MY ARTICLES "MATHEMATICAL CURIOSITIES" IN SIAM NEWS

 

Heron's formula - a simple derivation

Geometric sum, geometrically

Cauchy-Schwarz, via springs

Knife in the water

Lagrange multipliers and depth

Symmetry and polar decomposition of matrices

A physical interpretation of the  Wronskian

Feynman's flying saucer, II

Feynman's flying saucer, I

Cauchy-Schwarz inequality and a paradox/puzzle

Mirages on the road and the Poincare metric

Which energy is greater?

Getting focused

Opening a wine bottle with a  book

A perspective on altitudes

Orthocenter, Archimedean style

From Archimedes and Euclid to Hamilton and Poincare

Bedford's law and accelerated growth

A bike and a catenary

A boat paradox

The quicker solution to the brachistochrone problem

Measuring curvature with a  bike 

A cycloid is a tautochrone

Downwind, faster than the wind

An electrician's proof of Euler's polyhedral formula

Foucault's pendulum with a twist

Further upon reflections: caustics in a ball

A bike wheel and the Gauss-Bonnet theorem

Gromov's non-squeezing theorem and optics

Heat exchange and some frivolous aspects of e. 

A near-perfect heat exchange

An inverted pendulum: defying gravity and intuition

Kelvin's circulation theorem and an isoperimetric inequality

Particles of negative mass and the Krein-Moser theory

A Lagrange multiplier problem without multipliers

Bulletproof vests and Lie brackets

A minimalist minimizes and integral

Moebius map in hinges, bikes and more

The moon sine

Moser's theorem on Jacobians by diffusion

Focusing on nephroids

Parabola of safety and the Jacobian

Measuring areas with a shopping cart

Pythagorean theorem on ice

Reflecting on reflections

Riemann Mapping by steepest descent

Slings, bullets and blow-up

Some light geometry

Newtonian dynamics = spring theory

Symmetric metrics and a little work

Telescopes and symplectic maps

Perpetual motion and the Theorem of Cosines

The thin lens formula and springs 

A water-based solution of polynomial equations

 

EXPLORING THE UNKNOWN

LEARNING BY DOING

A THEORY COMPARISON

EXPLORING THE UNKNOWN

LEARNING BY DOING

A THEORY COMPARISON

EXPLORING THE UNKNOWN

 

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