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Measurement
... An ellipse is formed when a plane intersects a cone or cylinder at an angle, creating a closed curve. It can also be viewed as a circle that has been stretched vertically or horizontally [1]. This stretching can be explained using coordinate transformations or Affine Transformations [2], [3]. ...
Research on the perimeter of an ellipse has so far only found approximations. This occurs because the integral of the perimeter of an ellipse does not have an anti-derivative. Therefore, this study aims to find a new definite integral for the perimeter of an ellipse that has an anti-derivative. This study observed the relationship between the intersection of an elliptical cylinder, which results in a circle, and the perimeter of the base of the elliptical cylinder. This study found a new definite integral to obtain the exact formula for the perimeter of an ellipse, which can be solved analytically.
... An ellipse is formed when a plane intersects a cone or cylinder at an angle, creating a closed curve. It can also be viewed as a circle that has been stretched vertically or horizontally [1]. This stretching can be explained using coordinate transformations or Affine Transformations [2], [3]. ...
Research on the perimeter of an ellipse has so far only found approximations. This occurs because the integral of the perimeter of an ellipse does not have an antiderivative. Therefore, this study aims to find a new definite integral for the perimeter of an ellipse that has a derivative. This study observed the relationship between the intersection of an elliptical cylinder, which results in a circle, and the perimeter of the base of the elliptical cylinder. This study found a new definite integral to obtain the exact formula for the perimeter of an ellipse, which can be solved analytically.
... An ellipse is formed when a plane intersects a cone or cylinder at an angle, creating a closed curve. It can also be viewed as a circle that has been stretched vertically or horizontally [1]. This stretching can be explained using coordinate transformations or Affine Transformations [2], [3]. ...
Research on the perimeter of an ellipse has so far only found approximations. This occurs because the integral of the perimeter of an ellipse does not have an anti-derivative. Therefore, this study aims to find a new definite integral for the perimeter of an ellipse that has an anti-derivative. This study observed the relationship between the intersection of an elliptical cylinder, which results in a circle, and the perimeter of the base of the elliptical cylinder. This study found a new definite integral to obtain the exact formula for the perimeter of an ellipse, which can be solved analytically.
... This is not as trivial as one might suppose. Particularly in the context of geometry, the distinction between measurement and computation is in fact sometimes confused, and the computation of the length of segments or of the areas of surfaces is typically called a measurement (Lockhart, 2012). With the widespread use of numerical methods based on computers, the idea of purely computational (and therefore non-empirical) experiments, for example as performed through simulation, is now common. ...
This chapter aims to present the general context of a measurement system and basic concepts of measurement and related terms. The presentation develops according to a step-by-step, top-down strategy, which progressively characterizes measurement as (1) an empirical process, (2) designed on purpose, (3) whose input is a property of an object, and (4) that produces information in the form of values of that property. These are proposed as necessary but not sufficient conditions for a process to be identified as a measurement: as such the contents of this chapter should be uncontroversial to be read and accepted by most, if not all, researchers and practitioners.
This chapter aims to present the general context of a measurement system and basic concepts of measurement and related terms. The presentation develops according to a step-by-step, top-down strategy, which progressively characterizes measurement as (i) an empirical process, (ii) designed on purpose, (iii) whose input is a property of an object, and (iv) that produces information in the form of values of that property. These are proposed as necessary but not sufficient conditions for a process to be identified as a measurement: as such the contents of this chapter should be uncontroversial to be read and accepted by most, if not all, researchers and practitioners.
In this paper, we propose an explanation of the crucial role of measurement in our society by describing measurement as a bridge between the empirical world and the information world. We describe measurement science as built upon this feature, and we discuss its basic motivation and scope accordingly.
Bingham and Pagano (1998) described calibration as a mapping from embodied perceptual units to an embodied action unit and suggested that it is an inherent component of perception/action that yields accurate targeted actions. We tested two predictions of this "Mapping Theory." First, calibration should transfer between limbs, because it involves a mapping from perceptual units to an action unit, and thus is functionally specific to the action (Pan, Coats, and Bingham, submitted). We used distorted haptic feedback to calibrate feedforward right hand reaches and tested right and left hand reaches after calibration. The calibration transferred. Second, the Mapping Theory predicts that limb specific calibration should be possible because the units are embodied and anatomy contributes to their scaling. Limbs must be calibrated to one another given potential anatomical differences among limbs. We used distorted haptic feedback to calibrate feedforward reaches with right and left arms simultaneously in opposite directions relative to a visually specified target. Reaches tested after calibration revealed reliable limb specific calibration. Both predictions were confirmed. This resolves a prevailing controversy as to whether calibration is functional (Bruggeman & Warren, 2010; Rieser, Pick, Ashmead, & Garing, 1995) or anatomical (Durgin et al., 2003; Durgin & Pelah, 1999). Necessarily, it is both. (PsycINFO Database Record (c) 2013 APA, all rights reserved).
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