@article{oai:u-ryukyu.repo.nii.ac.jp:02000878, author = {Maehara, Hiroshi}, journal = {European Journal of Combinatorics}, month = {}, note = {The purpose of this note is to present an elementary proof of the fact that no more than twelve unit balls can simultaneously touch a unit ball in 3-space,a proof that is accessible for undergraduates., 論文}, title = {The problem of thirteen spheres : A proof for undergraduates}, year = {2006} }