Question

Part I. Perspective Experiments. 1. This problem may require the use of a flashlight and some cut out paper objects. By studying the nature of shadows cast you can get an idea of how the perspective correspondence works. After some experiments, use your three-dimensional imagination to figure out the answers. Below is a list of geometric shapes, properties of geometric shapes, and rela- tionships between geometric objects. What happens to these shapes, properties, and relationships under a perspective correspondence? For example, lines always correspond to lines (or possibly nothing in a special case) under any perspective correspondence. Be sure to think about different possible placements of planes Draw pictures (I want to see them!) and use your flashlight, if necessary. (a) parallel lines. (b) triangles (c) rectangles and squares (d) acute and obtuse angles (e) 4 points, no three of which are collinear (f) circles 2. For each of your answers to (a) through (f) in part 1, try to explain your observations using the principles of perspective that you developed during your in- class investigations on Thursday January 18. These principles of perspective will be discussed in greater detail and formulated in writing in class on Tuesday Jan 23. Some of what you observed above can be explained completely using these principles and some cannot. Explain as many as possible and offer theories of why you think what you observe is happening.

Answer 1

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