26 August 1999
The optimal distance for viewing a painting is the distance which maximizes the angle subtended by the painting in the viewer's eye.
Suppose that an art lover regards a 6 foot tall painting in a gallery. Suppose further that the painting is hung so that its bottom edge is 2 feet above eye level to this viewer. Say that the angle subtended by the painting in the viewer's eye is a. Find the optimal distance for this viewer from this painting.
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The angle a is the angle
subtended by the 6 foot painting in the viewer's eye. To maximize a, first find a as a function of
x. Hint: Use the angle b when you cook up a as
a function of x and assume that the triangle is a right triangle. How does the viewer's height affect where he/she should stand to best view a painting?
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Background image © copyright 1997 by Xah Lee, used with permission.