We survey the results on surfaces which contain many circles. First, we give two analyses of shapes which always look round. Then we introduce the Blum conjecture: “A closed surface in E³ which contains seven circles through each point is a sphere”, and give some partial affirmative results toward the conjecture. Moreover, we study some surfaces which contain many circles through each point, for example, cyclides.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc82-0-14,
author = {Nobuko Takeuchi},
title = {Surfaces which contain many circles},
journal = {Banach Center Publications},
volume = {83},
year = {2008},
pages = {201-207},
zbl = {1154.53005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc82-0-14}
}
Nobuko Takeuchi. Surfaces which contain many circles. Banach Center Publications, Tome 83 (2008) pp. 201-207. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc82-0-14/