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