NDLI: An interstice relationship for flowers with four petals

Content Provider	Springer Nature Link
Author	Mallows, Colin Guettler, Gerhard Butler, Steve Graham, Ron
Copyright Year	2013
Abstract	Given three mutually tangent circles with bends (related to the reciprocal of the radius) a, b and c respectively, an important quantity associated with the triple is the value $${\langle a,b,c \rangle:=ab+ac+bc}$$ . In this note we show in the case when a central circle with bend b 0 is “surrounded” by four circles, i.e., a flower with four petals, with bends b 1, b 2, b 3,b 4 that either $$\sqrt{\langle b_{0},b_{1},b_{2} \rangle}+\sqrt{\langle b_{0},b_{3},b_{4} \rangle}=\sqrt{\langle b_{0},b_{2},b_{3} \rangle}+\sqrt{\langle b_{0},b_{4},b_{1} \rangle}$$ or $$\sqrt{\langle b_{0},b_{1},b_{2} \rangle}=\sqrt{\langle b_{0},b_{2},b_{3} \rangle}+\sqrt{\langle b_{0},b_{3},b_{4} \rangle}+\sqrt{\langle b_{0},b_{4},b_{1} \rangle}$$ (where $${\langle b_{0},b_{1},b_{2} \rangle}$$ is chosen to be maximal). As an application we give a sufficient condition for the alternating sum of the $${\sqrt{\langle a,b,c\rangle}}$$ of a packing in standard position to be 0. (A packing is in standard position when we have two circles with bend 0, i.e., parallel lines, and the remaining circles are packed in between.)
Ending Page	438
Page Count	18
Starting Page	421
File Format	PDF
ISSN	00472468
e-ISSN	14208997
Journal	Journal of Geometry
Issue Number	3
Volume Number	104
Language	English
Publisher	Springer Basel
Publisher Date	2013-08-31
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Geometry flowers Circle packings and discrete conformal geometry Interstice apollonian petals
Content Type	Text
Resource Type	Article
Subject	Geometry and Topology

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

An interstice relationship for flowers with four petals.

Circle packings as differentiable manifolds

A Conformal Averaging Process on the Circle

Rigidity of circle packings with crosscuts

Approximation of conformal mappings by circle patterns

Effective Circle Count for Apollonian Packings and Closed Horospheres

Links in orthoplicial Apollonian packings

A note on circle patterns on surfaces

Apollonian Circle Packings: Geometry and Group Theory II. Super-Apollonian Group and Integral Packings

An interstice relationship for flowers with four petals

Similar Documents

An interstice relationship for flowers with four petals.

Circle packings as differentiable manifolds

A Conformal Averaging Process on the Circle

Rigidity of circle packings with crosscuts

Approximation of conformal mappings by circle patterns

Effective Circle Count for Apollonian Packings and Closed Horospheres

Links in orthoplicial Apollonian packings

A note on circle patterns on surfaces

Apollonian Circle Packings: Geometry and Group Theory II. Super-Apollonian Group and Integral Packings

An interstice relationship for flowers with four petals