In practice, it proved difficult to avoid these pesky close encounters eg. bottom right in https://www.dropbox.com/s/yl819xpiy716qwh/fano7pt7rg_1.gif?dl=0 The set of plane configurations has dimension 4, so in principle there might even be a finite number of (possibly complex or degenerate) configurations with 4 such "accidental" extra coincidences . WFL On 6/24/15, Bill Gosper <billgosper@gmail.com> wrote:

Is it possible to get that close point (https://www.dropbox.com/s/ymf2f9k4mcgmhac/fano7pt7rg.gif?dl=0) to actually lie on the circle? Then it would lie on four circles, and be the fourth point of one of them. Presumably this fails the definition of a Fano Plane, but does it have the (projective?) properties that motivated the definition? Seems to me like an interesting object, if it exists. --rwg On 6/23/15, Dan Asimov <asimov@msri.org> wrote:

By the way, is this 4th point's closeness really a problem?

WFL> It's largely an aesthetic matter: such collisions do make the diagram difficult to interpret.

And, is it really close in R^3 or only close in the displayed projection?

WFL> Note that all configurations so far constructed by myself are _planar_!

[ DWW has raised the question of whether they might be "shaken out" (as it were) so as to properly occupy 3-space --- which appears likely, though I do not currently know for sure. ] DanA>

Just clicked on this but got a 404 "The file you are looking for has either moved or been deleted: error."

Synching error apparently --- try instead https://www.dropbox.com/s/jeyqj76ng4z42s7/fano7pt7rg_2.gif?dl=0

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