# Definition:Loculus of Archimedes

## Definition

The **loculus of Archimedes** is a dissection of the square into $14$ pieces:

The dissection is constructed as follows:

- $T$ is the midpoint of $BD$
- $C$ is the midpoint of its line
- $M$ is the midpoint of $AG$
- $K$ is on the line $AH$
- $O$ is on the line $BC$.

The object is to rearrange the pieces to form different geometric figures.

## Also known as

The **loculus of Archimedes** is also known as:

- the
**ostomachion** - the
**stomachion** - the
**syntomachion**.

Spellings vary according to the language into which the original Greek is transliterated.

## Examples

### Elephant

Using the shapes in the loculus of Archimedes exactly once each, make the shape of an elephant:

## Also see

- Results about
**the loculus of Archimedes**can be found here.

## Source of Name

This entry was named for Archimedes of Syracuse.

## Historical Note

The **loculus of Archimedes** appears in a fragmentary form in an Arabic manuscript *The Book of Archimedes on the Division of the Figure Stomaschion*.

It also in the *Archimedes Palimpsest* which was discovered by Johan Ludvig Heiberg in $1906$.

Note that the version in the *Archimedes Palimpsest* is presented in rectangular form, and has been transformed here into a square, so as to match its usual presentation.

## Linguistic Note

The word **loculus** is Latin for **little box**.

The word **Ostomachion** derives from the Greek **Ὀστομάχιον**, which means **bone-fight**, from **ὀστέον** (**osteon**), meaning **bone**, and **μάχη** (**mache**), which means **fight**, **battle**, or **combat**.

That is, it is a **combat** (with the mind), a **puzzle**, whose tools are pieces manufactured out of **bones**, or pieces of ivory.

The word **Stomachion**, which appears in some ancient manuscripts, appears to be a corruption of **Ostomachion**.

While some sources state that **stomachion** derives from the word **stomach** (perhaps because the dissection problems cause disruption to one's digestion), this is believed to be a common mistake.

## Sources

- 1992: David Wells:
*Curious and Interesting Puzzles*... (previous) ... (next): Loculus of Archimedes