@jamestanton Yes. The circle through three points can be seen as the cross section of a sphere. If imagined as the cross section of an ever expanding sphere, all other points not in the plane of the first three will at some instant be found on the surface.
@jamestanton Intuitively, from the fixed point let the second vertex travel around the curve. The third vertex that forms the triangle must cross inside to outside the curve - hence yes, always true.
@AIsonArt To clarify, someone asked, the sliders allow adjustment of the numbers of points and the different multipliers. I was looking for modulo bases that created particular ‘clover leaf’ patterns, which can be explored but it throws up much more interesting complexity. #geogebra
@AIsonArt Very nice. A while back I spent some time looking for the patterns develop in these types of diagrams and created this https://t.co/7BAziPJkOK to delve about in the numbers. Without the hand drawn beauty of course but throws up some wonderful results.
Valentine on the North-East Face of Liskamm (4527m).
At three kilometres wide, the magnificent north-east face of Liskamm is one of the biggest ice faces in the Pennine Alps, first climbed by Ludwig Norman-Neruda, guided by Christian Klucker and Josef Reinstadler in 1890.