In this work, we study timelike rectifying slant helices in E 3 1. First, we find general equations of the curvature and the torsion of timelike rectifying slant helices. After that, by solving second order linear differential equations, we obtain families of timelike rectifying slant helices that lie on cones.

In this work, we give two methods to generate general helices that lie on the sphere S 2n in Euclidean (2n+1)-space E 2n+1 .

In this paper, we are investigating that under which conditions of the geodesic curvature of unit speed curve γ that lies on the unit sphere, the curve c which is obtained by using γ, is a spherical helix or slant helix.

In this study, we define two types of mappings that preserve the constant angle between the tangent vector field and the axis of a given helix in Euclidean spaces. The first type generates helices in the n‐dimensional Euclidean space from helices in the same space. The second type generates helices in the (n+1)‐dimensional Euclidean space from helices in the n‐dimensional Euclidean space. In addition, we give invariants of these mappings and study polynomial, rational, conical, ellipsoidal, and hyperboloidal helices supported by examples.

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In this study, we administrated dynamic geometry activities which provide students opportunities to explore and estimate geometric figures to connect measurement estimation with geometry. The aim of the study is to investigate effects of using dynamic geometry activities on eighth graders' achievement levels and estimation performances in triangles. The study was designed a quantitative research design. A pretestposttest experimental study was employed to investigate using dynamic geometry activities on eighth grade students' achievement level and estimation performance in triangles. Participants were 63 eighth graders. The participants' ages vary between 13 and 14 years. Since the school is a public school, it contains students at nearly every socio-economic level. Experimental group consists of 32 students and comparison group consists of 31 students. Dynamic geometry supported instruction and traditional instruction methods were used in experimental and comparison groups, respectively. The results revealed that teaching triangles with instruction supported by dynamic geometry activities increased eighth graders' performance in triangles. In addition, the instruction supported by dynamic geometry activities had significant effects on eighth graders' estimation performances in triangles. Using dynamic geometry activities provides students experiences about conceptual bases of the relations in triangles. Therefore, students who take a dynamic geometry instruction make better estimations than those who did not take.

We introduce two types of mappings that preserve nonnull helices in Minkowski spaces. The first type constructs helices in the [Formula: see text]-dimensional Minkowski space from helices in the same Minkowski space. The second type constructs helices in the [Formula: see text]-dimensional Minkowski space from helices in the [Formula: see text]-dimensional Minkowski space. Furthermore, we study invariants of these mappings and present examples.

If we transform definitions of the conics in Euclidean plane on sphere, we obtain spherical conics. To calculate the E. Study Map of the spherical conics, we have to find one parameter equations of them. We had done this before in (Altunkaya, Yaylı, Hacısalihoglu, & Arslan, 2011). In this paper, we not only developed the results that we have found before, but also calculated the E. Study Map of the spherical conics when they are great circles by using the theorems in (Hacısalihoglu, 1977).