A New Generalization of the Steiner Formula and the Holditch Theorem

The Cauchy-Length Formula and Holditch Theorem in the Generalized Complex Plane C_p

“…The formula (4.6) is also the area for the linear points in [5]. Thus, we can give the following corollary.…”

“…In this section, we give a new generalization of the Holditch theorem given by [5] by using non-linear points in the generalized complex plane C p .…”

“…This formula is the area formula given for the linear points in [5]. Namely, the formula (4.5) is generalization of the formula in [5].…”

“…Gürses and Yüce gave the one-parameter planar motion in Affine Cayley-Klein planes and p− complex plane C J = x + Jy : x, y ∈ R, J 2 = p, p ∈ {−1, 0, 1} ⊂ C p in the generalized complex plane C p , [1, 2]. Moreover, Erişir et al calculated the Steiner area formula and proved Holditch theorem in the generalized complex plane C p , [5]. Then, they calculated the polar moment of inertia of trajectories under the oneparameter planar motion and Holditch-type theorem in C p , [6].…”

On Holditch’s theorem

“…Further applications to mechanics were given in [11,12], and [14]. Some additional remarks on Holditch's theorem can be found also in [1,8,9], and [18], and recent related investigations are given in [15,16], and [10].…”