kimsh.kr/edu

kimsh.kr/edu
Demonstration Projects

Interactive explorations where abstract mathematics becomes something you can see, hear, and touch. Each project synthesizes its content in real time — no recordings, no pre-rendered assets. Just math.

01 Banach–Tarski: F₂ on S²

The most counterintuitive theorem in mathematics, visualized. Watch the free group F₂ act on the sphere via rotations, and see how a ball can be decomposed and reassembled into two identical copies of itself.

Free Groups Paradoxical Decomposition 3D Visualization
02 Can You Hear the Shape of a Drum?

Mark Kac's famous 1966 question, made audible. Strike virtual drums, see their vibrational modes as Bessel-function eigenstates, and hear why two differently shaped drums can produce identical spectra.

Spectral Geometry Bessel Functions Eigenvalues Modal Synthesis
03 The Mathematics of Sound

From Pythagoras to Fourier to your smartphone. Build waveforms from harmonics, compare tuning systems across instruments, and explore how the cochlea performs frequency analysis — all with live-synthesized audio.

Fourier Analysis Temperament Acoustics Web Audio
04 소리의 수학  Korean edition

The landscape is determined by the geometry that you are living in. We view, roam and imagine hyperbolic spaces, where there is too much room.

한국어 hyperbolic geometry Witten conjecture manifold
05 Living in a Hyperbolic Space  Korean edition

The same interactive exploration of sound, tuning, and Fourier analysis — written for a Korean-speaking audience.

한국어 Fourier Analysis Temperament Acoustics