𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the number of cylinders touching a ball

✍ Scribed by Aladár Heppes; László Szabó

Publisher
Springer
Year
1991
Tongue
English
Weight
248 KB
Volume
40
Category
Article
ISSN
0046-5755

No coin nor oath required. For personal study only.

✦ Synopsis

The following problem is due to W. Kuperberg. What is the maximum number of non-overlapping unit cylinders (a set in E 3 consisting of points whose distance from some line does not exceed I) that can be simultaneously tangent to a unit ball? In this paper we prove that this number is at most 8. It is conjectured that this number is 6.

📜 SIMILAR VOLUMES

On the face touching number
On the face touching number
✍ Sanders, Daniel P. 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 399 KB 👁 2 views

In a 3-connected plane graph, each pair of faces meet at at most either a vertex or an edge. Zha considered 3-connected graphs embedded on the projective plane, torus, and Klein bottle, showing that they meet at at most two, at most four, and a t most four vertices or edges, respectively, and demons

On the Maximum Number of Touching Pairs
On the Maximum Number of Touching Pairs in a Finite Packing of Translates of a Convex Body
✍ Károly Bezdek 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 102 KB

Minkowski space M d =(R d , || ||) is just R d with distances measured using a norm || ||. A norm || || is completely determined by its unit ball {x ¥ R d | ||x|| [ 1} which is a centrally symmetric convex body of the d-dimensional Euclidean space E d . In this note we give upper bounds for the maxi