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This item is a game information page
It belongs to categories: Orthodox chess, 
It was last modified on: 2010-01-23
 By Charles  Gilman. Cyclohex. 3-player round hex variant. (24x5, Cells: 120) [All Comments] [Add Comment or Rating]
Charles Gilman wrote on 2011-02-14 UTC
Actually you don't need to take my word for it about root 7, just the word of whichever mathematician it was - I cannot remember offhand - who extrapolated Pythagoras' theorem to
	a²+b²-2ab cosine(internal angle between a and b)=c²
for any sides of any triangle. For an internal angle of 180° - straight on - this renders c² as a²+b²+2ab which many will recognise as indeed the formula for (a+b)². Likewise for 0° - doubling back - it gives a²+b²-2ab which many will recognise as the formula for (a-b)². For 90° it gives Pythagoras' original a²+b². For 120° it gives a²+b²+ab. In the case of the Sennight this is 2²+1²+(2x1)=7.