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Mathematics is a hybrid subject with the idea of number tending to unfold while some major geometrical innovations cannot be understood in these terms. The deployment of evolutionary, critical and non‐evolutionary structuralist conceptions in the analysis of mathematical development draws the conclusion that, in order to fully understand this development, it is necessary to consider mathematics' relations with other (artistic and scientific) concerns, the tendencies implicit in its subsystems, and the connections between its various fields, as well as the ability of mathematicians to appraise critically any given formulation and thereby transcend it.

Accurate feature localization is a fundamental problem in computer vision and visual measurement. In a perspective projection model of the camera, the projected center of a spatial circle and the center of the projection ellipse are not identical. This paper aims to show how to locate the real projection center precisely in the perspective projection of a space circle target.

By analyzing the center deviation caused by projection transformation, a novel method is presented to precisely locate the real projection center of a space circle using projective geometry. Solution distribution of the center deviation is analyzed, and the quadratic equation for determining the deviation is derived by locating vanishing points. Finally, the actual projected center of the circular target is achieved by solving the deviation quadratic equations.

The procedures of the author’s method are simple and easy to implement. Experimental data calculated that maximum deviation occurs at approximately between 3π/10 and 2π/5 of the angle between the projection surface and the space target plane. The absolute reduction in error is about 0.03 pixels; hence, it is very significant for a high-accuracy solution of the position of the space circle target by minimizing systematic measurement error of the perspective projection.

The center deviation caused by the space circle projection transformation is analyzed, and the detailed algorithm steps to locate the real projection center precisely are described.

THE problem involved in obtaining satisfactory surface contours for assemblies such as are required in modern aircraft development demands for its successful solution the co‐ordinated, concentrated efforts of all those concerned with both the design and manufacturing processes. Even the casual observer can see that, if optimum performance is to be realized, the external skin or covering, whether made of thin sheet stock or precision machined from heavier plate stock, must be continuously smooth.

§ 1. My presentation to the Circle. When I presented my theory to the Circle, I found a mixed reception. Schlick, however, slightly shook his head, the mock-smile appeared on his face, and he tried to exchange glances. Only Waismann responded. Kaufmann was too loyal a friend to openly go against me even though he strongly felt that I was wrong. And Carnap was in deep thought.

[Chapter Thirteen of Menger's Reminiscences deals with Menger's visit to the United States in the academic year1930/31, but it is restricted to Menger's stay at Harvard, where he spent the fall semester and lectured on dimension theory and metric geometry. At Cambridge, Menger met, among others, ‘the outstanding mathematician’ G.D. Birkhoff; the philosopher H. M. Sheffer, who ‘had discovered in 1913 that all particles of the calculus of propositions can be expressed in terms of a single one’, ‘extensive[ly] used’ in Wittgenstein's Tractatus ‘without mentioning its author’; P. Weiss, N. Wiener and J. Schumpeter, the latter being a visiting scholar as well. But the person who most impressed Menger was P. Bridgman, who ‘appeared to him as a modern reincarnation of Mach’(Menger, 1994, pp. 158–173). The ‘Harvard sections’ of Menger's Reminiscences are comprised between paragraphs 14 and 15 of the present publication and are not reprinted].

The Smarandache anti‐geometry is a non‐euclidean geometry that denies all Hilbert’s 20 axioms, each axiom being denied in many ways in the same space. In this paper, one finds an economics model to this geometry by making the following correlations: a point is the balance in a particular checking account, expressed in US currency (points are denoted by capital letters); a line is a person, who can be a human being (lines are denoted by lower case italics); and a plane is a US bank, affiliated to the FDIC (planes are denoted by lower case boldface letters).

The purpose of this paper is to propose a calibration method that can calibrate the relationships among the robot manipulator, the camera and the workspace.

The method uses a laser pointer rigidly mounted on the manipulator and projects the laser beam on the work plane. Nonlinear constraints governing the relationships of the geometrical parameters and measurement data are derived. The uniqueness of the solution is guaranteed when the camera is calibrated in advance. As a result, a decoupled multi‐stage closed‐form solution can be derived based on parallel line constraints, line/plane intersection and projective geometry. The closed‐form solution can be further refined by nonlinear optimization which considers all parameters simultaneously in the nonlinear model.

Computer simulations and experimental tests using actual data confirm the effectiveness of the proposed calibration method and illustrate its ability to work even when the eye cannot see the hand.

Only a laser pointer is required for this calibration method and this method can work without any manual measurement. In addition, this method can also be applied when the robot is not within the camera field of view.

To discuss some of the work of Heinz von Foerster with regard to multidimensional visualization.

An introduction to multidimensional visualization, followed with the connections derived from the Biological Computer Laboratory.

Visualization provides insight through images. Considers the steps involved in interacting and learning so that this will lead the individual into their own “concept formation”.

Studies aspects of Heinz von Foerster's work that are of importance for understanding multidimensional visualization.