This is an announcement for the paper "Seven views on approximate convexity and the geometry of K-spaces" by Felix Cabello Sanchez, Jesus M. F. Castillo and Pier Luigi Papini. Abstract: As in Hokusai's series of paintings "Thirty six views of mount Fuji" in which mount Fuji's is sometimes scarcely visible, the central topic of this paper is the geometry of $K$-spaces although in some of the seven views presented $K$-spaces are not easily visible. We study the interplay between the behaviour of approximately convex (and approximately affine) functions on the unit ball of a Banach space and the geometry of Banach K-spaces. Archive classification: Functional Analysis Mathematics Subject Classification: 46B20; 52A05; 42A65; 26B25 Remarks: 2 figures The source file(s), ccp.tex: 61322 bytes, cubo.eps: 19389 bytes, kominek.eps: 82795 bytes, is(are) stored in gzipped form as 0505291.tar.gz with size 38kb. The corresponding postcript file has gzipped size 119kb. Submitted from: castillo@unex.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0505291 or http://arXiv.org/abs/math.FA/0505291 or by email in unzipped form by transmitting an empty message with subject line uget 0505291 or in gzipped form by using subject line get 0505291 to: math@arXiv.org.