Papers by Bülent Altunkaya
Hacettepe Journal of Mathematics and Statistics
TURKISH JOURNAL OF MATHEMATICS, 2018
In this paper, we study the position vector of a spacelike rectifying slant helix with non-lightl... more In this paper, we study the position vector of a spacelike rectifying slant helix with non-lightlike principal normal vector field in E 3 1. First we find the general equations of the curvature and the torsion of spacelike rectifying slant helices. After that, we construct second-order linear differential equations. By their solutions, we determine families of spacelike rectifying slant helices that lie on cones.
TURKISH JOURNAL OF MATHEMATICS, 2018
In this paper, we study the position vector of a spacelike rectifying slant helix with non-lightl... more In this paper, we study the position vector of a spacelike rectifying slant helix with non-lightlike principal normal vector field in E 3 1. First we find the general equations of the curvature and the torsion of spacelike rectifying slant helices. After that, we construct second-order linear differential equations. By their solutions, we determine families of spacelike rectifying slant helices that lie on cones.
In this paper, we are investigating that under which conditions of the geodesic curvature of unit... more In this paper, we are investigating that under which conditions of the geodesic curvature of unit speed curve γ that lies on S_1^2 or H_0^2, the curve α which is obtained by using γ, is a spherical helix or slant helix in Minkowski space.
In this paper, we investigate constant breadth curves on a surface according to Darboux frame and... more In this paper, we investigate constant breadth curves on a surface according to Darboux frame and give some characterizations of these curves.
In this paper, we are investigating that under which conditions of the geodesic curvature of unit... more In this paper, we are investigating that under which conditions of the geodesic curvature of unit speed curve gamma that lies on the unit sphere, the curve c which is obtained by using gamma, is a spherical helix or slant helix.
In this paper, we study the position vectors of rectifying slant helices in E^3. First, we have f... more In this paper, we study the position vectors of rectifying slant helices in E^3. First, we have found the general equations of the curvature and the torsion of rectifying slant helices. After that, we have constructed a second order linear differential equation and by solving the equation, we have obtained a family of rectifying slant helices which lie on cones.
In this article, we investigate polynomial helices in the n-dimensional semi-Euclidean space with... more In this article, we investigate polynomial helices in the n-dimensional semi-Euclidean space with index two for n ? 4. We obtain some families of spacelike and timelike polynomial helices. These helices have spacelike or timelike or null axes. After that, we give some examples of the spacelike and the timelike polynomial helices in the n-dimensional semi-Euclidean space with index two for n = 4,5 and 6.
Participatory Educational Research, 2015
In this study, we administrated dynamic geometry activities which provide students opportunities ... more 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 socioeconomic 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.
In this paper, we are investigating that under which conditions of the geodesic curvature of unit... more In this paper, we are investigating that under which conditions of the geodesic curvature of unit speed curve $\gamma$ that lies on $S_1^2$ or $H_0^2$, the curve $\alpha$ which is obtained by using $\gamma$, is a spherical helix or slant helix in Minkowski space.
Journal of Mathematics Research, 2014
If we transform definitions of the conics in Euclidean plane on sphere, we obtain spherical conic... more 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).
Results in Physics
Abstract In this work, we find position vectors of non-null helices in the n-dimensional Minkowsk... more Abstract In this work, we find position vectors of non-null helices in the n-dimensional Minkowski spacetime. We present methods to generate helices from polynomial curves. We also present methods to generate helices from other helices which lie in different dimensional Minkowski spacetime.
arXiv: General Mathematics, 2016
In this paper, we study the position vectors of rectifying slant helices in $E^3$. First, we have... more In this paper, we study the position vectors of rectifying slant helices in $E^3$. First, we have found the general equations of the curvature and the torsion of rectifying slant helices. After that, we have constructed a second order linear differential equation and by solving the equation, we have obtained a family of rectifying slant helices which lie on cones.
Bu calismada ortaokul ogrenci velilerinin matematik egitiminden beklentilerini ortaya cikarmak ic... more Bu calismada ortaokul ogrenci velilerinin matematik egitiminden beklentilerini ortaya cikarmak icin gecerlik ve guvenirligi saglanmis bir olcek gelistirmek amaclanmistir. Arastirmaya dort farkli devlet okulundan toplam 321 ogrenci velisi katilmistir. Madde havuzu icin literatur ve uzman gorusleri goz onunde bulundurularak 29 madde olusturulmustur. Yapi gecerliginin saglanmasi icin acimlayici ve dogrulayici faktor analizi yapilmistir. Olcegin bir butun olarak guvenilir olup olmadiginin incelenmesi icin Cronbach Alpha tutarlilik katsayisi hesaplanmistir. Matematik Egitimi Veli Beklenti Olcegi (MEVBO) olceginin butunun guvenirlik katsayisinin 0,843 oldugu gorulmustur. Olcegin, acimlayici faktor analizi sonucunda 15 maddeden ve 3 alt boyuttan olustugu anlasilmistir. Bu alt boyutlar sirasiyla; “Kavramsal Anlama ve Ogrencinin Aktif Oldugu Ogretim Beklentisi”, “Olumlu Tutum ve Davranis Kazandirma Beklentisi”, “Ogretmenin Otorite Oldugu ve Kural Agirlikli Bir Ogretim Beklentisi” seklinde is...
Participatory Educational Research, 2014
Bu tez yedi bolumden olusmaktadir.Birinci bolum giris kismina ayrilmistir.Ikinci bolumde, konikle... more Bu tez yedi bolumden olusmaktadir.Birinci bolum giris kismina ayrilmistir.Ikinci bolumde, koniklerle ve kuresel koniklerle ilgili temel tanimlar ve ozellikler verilmistir.Ucuncu ve dorduncu bolumlerde, literaturde daha onceden bulunan kuresel konik denklemleri incelenmistir.Besinci bolumde, bir parametreli kuresel konik denklemleri bulunmus ve bu formuller yardimiyla bazi ozel durumlar incelenmistir.Altinci bolumde, dual sayilar ve D-Modul ile ilgili temel tanimlar verilmistir.Yedinci bolumde, bazi ozel durumlarda kuresel koniklerin E-study donusumleri incelenmistir.AbstractThis thesis consists of seven chapters.First chapter is devoted to the introduction.Second chapter consist of, basic definitions and properties about the conics and the spherical conics.Third and fourth chapters related to previously known spherical conic equations.Fifth chapter, one parameter spherical conic equations have been obtained and some special cases have been examined with the help of these equations.Sixth chapter involes, some basic definitions of the dual numbers and D-modul.Last chapter, E-study transformations of spherical conics have been obtained in some special cases.
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics
In this paper, we de…ne null curves of constant breadth in Minkowski 4-space and obtain a charact... more In this paper, we de…ne null curves of constant breadth in Minkowski 4-space and obtain a characterization of these curves. Also we give an example for such curves.
Bu tez yedi bolumden olusmaktadir.Birinci bolum giris kismina ayrilmistir.Ikinci bolumde, konikle... more Bu tez yedi bolumden olusmaktadir.Birinci bolum giris kismina ayrilmistir.Ikinci bolumde, koniklerle ve kuresel koniklerle ilgili temel tanimlar ve ozellikler verilmistir.Ucuncu ve dorduncu bolumlerde, literaturde daha onceden bulunan kuresel konik denklemleri incelenmistir.Besinci bolumde, bir parametreli kuresel konik denklemleri bulunmus ve bu formuller yardimiyla bazi ozel durumlar incelenmistir.Altinci bolumde, dual sayilar ve D-Modul ile ilgili temel tanimlar verilmistir.Yedinci bolumde, bazi ozel durumlarda kuresel koniklerin E-study donusumleri incelenmistir.AbstractThis thesis consists of seven chapters.First chapter is devoted to the introduction.Second chapter consist of, basic definitions and properties about the conics and the spherical conics.Third and fourth chapters related to previously known spherical conic equations.Fifth chapter, one parameter spherical conic equations have been obtained and some special cases have been examined with the help of these equations.S...
TURKISH JOURNAL OF MATHEMATICS, May 8, 2018
In this paper, we study the position vector of a spacelike rectifying slant helix with non-lightl... more In this paper, we study the position vector of a spacelike rectifying slant helix with non-lightlike principal normal vector field in E 3 1. First we find the general equations of the curvature and the torsion of spacelike rectifying slant helices. After that, we construct second-order linear differential equations. By their solutions, we determine families of spacelike rectifying slant helices that lie on cones.
Advances in Applied Clifford Algebras
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Papers by Bülent Altunkaya