Abstract
Two simple least squares approaches for connecting two carbon nanos-tructures are determined here. We speculate that the basis of joining carbon nanos-tructures is an underlying requirement that each inter-atomic distance be as close as possible to the ideal carbon-carbon bond length, or that the bond angle be as close as possible to the ideal bond angle. Both least squares approaches to bond lengths and to bond angles are applied for three systems, including nanotori formed from two and three distinct carbon nanotube sections, the joining between a carbon nanotube and a flat graphene sheet and nanobuds, which comprise a carbon nanotube joined to a fullerene. Moreover, Euler's theorem is utilised to verify that the correct polygons occur at the connection sites. We comment that these purely geometrical approaches can be formally related to certain numerical energy minimisation methods used by a number of authors.
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