Home The Atlas of Advanced Mathematics

Reader's Guide

Mathematics and Physics

Euler's Identity The Hyperbolic Plane Euler's Polyhedron Formula Infinitely Many Primes The Prime Number Theorem The Irrationality of √2 The Principle of Stationary Action The Euler–Lagrange Equation Noether's Theorem Bayes' Theorem Maxwell's Equations Einstein's Field Equations Schrödinger's Equation The Dirac Equation

Subatomic Matter Mass in the Quantum World The Hierarchy of Cosmic Structure Cosmology and Astrophysics Glossary

Quantum Technologies

Quantum Foundations and Theory Quantum Information Quantum Algorithms Quantum Communications Quantum Networking Quantum AI Building a Quantum Computer Quantum Hardware Engineering Glossary

Connected Systems

Information Theory Coding Theory Digital Signal Processing Cryptography Graph Theory Network Science 6G: The Mathematical Frontier

Brain

Regions of the Brain

Neuroscience

Computational Neuroscience

Cells and Development

How Cells Find Their Role

Musculoskeletal Atlas

Head and Neck The Spine The Shoulder The Arms The Hands The Abdomen The Hip The Legs The Knee The Foot and Ankle The Feet

The Principle of Stationary Action

Physical trajectories make the action stationary: one principle behind mechanics, optics, relativity, field theory and quantum physics

The Principle of Stationary Action — a thrown ball and six trial paths with their actions, the derivation of the Euler–Lagrange equation, light in a circular mirror with shortest and longest paths, four stationary paths of a pendulum and their Morse indices, a ball's path as a light ray, proper time and the twin paradox, the quantum sum over paths, and the actions of the main physical theories

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