Arnold's Cabinet of Curiosities
Vladimir I. Arnold is my favourite mathematician. I created this 3D model of a cabinet to store some of his great mathematical ideas which I found to be most intriguing. Every object and symbol in the cabinet can be related to one of his theorems or proofs, which include: KAM Theorem, Hilbert's 13th Problem, Liouville-Arnold Theorem, adiabatic invariants, topological Galois theory, orthocenters in spherical geometry, geodesics on SO(3) traced by a spinning top, simple proof of Bertrand's Theorem, duality in central fields, singularity theory, Arnold's Stability Theorem, stability of L4 and L5 in the restricted 3-body problem, ABC flow, Arnold's Cat Map, ... , and his bad luck with bicycles (with a wrong model unchanged in one of his books). The citation on the top of the cabinet is extracted from Arnold's famous article "On Teaching Mathematics" (translated by A. V. Goryunov). If you are a mathematician, I hope you could recognize all of them and have fun! If you don't know about any of the math presented here, just simply feel the beauty of it and have much more fun than a mathematician do.
The design of this cabinet is inspired by Walter Wick's wonderful book series "Can You See What I See", which have brought so much happiness to my childhood.
Arnold's Cabinet of Curiosities
Arnold's geometric construction for proving that the alternating group A5 is not soluble. The last step in his elementary proof of the insolvability of quintic equations.
KAM theorem, invariant tori and quasi-periodic orbits.
Proving KAM Theorem involves the iteration of a series of canonical transformations, analogous to Newton's method of finding roots of nonlinear equations. Here, the series of canonical transformations are represented by nesting dolls in the form of cats.
Liouville-Arnold Theorem.
Existence of orthocenters in spherical geometry. Proof by Arnold (originally in the context of hyperbolic geometry) using Jacobi identity.
Arnold's proof of the insolability of the quintic, leading to topological Galois Theory.
The first mathematically rigorous proof of adiabatic invariants is attributed to Arnold. The pendulum example was originally given by Lord Rayleigh.
Special guest invited from Walter Wick's studio to pull the string of the pendulum (unwillingly).