3D Simulator of a Rolling Baton on Cylindrical Surfaces
Summary form only given. We make physical analysis of a baton rolling on cylindrical surfaces and then present a 3D simulator which helps us design actual surfaces to be used for a physical performance and for an interactive entertainment system.
Geometric Visual Instruments Based on Object Rolling
If some object can be manipulated using a part of a body, especially, using hands, to create a sequence of aesthetically or geometrically attractive visual patterns, we call it the visual instrument. In this paper, we present visual instruments based on rolling objects on geometric surfaces. First, we present visual instruments that use line segments (or physically, batons) and geometric surfaces such as a cylinder, a globe, and a sequence of truncated cylindrical surfaces on which to roll the batons. We also present the visual instrument called the “gourds”, which are made of some circular arcs. We made simulation for visualizing tempo-spatial patterns and roulettes the instruments create. Through construction of the visual instruments and their manipulation, we have confirmed that they have a high potential for use in manipulative visual performance and play.
A Treatise on the Cycloid and all Forms of Cycloidal Curves, and on the Use of such Curves in dealing with the Motions of Planets, Comets, &#38;c, and of Matter projected from the Sun
THIS is a very full book on the curves enumerated; marked by much elegance in the geometrical portion of the work. It is by far the completest treatise we know, and is likely to take its place as a standard work on the subject. It is marvellous how much can be said about these curves, and one is ready to indorse Chasles' opinion—referring to the cycloid—“ Cette courbe merveilleuse.” Mr. Proctor only slightly glances at the historical side, and merely refers to Pascal's famous questions, a proof of which, we believe, could hardly, if at all, be effected by purely geometrical methods. Use has been made of De Morgan's article on trochoidal curves, the fullest previous exposition of the properties of these curves in relation to epicyclics, and the work, which is admirably printed, has had the advantage of being embellished with drawings from Mr. Perigal's well-known mechanically-traced curves (bicircloids). One section is devoted to the analytical equations to the curves, and the last section is a reprint of two papers which have already appeared in the Monthly Notices of the Astronomical Society, entitled “The Graphical Use of Cycloidal Curves to determine (1) the Motion of Planets and Comets, (2) the Motion of Matter projected from the Sun.”A Treatise on the Cycloid and all Forms of Cycloidal Curves, and on the Use of such Curves in dealing with the Motions of Planets, Comets, &c., and of Matter projected from the Sun.By Richard A. Proctor. With 161 Illustrations and many Examples. (London: Longmans, 1878.)