In Euclidean geometry, this is the number of points required to completely define a conic.  This is the number of sides on the convex polygon with the same number of sides as diagonals. This is the only number which is included in two pairs of twin primes. According to the Abel-Ruffini theorem, general polynomials of this degree and higher cannot be solved analytically. The square root of this number appears in the defini
In Euclidean geometry, this is the number of points required to completely define a conic.  This is the number of sides on the convex polygon with the same number of sides as diagonals. This is the only number which is included in two pairs of twin primes. According to the Abel-Ruffini theorem, general polynomials of this degree and higher cannot be solved analytically. The square root of this number appears in the definition of the golden ratio. Euclid proposed this many postulates of geometry in the Elements. This is the number of Platonic solids. For 10 points, give this number of sides on a pentagon. 
In Euclidean geometry, this is the number of points required to completely define a conic.  
five