Honam Mathematical J. 36 (2014), No. 2, pp. 233–251 http://dx.doi.org/10.5831/HMJ.2014.36.2.233 POSITION VECTOR OF SPACELIKE SLANT HELICES IN MINKOWSKI 3-SPACE Ahmad T. Ali ∗ and S. R. Mahmoud Abstract. In this paper, position vector of a spacelike slant he- lix with respect to standard frame are deduced in Minkowski space E 3 1 . Some new characterizations of a spacelike slant helices are presented. Also, a vector differential equation of third order is constructed to determine position vector of an arbitrary spacelike curve. In terms of solution, we determine the parametric repre- sentation of the spacelike slant helices from the intrinsic equations. Thereafter, we apply this method to find the parametric represen- tation of some special spacelike slant helices such as: Salkowski and anti-Salkowski curves. 1. Introduction Helix is the most fascinating curve in science and nature. Scientists have long held a fascination, sometimes bordering on mystical obsession for helical structures in nature. Helices arise in nanosprings, carbon nanotubes, α−helices, DNA double and collagen triple helix, the double helix shape is commonly associated with DNA, since the double helix is structure of DNA, [1, 2]. This fact was published for the first time by Watson and Crick in 1953 [3]. They constructed a molecular model of DNA in which there were two complementary, antiparallel (side-by-side in opposite directions) strands of the bases guanine, adenine, thymine and cytosine, covalently linked through phosphodiesterase bonds [4, 5]. In the fields of computer aided design and computer graphics, helices can be used for the tool path description, the simulation of kinematic motion or design of highways, etc. [6]. Received January 3, 2014. Accepted June 5, 2014. 2010 Mathematics Subject Classification. 53C40, 53C50, 53A04. Key words and phrases. Minkowski 3-space, slant helix, intrinsic equations. * Corresponding author