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ON A FABRIC OF KISSING CIRCLES

Part of: Sequences and sets Discrete geometry

Published online by Cambridge University Press:  08 January 2021

VIERA ČERŇANOVÁ Open the ORCID record for VIERA ČERŇANOVÁ [Opens in a new window]
VIERA ČERŇANOVÁ*
Affiliation:
Department of Mathematics and Computer Science, Faculty of Education, Trnava University, Priemyselná 4, P.O. Box 9, 918 43Trnava, Slovakia e-mail: viera.cernanova@truni.sk
*
e-mail: vieracernanova@hotmail.com
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Abstract

Applying circle inversion on a square grid filled with circles, we obtain a configuration that we call a fabric of kissing circles. We focus on the curvature inside the individual components of the fabric, which are two orthogonal frames and two orthogonal families of chains. We show that the curvatures of the frame circles form a doubly infinite arithmetic sequence (bi-sequence), whereas the curvatures in each chain are arranged in a quadratic bi-sequence. We also prove a sufficient condition for the fabric to be integral.

Keywords

curvaturefabric of kissing circlesframeinversion in a circlePL chain

MSC classification

Primary: 52C26: Circle packings and discrete conformal geometry
Secondary: 11B37: Recurrences
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 104 , Issue 2 , October 2021 , pp. 320 - 329
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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References

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