# Approximation of convex bodies by rectangles

@article{Lassak1993ApproximationOC, title={Approximation of convex bodies by rectangles}, author={Marek Lassak}, journal={Geometriae Dedicata}, year={1993}, volume={47}, pages={111-117} }

For every plane convex body there is a pair of inscribed and circumscribed homothetic rectangles. The positive ratio of homothety is not greater than 2.

## 22 Citations

### Translative covering a convex body by its homothetic copies

- Mathematics
- 2003

Any sequence of positive homothetic copies of a planar convex body C with total area not smaller than 6.5 times the area of C permits a translative covering of C.

### Translative packing of a convex body by sequences of its positive homothetic copies

- Mathematics
- 2007

Every sequence of positive homothetic copies of a planar convex body C whose total area does not exceed a quarter of the area of C can be translatively packed in C.

### Approximation of convex sets by polytopes

- Mathematics
- 2008

The survey contains results related to different aspects of polyhedral approximation of convex bodies and some adjacent problems.

### Translative Covering by Sequences of Homothetic Copies

- Mathematics
- 2001

Every convex disk with unit area can be translatively covered by any sequence of homothetic copies with total area 8.

### Approximation of convex bodies by axially symmetric bodies

- Mathematics
- 2002

We present an analog of the well-known theorem of F. John about the ellipsoid of maximal volume contained in a convex body. Let C be a convex body and let D be a centrally symmetric convex body in…

### Relationships between widths of a convex body and of an inscribed parallelotope

- MathematicsBulletin of the Australian Mathematical Society
- 2001

Assume that a parallelotope P is inscribed in a three-dimensional convex body C A conjecture says that , where Wi is the ratio of the width of C to the width of P for the direction perpendicular to…

### Inner and outer approximation of convex sets using alignment

- MathematicsOptim. Lett.
- 2016

We show that there exists, for each closed bounded convex set C in the Euclidean plane with nonempty interior, a quadrangle Q having the following two properties. Its sides support C at the vertices…

### TRANSLATIVE PACKING OF A CONVEX BODY BY SEQUENCES OF ITS HOMOTHETIC COPIES

- Mathematics
- 2008

Every sequence of positive or negative homothetic copies of a planar convex body C whose total area does not exceed 0.175 times the area of C can be translatively packed in C. Let C be a planar…

### Largest Inscribed Rectangles in Geometric Convex Sets

- Computer Science, MathematicsArXiv
- 2019

This work considers the problem of finding inscribed boxes and axis-aligned inscribed boxes of maximum volume, inside a compact and solid convex set, and presents an exact optimization algorithm which solves the problem in $\mathcal{O}(d^3+d^2n)$ time, where d is the dimension and n is the number of inequalities defining the conveX set.

## References

SHOWING 1-5 OF 5 REFERENCES