N-curve
We take the functional theoretic algebra ''C''[0, 1] of curves. For each loop ''γ'' at 1, and each positive integer ''n'', we define a curve \gamma_n called ''n''-curve. The ''n''-curves are interesting in two ways. #Their f-products, sums and differences give rise to many beautiful curves. #Using the ''n''-curves, we can define a transformation of curves, called ''n''-curving. Multiplicative inverse of a curve A curve ''γ'' in the functional theoretic algebra ''C''[0, 1], is invertible, i.e. : \gamma^ \, exists if : \gamma(0)\gamma(1) \neq 0. \, If \gamma^=(\gamma(0)+\gamma(1))e - \gamma , where e(t)=1, \forall t \in [0, 1], then : \gamma^= \frac. The set ''G'' of invertible curves is a non-commutative group under multiplication. Also the set ''H'' of loops at 1 is an Abelian subgroup of ''G.'' If \gamma \in H, then the mapping \alpha \to \gamma^\cdot \alpha\cdot\gamma is an inner automorphism of the group ''G.'' We use these concepts to define ''n''-curve ...
[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   [Amazon]