## Experimental Mathematics

- Experiment. Math.
- Volume 5, Issue 2 (1996), 139-159.

### Packing lines, planes, etc.: packings in Grassmannian spaces

John H. Conway, Ronald H. Hardin, and Neil J. A. Sloane

#### Abstract

We address the question: How should $N$ $n$-dimensional subspaces of $m$-dimensional Euclidean space be arranged so that they are as far apart as possible? The results of extensive computations for modest values of $N, n,m$ are described, as well as a reformulation of the problem that was suggested by these computations. The reformulation gives a way to describe $n$-dimensional subspaces of $m$-space as points on a sphere in dimension $\half(m-1) (m+2)$, which provides a (usually) lower-dimensional representation than the Plücker embedding, and leads to a proof that many of the new packings are optimal. The results have applications to the graphical display of multi-dimensional data via Asimov's grand tour method.

#### Article information

**Source**

Experiment. Math., Volume 5, Issue 2 (1996), 139-159.

**Dates**

First available in Project Euclid: 13 March 2003

**Permanent link to this document**

https://projecteuclid.org/euclid.em/1047565645

**Mathematical Reviews number (MathSciNet)**

MR1418961

**Zentralblatt MATH identifier**

0864.51012

**Subjects**

Primary: 52C17: Packing and covering in $n$ dimensions [See also 05B40, 11H31]

Secondary: 65Y25

#### Citation

Conway, John H.; Hardin, Ronald H.; Sloane, Neil J. A. Packing lines, planes, etc.: packings in Grassmannian spaces. Experiment. Math. 5 (1996), no. 2, 139--159. https://projecteuclid.org/euclid.em/1047565645

#### See also

- See editors' note: Editors' note on "Packing lines, planes, etc.: packings in Grassmannian spaces". Experiment. Math. vol. 5, iss. 2, (1997), p.175.Project Euclid: euclid.em/1047650003