Obvious is the most dangerous word in mathematics.
—
Eric Temple Bell (1883–1960)4.1 Investigate Perspective View with a Dynamic
Illustration
Obvious is the most dangerous word in
mathematics.
—Eric Temple Bell (1883–1960)
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Consider a square being viewed from the side by two viewers, v1 and v2, from different
perspectives as in the given figure. Each viewer would see the vertices of the
square along a line. The perspective of viewer, v1, of the vertices of
the square is the points along a line in the order C, D, A, B; whereas,
the perspective of viewer, v2, of the vertices of the square is the
points along a line in the order D, A, C, B. Drag v2 to see how the viewer's perspective changes as v2 moves around the square. Note how the order of the vertices changes as viewer 2's perspective changes. To reset to the original settings, type the letter "R" on the keyboard. |
The points along the line from which
the viewer sees the vertices of the square will be defined in a later section as
a pencil of points. Each diagram of a viewers perspective (observation
point, view lines, and pencil of points) will be called a perspectivity
with the point representing the viewer called the center of the
perspectivity.
In the section on perspectivities and
projectivities, we will study relationships between the views (pencil of points)
of the two viewers. How can the perspective of one viewer be projected onto the
perspective of the other? This leads to the more general concept of
projectivity, which will be defined as a product of perspectivities.
JavaSketchpad,
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The Geometer's Sketchpad.
Copyright © 1990-2001 by KCP Technologies, Inc. Licensed only for non-commercial
use.
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© Copyright 2005, 2006 - Timothy Peil |
