New Insight into Cycloidal Areas
نویسندگان
چکیده
1. INTRODUCTION. A cycloid is the path traced by a point on the boundary of a circular disk that rolls without slipping along a straight line. It forms a sequence of arches resting on the line, as shown in Figure 1. It is known that the area of the shaded region below one arch is three times the area of the rolling disk. Our analysis shows that the factor 3 reflects a much deeper property of cycloidal sectors. Figure 2 shows various stages of rotation of the disk, together with cycloidal sector OPC bounded by arc OP and two line segments OC and PC. At each stage we have:
منابع مشابه
Improper magnetic ferroelectricity of nearly pure electronic nature in cycloidal spiral CaMn7O12
The noncollinear cycloidal magnetic order breaks the inversion symmetry in CaMn7O12, generating one of the largest spin-orbit driven ferroelectric polarizations measured to date. In this Letter, the microscopic origin of the polarization, including its direction, charge density redistribution, magnetic exchange interactions, and its coupling to the spin helicity, is explored via first principle...
متن کاملKinematical and Dynamic Aspects of a Cycloidal Planetary Reducer with Modified Structure
The paper deals with some representative geometrical and dynamic aspects of a new cycloidal reducer variant with modified structure, proposed by the authors: geometrical optimization of the cycloidal gear, analysis of the transmission ratio and efficiency, and analysis of the dynamic response in a relevant functioning case.
متن کاملCycloidal Cyclical Surfaces
The paper presents a family of cycloidal cyclical surfaces, which are created by a movement of a circle alongside the special spatial cycloidal curve, where the circle is located in the curve normal plane and its centre is on this curve. The spatial cycloidal curve can be created by simultaneous revolution of a point about three different axes 3o,2 o and 1o in the space. The form of the cycloid...
متن کاملA New Insight into Morphology of Solvent Resistant Nanofiltration (SRNF) Membranes: Image Processing Assisted Review
The aim of this review is to investigate the morphological properties of polyimide based SRNF membranes by mean of image processing. Effect of phase inversion parameters like polymer concentration, volatile co-solvent, pre-evaporation time, additives in coagulation bath, polymers weight ratio in composite membranes, addition of nano particles and cross-linking agents have been reviewed. The voi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- The American Mathematical Monthly
دوره 116 شماره
صفحات -
تاریخ انتشار 2009