Drawing Shadows

People have long been fascinated by the positions of shadows, as we can easily see by examining the placement of temples in many ancient cultures. Nearly all religious structures were arranged to take account of the position of the sun and of shadows at certain key times of the year. Many of these structures actually functioned as rudimentary observatories, precisely identifying crucial days like the summer or winter solstice by the positions of shadows cast by their monuments. Artisans and astronomers in many cultures devised sundials for precise measurement of time, effectively transforming the passage of time into the movement of a shadow across a plane.

For the most part, shadows are images cast on a plane surface, like a wall or the ground, by some object located between the surface and a light source. In this chapter, we consider shadows cast by the sun, where the light rays are for all practical purposes parallel. (In Chapter 6, we will consider the case where the light rays spread out from a concentrated source, like a candle flame or a laser.) If two parallel lines in space have shadows that are two different lines in a plane, then these shadows are also parallel. This fundamental fact enables us to use shadows to obtain images of complicated structures in three-dimensional space and ultimately in spaces of higher dimension.

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