Check out Grant Acedrex, our featured variant for April, 2024.

[ Help | Earliest Comments | Latest Comments ]
[ List All Subjects of Discussion | Create New Subject of Discussion ]
[ List Earliest Comments Only For Pages | Games | Rated Pages | Rated Games | Subjects of Discussion ]

Single Comment

Cyclohex. 3-player round hex variant. (24x5, Cells: 120) [All Comments] [Add Comment or Rating]
💡📝Charles Gilman wrote on Mon, Feb 14, 2011 06:49 AM 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.