Geometry was the mathematics of spatial relations.

Several Vulcans, including Tuvok and Mestral, observed that the game of pool can be easily mastered by using simple geometry. Mestral stated that that the game "wouldn't challenge a Vulcan child." Jack later stated that he had an upcoming geometry midterm, and he played pool as a means of study. (ENT: "Carbon Creek")

In 2365, Hikaru Sulu noted at a staff meeting, after the USS Enterprise had crossed the galactic barrier, and caused Gary Mitchell to acquire new mental abilities, that "if you want the mathematics of this, Mitchell's ability is increasing geometrically. That is, like having a penny, doubling it every day. In a month, you'll be a millionaire." (TOS: "Where No Man Has Gone Before")

When Chakotay was given a message from Kid Chaos's species it was correctly determined to be "some sort of alien geometry"; in fact, it was the rentrillic trajectory necessary to escape from chaotic space. (VOY: "The Fight")

Seven of Nine gave Naomi Wildman geometry lessons in 2376. One of her assignments was to build a tetragon using everyday objects, rather than using a replicator. She eventually decided on using carrots and celery. (VOY: "Memorial")

Topics of geometry

Utilization of geometry

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