Heavenly Half Moon (Archive: NASA, International Space Station)

Math and Beauty

Understanding creates a deeper appreciation for the things around us, and allows us to infer unseen things.

For example, the moon can be appreciated without any context. It’s pretty.

Heavenly Half Moon (Archive: NASA, International Space Station)
Heavenly Half Moon (Archive: NASA, International Space Station) by NASA’s Marshall Space Flight Center is licensed under CC-BY-NC 2.0

With some understanding of how the moon moves, it can also be informative. Say, for example, there is a half-full moon directly overhead, with the east side lit. That tells one it is about time for the sun to rise. The lit side of the moon points at the sun. If we’re looking at a half-lit moon, then we know that the moon is the right angle in a triangle defined by the viewer, the moon, and the sun. Approximately.

Being able to infer the position of the sun from the position of the moon also allows us to get an idea of the time. For example, if the moon is full and overhead, it’s about midnight. If the moon is 3/4 full and overhead, then it’s a few hours after sunset or a few hours before sunrise, depending on whether the moon’s west or east side is lit.

Understanding the geometries involved can take some practice. But once one is used to thinking about this, the concepts fit together in a natural and beautiful way.






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