Trigonometry is to triangle as _____ is to circle.

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What is the most suitable word to put in that gap? Something that corresponds to the study of circles.

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The word trigonometry comes from the Greek words for triangle and measure. If you wanted to create a word for measurement of circles with a similar etymology, you could use the Greek word κύκλος, meaning circle, to get "cyclometry".

This word appears to be in at least some use:

  1. http://en.wiktionary.org/wiki/cyclometry.
  2. http://en.wikipedia.org/wiki/Inverse_trigonometric_functions
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circle geometry. Trigonometry means the study of triangles. So the study of circles is circle geometry.