We studied the patient JP who has exceptional abilities to draw complex geometrical images by hand and a form of acquired synesthesia for mathematical formulas and objects, which he perceives as geometrical figures. JP sees all smooth curvatures as discrete lines, similarly regardless of scale. We carried out two preliminary investigations to establish the perceptual nature of synesthetic exper...

In the first stage of Experiments 1-3, subjects learned to associate different geometrical figures with colors or with verbal labels. Performance in Stage 2, in which the figures signaled which of 2 motor responses should be performed, was superior in subjects required to make the same response to figures that had shared the same Stage 1 associate. A third stage of testing showed that the event...

Knowledge discovery is one of the humans' most creative activities. As is often pointed out, humans often draw figures in the process of reasoning and problem solving. Diagrammatic information from a figure gives us numerical and relational data for reasoning, and it also gives us cues for controlling reasoning. The author has developed four discovery systems in the domain of plane geometry. Th...

This paper provides a broad review of the state of the art in Lissajous curve techniques, with particular regard to rotating machinery. Lissajous figure is a subject too wide-ranging to allow a comprehensive coverage of all of the areas associated with this field to be undertaken, and it is not the authors' intention to do so. However, a general overview of the broader issues of Lissajous curve...

In the past Euler has shown considerable interest in specific cases of similarity in which one figure is constructed from another in some way (consider, e.g., E-129, Opera Omnia I.27 130-180 “Investigatio curvarum quae evolutae sui similes producant”, in which the objects of study are planar curves which are similar to their own evolutes). In the current work, he considers any two similar figur...

[Natural] philosophy is written in that great book which ever lies before our eyes—I mean the universe—but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The book is written in the mathematical language, and the symbols are triangles, circles, and other geometrical figures, without whose help it is impossible to comprehend a single wo...

In this paper we show how the mass properties of an articulated body, such as its center of mass and its moments of inertia, may be manipulated like any conventional end effector, with well-known iterative, numerical techniques. Within our interactive simulation testbed software, we illustrate this tool for the geometrical design of rigid bodies with prescribed mass properties, and for the mani...