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On the number of tubes touching a sphere or a tube

Starostin, EL; (2006) On the number of tubes touching a sphere or a tube. Geometriae Dedicata , 117 (1) pp. 47-64. 10.1007/s10711-005-9010-7. Green open access

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Abstract

A problem is formulated about how many unit-radius tubes can toucha ball of given radius from the outside and from the inside. Upper bounds for themaximum numbers of contacts are obtained for both interior and exterior contacts.It is also shown that the maximum number of unit-radius tubes touching the sameorthogonal cross-section of a particular tube of radius P is [?(arcsin(P + 1)-1)-1]and if the number of contacts takes on its maximum, then all tubes are locallyaligned.

Type: Article
Title: On the number of tubes touching a sphere or a tube
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s10711-005-9010-7
Additional information: Imported via OAI, 7:29:01 16th May 2006
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
URI: https://discovery.ucl.ac.uk/id/eprint/1396
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