Document Zbl 0572.52020

Structured Search

Help

Examples

Geometry Search for the term Geometry in any field. Queries are case-independent.

Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.

"Topological group" Phrases (multi-words) should be set in "straight quotation marks".

au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.

Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.

Quasi* map* py: 1989 The resulting documents have publication year 1989.

so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.

"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.

dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.

py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).

la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Fields

any	anywhere
an	internal document identifier
au	author, editor
ai	internal author identifier
ti	title
la	language
so	source
ab	review, abstract
py	publication year
rv	reviewer
cc	MSC code
ut	uncontrolled term
dt	document type (j: journal article; b: book; a: book article)

Operators

a & b	logic and
a \| b	logic or
!ab	logic not
abc*	right wildcard
"ab c"	phrase
(ab c)	parentheses

Harborth, Heiko

Einheitskreise in ebenen Punktmengen. (German) Zbl 0572.52020

Diskrete Geometrie, 3. Kolloq., Salzburg 1985, 163-168 (1985).

[For the entire collection see Zbl 0563.00013.]
Let n points in the plane be given. What is the maximum number f(n) of congruent circles which are determined by non-collinear triples of these points? In a joint paper with Mengersen the author determined \(f(3)=1\), \(f(4)=4\), \(f(5)=4\), \(f(6)=8\) and \(f(7)=12\). In the present article he shows that \(f(8)=16\). The proof is elementary but involved.

Reviewer: P.Gruber

Cited in 1 Document

MSC:

52A37	Other problems of combinatorial convexity
52A10	Convex sets in \(2\) dimensions (including convex curves)
52A40	Inequalities and extremum problems involving convexity in convex geometry

Keywords:

arrangement of points; combinatorial problems; congruent circles

Citations:

Zbl 0563.00013

PDF BibTeX XML