A pointed end or corner where two curves meet, or the position of being on the edge of something new about to happen.
From Latin 'cuspis' (pointed end, spearhead). Medieval astronomers used 'cusp' for the intersection points of zodiacal divisions.
We say we're 'on the cusp' of change or a new era, but the metaphor comes from medieval astronomy where cusps were literal boundary points between zodiacal houses—it's a very old way of thinking about thresholds.
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