Tangent is mainly a mathematical term, meaning a line or plane that intersects a curved surface at exactly one point. The non-mathematical meaning of tangent comes from this sense of barely touching something: when a conversation heads off on a tangent, it's hard to see how or why it came up. When talking about history, someone suddenly brings last night's basketball game? Definitely a tangent.
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Tangent is mainly a mathematical term, meaning a line or plane that intersects a curved surface at exactly one point. The non-mathematical meaning of tangent comes from this sense of barely touching something: when a conversation heads off on a tangent, it's hard to see how or why it came up. When talking about history, someone suddenly brings last night's basketball game? Definitely a tangent.