# A Circle-Stacking Theorem

Bottle stacking in a wine rack leads to a delightful and unexpected result. However mathematics does not end there. A. Brown has observed that if the bottles form a pyramid then the center of the top bottle always projects onto the midpoint of the base.

### Theorem

Let N > 1 and place N bottles of equal radius into a rack capable of holding N, but not

What if applet does not run? |

In fact even more is true. The heavy broken lines (make sure the Hint box is checked) formed by connecting the first and the last bottles of successive layers can be obtained from each other by reflection and translation. A. Brown's *Circle-Stacking Theorem* is then obtained as a simple corollary. We'll do that elsewhere with a proof without words.

### References

- A Circle-Stacking Theorem
- A Property of Rhombi
- Bottles in a Slanted Rack
- Bottles in a Wine Rack
- More Bottles in a Wine Rack
- Proofs and Generalizations

|Activities| |Contact| |Front page| |Contents| |Geometry|

Copyright © 1996-2018 Alexander Bogomolny

71047736