المنحني الناتج من دوران دائرة على مسار قاعدة مخروط قائم عند دورانها دورة كاملة بحيث تكون كل نقط محيط الدائرة مماسه دائما لسطح المخروط - دراسة رسم حالة المنحني من نقطة ثابتة على المحيط الخارجي لدائرة

Abstract

This paper is an attempt to study the case that a new type of curves through rolling (not sliding) of the geometric shape on the path to, a specific research was to study the composition of a special case of rounded shapes-circle by making them in contact permanently with the surface of rounded surface of the R-Cone based as a case study especially to search for study a current research, the paper continues with the new curves resulting from the fixed point on the circumference of a circle which was plotter curves of"cycloids" and its derivatives, which uses it in this study purpose to renew the designs of bulbar form domes, especially in Islamic architecture dome in shapes in past and present .The paper aimed to develop these cases, as a standard curves over the study status of the three coordinates not in two as previously studied by the extraction of a new type of curve which can generate for its ratio a new architecture domes or roofs of three-dimensional curves in new formations provided by the researcher as models of past forms that was researched in depth.The paper is focused for the first time the formation of this type of curves within the three-dimensional space by using the cone surface-based path of the movement of a circular situation of complete contact with the surface of the cone existing at any moment of his side induced in this research to be adopted to configure circular shape ,the status of the inter section of ball perpendicular (i.e. the case of the search) and tangent to complete each point with three-dimensional surface as the surface of the cone has been studied from a specified paths with the base of the cone, to consist of the intersection curve is closed symmetrical circular where all the points surrounding in contact permanently with surface of the cone-based,,which makes a circle plotter in the special case where flattens all points around the surface of the cone from the two sides parallel with the base (horizontal), and axis inclination surface of the cone (angle-slop surface of the cone with the line of the horizon of its base=(u), which gives the distinctive shape of the area intersection in the Departments of the plotter flat,perfectly with the points of angle-slop surface of the cone of any situation of complete contact with the points in which case that have been studied in 3d-space, relying on the case of the intersection of a sphere or cylinder (the case outside the field of research), the spiral new curve based is the shop geometric closed to all points of intersection cylinder or ball and perpendicular with them so there is only one point at the base of the cone.