# Mark Levi

Mark Levi ([email protected]) is a professor of mathematics at the Pennsylvania State University.

- "Bike Tracks," Quasi-magnetic Forces, and the Schrödinger Equation
- Perpetual Motion and the Theorem of Cosines
- A Lagrange Multiplier Problem Without Multipliers
- Kelvin’s Circulation Theorem and an Isoperimetric Inequality
- Riemann Mapping by Steepest Descent
- A Minimalist Minimizes an Integral
- Quick! Find a Solution to the Brachistochrone Problem
- A Cycloid is a Tautochrone
- Moser’s Theorem on the Jacobians
- Telescopes and Symplectic Mappings
- Gromov’s Non-squeezing Theorem and Optics
- An Inverted Pendulum: Defying Gravity (and Intuition)
- Classroom Notes: Symmetric Matrices and (a Little) Work
- A Boat Paradox
- Newtonian Dynamics = “Spring Theory”
- Particles with Negative Mass and the Krein–Moser Theory
- Some Light Geometry
- A Bike Wheel and the Gauss-Bonnet Theorem
- The Thin Lens Formula and Springs
- From Archimedes and Euclid to Hamilton and Poincaré
- Pythagorean Theorem on Ice
- A Bike and a Catenary
- Measuring Curvature with a Bike
- An Electrician’s (or a Plumber’s) Proof of Euler’s Polyhedral Formula
- Foucault’s Pendulum with a Twist
- Benford’s Law and Accelerated Growth
- Parabola of Safety and the Jacobian
- Downwind, Faster Than the Wind
- Reflecting on Reflections
- A Water-based Solution of Polynomial Equations
- Slings, Bullets, Blow-up, and Linearity
- Measuring Areas with a Shopping Cart
- Focusing on Nephroids
- Möbius Map in Hinges, Bikes, Fluids, and Ellipses
- Further Upon Reflection: Caustics in a Ball
- A Perspective on Altitudes
- Orthocenter, Archimedean Style
- The Moon Sine
- Heat Exchange and Some Frivolous Aspects of e
- A Near-perfect Heat Exchange
- Lie Brackets and Bulletproof Vests
- The Vinous Shock: How to Open a Bottle with a Book
- Getting Focused
- Which Energy is Greater?
- Spinning Out
- A Mirage on the Road and the Poincaré Metric
- The Cauchy-Schwarz Inequality and a Paradox/Puzzle
- Feynman’s Flying Saucer Explained
- Feynman’s Flying Saucer: The Second Serving
- Wronskian = Angular Momentum; Abel’s Formula = Newton’s Second Law
- Symmetry and Polar Decomposition by Mechanics
- Lagrange Multiplier as Depth or Pressure
- Balancing a Knife, Euler’s Elastica, and the Mathematical Pendulum
- The Cauchy-Schwarz Inequality via Springs
- Geometric Sum, Geometrically
- A Simple Derivation of Heron’s Formula
- A Coriolis Pair Paradox
- A Western Sunrise
- A Moving Argument
- Hanging Cables and Hydrostatics
- Strolling Through Jacobi Fields
- An Incompetence Problem
- Minimizing the Length — and the Algebra
- Ulam’s Ping-pong, Adiabatic Invariants, and Entropy
- Elliptical Eyes, Eccentricity, and the Speed of Light
- Cosine Addition Formula and Perpetual Motion
- Spinning Tops in Spinning Frames
- Right Results via Wrong Arguments and Wrong Results via Right Arguments
- How Do Snakes Slither? A Recipe for Reptation
- On the Air
- A Pressure Puzzle: More is Less
- Conformal Deformation of Conductors
- Some Shallow Observations
- Astroids Under Water
- A Hamiltonian Look at a Soap Film
- What is Entropy?
- Electrical Resistance and Conformal Maps
- Running in the Rain