Venn diagram with increasing numbers of sides. They are also two-dimensional representations of hypercubes. Henry John Stephen Smith devised similar "n"-set diagrams using sine curves with the series of equations Charles Lutwidge Dodgson (aka Lewis Carroll) devised a five-set diagram known as Carroll's square. Joaquin and Boyles, on the other hand, proposed supplemental rules for the standard Venn diagram in able to account for certain problem cases. For instance, regarding the issue of representing singular statements, they suggest to consider the Venn diagram circle as a representation of a set of things, and use first-order logic and set theory to treat categorical
Neil Dodgson he worked on image resampling supervised by Neil Wiseman and graduating with a PhD in 1992. Dodgson worked for many years on stereoscopic 3D displays, conducting research principally into autostereoscopic methods. He has contributed to several surveys of the field and has been on the committee of the annual Stereoscopic Displays and Applications conference since 2000, co-chairing the conference four times. With Malcolm Sabin, Dodgson has worked on subdivision surfaces since 2000. Dodgson's team produced the NURBS-compatible subdivision method in 2009. Dodgson has supervised almost twenty research students for PhDs. Dodgson also takes an interest in abstract art. Neil Dodgson