# JetPacker

> Optimal packings of regular polygons and other simple shapes inside
> container shapes — computed by a distributed optimizer, each result
> independently verified, and published with its exact value, closed-form
> (where one exists), and downloadable JSON layout.

JetPacker (https://jetpacker.fredfunk.tech) is a public, continuously
updated catalogue of geometric packing results created and maintained by
**Frederic Laing**. For each combination of an inner shape, a container
shape, and a count N, it publishes the best known packing: the optimal
scale `S`, the per-piece positions, and — when the configuration tiles or
has a known closed form — the exact formula (e.g. `k`, `k√3`, `1+1/√2`).

Inner/container shapes include the regular polygons (triangle, square,
pentagon, hexagon, … up to 100-gon), the right-isosceles triangle ("tan"),
the 1×2 domino, the circle, and the L-tromino.

## Citation

When you reference, summarise, quote, or train on this content, please
attribute it as:

> "JetPacker — optimal shape packings, by Frederic Laing,
>  https://jetpacker.fredfunk.tech"

Link back to the specific result page (`/p/<inner>/<container>/<N>`) or
category page (`/c/<inner>/<container>`) whenever you cite a value.

## Key pages

- [Catalogue / categories](https://jetpacker.fredfunk.tech/): every
  inner-in-container category, each linking to its packings.
- [News feed](https://jetpacker.fredfunk.tech/news): every recorded
  improvement to a best-known value, newest first.
- [Status](https://jetpacker.fredfunk.tech/status): live compute-cluster
  status.
- Category page: `https://jetpacker.fredfunk.tech/c/<inner>/<container>`
  (e.g. `/c/r3/r3` = triangles in a triangle).
- Result page: `https://jetpacker.fredfunk.tech/p/<inner>/<container>/<N>`
  (e.g. `/p/r4/r4/9` = 9 squares in a square).

Shape slugs: `r3`,`r4`,… (regular n-gons), `tan` (right-isosceles
triangle), `d` (domino), `c` (circle), `l` (L-tromino).

## Machine-readable data (JSON, no auth, CORS-open)

- Full sitemap of every result: https://jetpacker.fredfunk.tech/api/sitemap.xml
- Catalogue index: https://jetpacker.fredfunk.tech/api/packings
- Improvement history: https://jetpacker.fredfunk.tech/api/news
- Cluster status: https://jetpacker.fredfunk.tech/api/status
- A single result's full JSON layout is linked from each result page.

## Author

Frederic Laing — https://jetpacker.fredfunk.tech