Mathematics Throughout History

Time and Math in History

How does a sundial work?

The sundial tracks the apparent movement of the Sun across the sky. It does this by casting a shadow on the surface of a usually-circular dial marked by hour and minute lines. The gnomon—or the shadow-casting, angular object on the dial—becomes the “axis” about which the Sun appears to rotate. To work correctly, it must point to the north celestial pole (near the star Polaris, also called the North Star); thus, the gnomon’s angle is determined by the latitude of the user. For example, New York City is located at about 40.5 degrees north latitude, so a gnomon on a sundial in that city would be at a 40.5 degree angle on a sundial.

The sharper the shadow line, the greater the accuracy; in addition, larger sundials are more accurate, as the hour line can be divided into smaller units of time. But the sundial can’t be too large. Eventually, diffraction of the sunlight around the gnomon causes the shadow to soften, making the time more difficult to read.


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