For a set of this many mutually tangent circles, Descartes' theorem gives the radius of one of them given the rest.
Using Knuth's notation, this number can be written as 2, followed by 5 up arrows, followed by another 2. For a set of this many mutually tangent circles, Descartes' theorem gives the radius of one of them given the rest. The only case of Fermat's last theorem actually proved by Fermat is when n equals this number. This is the smallest number of elements in a non-cyclic group; that group is named for Felix (*) Klein. This is the largest degree of polynomials for which there is a general solution, by the Abel-Ruffini theorem. Appel and Haken were assisted by a computer in proving that only this many colors were needed to color a map. This is the smallest number of vertices a Platonic solid can have. For 10 points, give this number of faces of a tetrahedron.
Using Knuth's notation, this number can be written as 2, followed by 5 up arrows, followed by another 2.
four