# Marble Run

> A self-contained browser page about the oldest question a marble run poses: between two fixed
> points, which track gets the marble down first? Race four tracks, shape your own, and watch a
> numerical search rediscover the answer without ever being told it.

URL: https://marble-run.skillsafe.ai/

## What it does

- **Race** — four tracks joining the same start and finish (straight ramp, circular arc,
  parabola, and the curve of fastest descent), four marbles released together, timed to the
  millisecond. Optionally a fifth track you shape yourself with draggable handles.
- **Equal time** — six marbles at six different heights on one track, released at once. On the
  right curve they land together from every height; on the two near-miss shapes they do not.
- **Workshop** — the numbers: a convergence table for the search, two independent cross-checks
  (a refraction construction from optics, a Runge-Kutta integration of Newton's second law),
  the regime in which a straight ramp is good enough, and what changes when the body rolls
  rather than slides.

## The headline finding

The steepest ramp is not the fastest way down. A longer, curved track beats the straight line
between the same two points, and the margin depends only on the aspect ratio of the drop — how
far the finish is sideways compared with how far it is down. At equal sideways and downward
distance the straight ramp is about 9.5% slower; when the finish is twice as far sideways as it
is down, about 25% slower. The penalty falls below 1% only when the drop is at least about 3.5
times the sideways distance — that is the regime in which a straight ramp really is good enough.

A rolling marble does **not** change which curve wins. Rolling replaces gravity by a smaller
constant (5g/7 for a solid sphere), and a constant rescales every candidate track by the same
factor, so the shape of the winner is untouched; a marble is just uniformly sqrt(7/5) slower.
Re-running the whole search under each body confirms it to eight decimal places.

## What it is not

No account, no sign-in, no network request of any kind, no model call, no credits, no cookies,
no analytics. Everything runs in the page. No third-party library is loaded or vendored.

## Provenance

Historical and physical facts are tagged on the page and sourced to English Wikipedia's articles
on the brachistochrone curve, the tautochrone curve and the cycloid. Everything about rolling
bodies is derived and verified numerically here, not quoted: those articles say nothing about
moments of inertia. Every figure in the Workshop is generated by the project's test harness.

## Attribution

A marble run is a generic toy with no single author. The question it poses was answered by
Huygens (1659), Bernoulli (1696) and Newton (1697), after Galileo got it wrong in 1638. See
/CREDITS.txt, which also records the trade-mark register search made for the name.