A two-dimensional representation of a Klein bottle--a shape with no inside or outside, just one continuous surface. A true Klein bottle needs at least four dimensions; in other words, it can't be blown from glass. Two- and three-dimensional representations like this one exist to help us visualize the topology, but they are not completely faithful to the original shape. The surface cannot be built in two- or three-dimensional space without self-intersection, as shown here with the "handle" passing through the side of the surface.
Credit: Thomas Banchoff, Brown University, and Davide Cervone, Union College.
Precise control of thedistribution of specific proteins is essential for many biological processes. An LMU team has now described a new model for intracellular pattern formation. Here, the shape of the cell itself plays a ...
S. Schlickum, H. Sennefelder, M. Friedrich, G. Harms, M. Lohse, P. Kilshaw, and M. Schon. Blood, 112 (3):
619-25(August 2008)Schlickum, Stephanie Sennefelder, Helga Friedrich, Mike Harms, Gregory
Lohse, Martin J Kilshaw, Peter Schon, Michael P Research Support,
Non-U.S. Gov't United States Blood Blood. 2008 Aug 1;112(3):619-25.
Epub 2008 May 20..
T. Sederberg, P. Gao, G. Wang, and H. Mu. Proceedings of the 20th annual conference on Computer graphics and interactive techniques, page 15--18. New York, NY, USA, ACM, (1993)
T. Sederberg, and E. Greenwood. Proceedings of the 19th annual conference on Computer graphics and interactive techniques, page 25--34. New York, NY, USA, ACM, (1992)
X. Wu, and J. Johnstone. Computational Science and Its Applications - ICCSA 2006, volume 3980 of Lecture Notes in Computer Science, Springer, Berlin / Heidelberg, (2006)
D. Xu, H. Zhang, Q. Wang, and H. Bao. Proceedings of the 2005 ACM symposium on Solid and physical modeling, page 267--274. New York, NY, USA, ACM, (2005)