designed for iPhone and iPad with full split-view support. • Offline-first - everything is on device. WHO IT'S FOR Curious kids who want to know what makes things go. Students who'd rather feel an equation than memorize it. Self-learners coming back to math years later. Grad students looking for the cleanest one-page mental model of a topic. Teachers and parents who want a single shareable demo for any concept that comes up. If you've ever wondered why airplanes turn the way they do, why time slows down at high speeds, why a pendulum can be predictable AND chaotic, or what a quantum bit actually is - this is the app. One scroll. One slider. One badge at a time. The universe, unlocked.