2018 # The quaternionic expression of ruled surfaces

**Abstract:** In this paper, firstly, the ruled surface is expressed as a spatial
quaternionic. Also, the spatial quaternionic definitions of the Striction
curve, the distribution parameter, angle of pitch and the pitch are given.
Finally, integral invariants of the closed spatial quaternionic ruled
surfaces drawn by the motion of the Frenet vectors {t,n1,n2} belonging to
the spatial quaternionic curve ? are calculated.

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“…Let φ, x and * x be the spatial quaternionic ruled surface, the directrix of this surface and the vectorial moment of x, respectively. Then there exists a point Z , such that [10]:…”

confidence: 99%

“…Let φ, x and * x be the spatial quaternionic ruled surface, the directrix of this surface and the vectorial moment of x, respectively. Then there exists a point Z , such that [10]:…”

confidence: 99%

“…However, the ruled surface was not studied as a quaternionic. Altough in [10], Senyurt and Caliskan investigated the ruled surfaceas quaternoic, the rules surface has not studied as a quaternionic. They have quaternionally calculated the integral invariants of the ruled surface.…”

confidence: 99%

“…A ruled surface is defined as the surface represented by moving a straight line in ℝ 3 , along a space curve defined as the base curve, see [4]. In the literature, there are a lot of studies about the properties of ruled surfaces, see [5][6][7][8][9][10][11][12]. W. K. Clifford pioneered the properties of dual numbers in 1873.…”

confidence: 99%

“…In 3 , a ruled surface is a curved surface represented by moving a straight line along a space curve called the base curve [4]. In literature, ruled surfaces have been widely studied by different authors [5][6][7][8][9][10].…”

confidence: 99%