Diagrammatic Representation and Reasoning by Aaron Sloman (auth.), Michael Anderson MSc, PhD, Bernd Meyer

By Aaron Sloman (auth.), Michael Anderson MSc, PhD, Bernd Meyer Dr rer nat, Patrick Olivier MA, MSc, PhD (eds.)

Diagrams are crucial in so much fields of human job. there's substan­ tial curiosity in diagrams and their use in lots of educational disciplines for the aptitude advantages they might confer on a variety of initiatives. Are we now capable of declare that we've got a technology of diagrams-that is, a technological know-how which takes the character of diagrams and their use because the imperative phenom­ ena of curiosity? If now we have a technology of diagrams it's definitely constituted from a number of disciplines, together with cognitive technology, psychology, man made intelligence, good judgment, arithmetic, and others. If there's a technology of diagrams, then like different sciences there's an appli­ cations, or engineering, self-discipline that exists along the technological know-how. Applica­ tions and engineering supply assessments of the theories and ideas came upon through the technology and expand the scope of the phenomena to be studied through gen­ erating new makes use of of diagrams, new media for providing diagrams, or novel sessions of diagram. This purposes and engineering facet of the technology of di­ agrams additionally contains a number of disciplines, together with schooling, structure, desktop technology, arithmetic, human-computer interplay, wisdom ac­ quisition, photograph layout, engineering, background of technological know-how, facts, drugs, biology, and others.

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That observation, triggered by the search for significant directions, may be valuable (in particular, it helps to understand the textbook proof given later). What happens if vertex C of Fig. 1 is moved in the direction of the orientation of segment PQ (from P toward Q, roughly "east"), directly away from its opposite vertex A? What happens if vertex C of Fig. 1 is moved in the direction of segment QR? We could actually make these movements and observe that the parallelogram property is preserved, but can we show in a deeper sense why it must be preserved?

The definition of arbitrary selection is difficult to capture. Usually it means that no 42 2. grams constraints are placed on the example to make it a "special" case. The constraints are those that apply to the properties of the figure class in question. Thus "any quadrilateral" should exclude special cases, such as degenerate cases (where two or more vertices are identical, for example). A special case is where any subset of elements of the figure are related in "special ways" . "Special ways" is an inventory of properties that are known, presumably from prior learning, to be important.

This means that QR moves parallel to itself to Q'R', and thus remains parallel to its opposite side SP, which remained unchanged since its endpoints were not altered. Also, while the orientations of the other two sides change, they change equally because their moved endpoints move in the same direction by the same amount. Thus they remain parallel, and the parallelogram property is maintained. Can this relation be generalised to arbitrary movements of C? Move point C in any direction other than from D toward C, say in the direction of the diagonal PRo See Fig.

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