Download or read book On Ruled Surfaces Defined by Smarandache Curve written by Amine Yılmaz and published by Infinite Study. This book was released on with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the surfaces theory, it is well-known that a surface is called to be a ruled surface if it is generated by a continuously moving of a straight line in the space. Since a ruled surface is obtained by a line movement, its geometry has many nice properties and such surfaces have been studied by many authors, see: [4, 5, 6] and references therein. Ruled surfaces are also important subject in many applications. In particular, such surfaces have been used in computer aided engineering design (CAD) [7].
Download or read book Special Smarandache Ruled Surfaces According to Flc Frame written by Suleyman Senyurt and published by Infinite Study. This book was released on 2023-01-01 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this study, we introduce some special ruled surfaces according to the Flc frame of a given polynomial curve. We name these ruled surfaces as Smarandache ruled surfaces and provide their characteristics such as Gauss and mean curvatures in order to specify their developability and minimality conditions. Moreover, we examine the conditions if the parametric curves of the surfaces are asymptotic, geodesic or curvature line. Such conditions are also argued in terms of the developability and minimality conditions. Finally, we give an example and picture the corresponding graphs of ruled surfaces by using Maple17.
Download or read book Dual Smarandache Curves and Smarandache Ruled Surfaces written by Tanju KAHRAMAN and published by Infinite Study. This book was released on with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, by considering dual geodesic trihedron (dual Darboux frame) we define dual Smarandache curves lying fully on dual unit sphere 2 S and corresponding to ruled surfaces. We obtain the relationships between the elements of curvature of dual spherical curve (ruled surface) a (s) and its dual Smarandache curve (Smarandache ruled surface) 1a (s) and we give an example for dual Smarandache curves of a dual spherical curve.
Download or read book Smarandache Ruled Surfaces according to Frenet Serret Frame of a Regular Curve in E3 written by Soukaina Ouarab and published by Infinite Study. This book was released on with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we introduce original definitions of Smarandache ruled surfaces according to Frenet-Serret frame of a curve in E3. It concerns TN-Smarandache ruled surface, TB-Smarandache ruled surface, and NB-Smarandache ruled surface. We investigate theorems that give necessary and sufficient conditions for those special ruled surfaces to be developable and minimal. Furthermore, we present examples with illustrations.
Download or read book Investigation of Special Type Smarandache Ruled Surfaces Due to Rotation Minimizing Darboux Frame written by Emad Solouma and published by Infinite Study. This book was released on 2024-01-01 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study begins with the construction of type-Π Smarandache ruled surfaces, whose base curves are Smarandache curves derived by rotation-minimizing Darboux frame vectors of the curve in E3. The direction vectors of these surfaces are unit vectors that convert Smarandache curves. The Gaussian and mean curvatures of the generated ruled surfaces are then separately calculated, and the surfaces are required to be minimal or developable. We report our main conclusions in terms of the angle between normal vectors and the relationship between normal curvature and geodesic curvature. For every surface, examples are provided, and the graphs of these surfaces are produced.
Download or read book DUAL SMARANDACHE CURVES AND SMARANDACHE RULED SURFACES written by TANJU KAHRAMAN and published by Infinite Study. This book was released on with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, by considering dual Darboux frame, we define dual Smarandache curves lying fully on unit dual sphere S2 and corresponding ruled surfaces. We obtain the relationships between the elements of curvature of dual spherical curve (ruled surface) α(s) and its dual Smarandache curve (Smarandache ruled surface) α1(s) and we give an example for dual Smarandache curves of a dual spherical curve.
Download or read book On Geometry of Equiform Smarandache Ruled Surfaces via Equiform Frame in Minkowski 3 Space written by Emad Solouma and published by Infinite Study. This book was released on 2023-01-01 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, some geometric properties of equiform Smarandache ruled surfaces in Minkowski space E13 using an equiform frame are investigated. Also, we give the sufficient conditions that make these surfaces are equiform developable and equiform minimal related to the equiform curvatures and when the equiform base curve contained in a plane or general helix. Finally, we provide an example, such as these surfaces.
Download or read book The Theory of Ruled Surfaces written by W. L. Edge and published by Cambridge University Press. This book was released on 2011-06-30 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 1931 book contains tables of quintic and sextic ruled surfaces, classified by their double curves and bitangent developables.
Download or read book NC Smarandache Ruled Surface and NW Smarandache Ruled Surface according to Alternative Moving Frame in E3 written by Soukaina Ouarab and published by Infinite Study. This book was released on with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this study, original definitions of NC−Smarandache ruled surface and NW−Smarandache ruled surface according to the alternative moving frame are introduced in E3. (e main results of the study are presented in theorems that give necessary and sufficient conditions for those special surfaces to be developable and minimal. Finally, an example with illustrations is presented.
Download or read book Smarandache Curves of a Spacelike Curve lying on Unit dual Lorentzian Sphere written by Tanju Kahraman and published by Infinite Study. This book was released on with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we give Darboux approximation for dual Smarandache curves of spacelike curve on unit dual Lorentzian sphere.
Download or read book Ruled and Rotational Surfaces Generated by Non Null Curves with Zero Weighted Curvature written by Mustafa Altın and published by Infinite Study. This book was released on with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this study, firstly we give the weighted curvatures of non-null planar curves in Lorentz-Minkowski space with density eax2+by2 and obtain the planar curves whose weighted curvatures vanish in this space under the condition that the constants a and b are not zero at the same time. After giving the Frenet vectors of the non-null planar curves with zero weighted curvature in Lorentz-Minkowski space with density eax2 , we create the Smarandache curves of them.
Download or read book Pointwise 1 Type Gauss Map os Developable Smarandache Rules Surfaces written by Stuti Tamta and published by Infinite Study. This book was released on 2023-01-01 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we study the developable TN, TB, and NB-Smarandache ruled surface with a pointwise 1-type Gauss map. In particular, we obtain that every developable TN-Smarandache ruled surface has constant mean curvature, and every developable TB-Smarandache ruled surface is minimal if and only if the curve is a place curve with non-zero curvature or a helix, and every developable NB-Smarandache ruled surface is always plane. We also provide some examples.
Download or read book Dual Smarandache Curves of a Timelike Curve lying on Unit dual Lorentzian Sphere written by Tanju Kahraman and published by Infinite Study. This book was released on with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we give Darboux approximation for dual Smarandache curves of timelike curve on unit dual Lorentzian sphere.
Download or read book 2nd International Students Science Congress Proceedings written by Mahamat Ali Amine Ouchar and published by Infinite Study. This book was released on with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this study is to determine PstI polymorphism in the exon 6 region of the Pituitary-specific Transcription Factor (Pit-1) gene which is regarded as a candidate gene in mammals in regulating growth and development in 6 different goat breeds reared in Turkey. PstI polymorphism in Pit-1 gene (450 bp) was investigated by Restriction Fragment Length Polymorphism (RFLP) method in a total of 217 goats including 36 Hair, 18 Angora, 43 Kilis, 37 Honamlı, 46 Halep and 37 heads of Saanen breeds.
Download or read book Computation of Smarandache curves according to Darboux frame in Minkowski 3 space written by H.S. Abdel-Aziz and published by Infinite Study. This book was released on with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we study Smarandache curves according to Darboux frame in the three-dimensional Minkowski space E 3 1. Using the usual transformation between Frenet and Darboux frames, we investigate some special Smarandache curves for a given timelike curve lying fully on a timelike surface. Finally, we defray a computational example to confirm our main results.
Download or read book Surfaces family with a common Mannheim geodesic curve written by Gülnur ŞAFFAK ATALAY and published by Infinite Study. This book was released on with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we analyzed surfaces family possessing a Mannheim partner curve of a given curve as a geodesic. Using the Frenet frame of the curve in Euclidean 3-space, we express the family of surfaces as a linear combination of the components of this frame and derive the necessary and sufficient conditions for coefficients to satisfy both the geodesic and isoparametric requirements. The extension to ruled surfaces is also outlined. Finally, examples are given to show the family of surfaces with common Mannheim geodesic curve.
Download or read book On Properties of Ruled Surfaces and Their Asymptotic Curves written by Sokphally Ky and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ruled surfaces are widely used in mechanical industries, robotic designs, and architecture in functional and fascinating constructions. Thus, ruled surfaces have not only drawn interest from mathematicians, but also from many scientists such as mechanical engineers, computer scientists, as well as architects. In this paper, we study ruled surfaces and their properties from the point of view of differential geometry, and we derive specific relations between certain ruled surfaces and particular curves lying on these surfaces. We investigate the main features of differential geometric properties of ruled surfaces such as their metrics, striction curves, Gauss curvature, mean curvature, and lastly geodesics. We then narrow our focus to two special ruled surfaces: the rectifying developable ruled surface and the principal normal ruled surface of a curve. Working on the properties of these two ruled surfaces, we have seen that certain space curves like cylindrical helix and Bertrand curves, as well as Darboux vector fields on these specific ruled surfaces are important elements in certain characterizations of these two ruled surfaces. This latter part of the thesis centers around a paper by Izmuiya and Takeuchi, for which we have considered our own proofs. Along the way, we also touch on the question of uniqueness of striction curves of doubly ruled surfaces.
