The Star Trek lemma

John D. Cook is a mathematician and blogger who writes about math, computing, and connections between them. The "Star Trek lemma" is a nickname for a result in projective geometry: given a triangle and a point not on any side, lines connecting that point to the vertices will intersect the opposite sides at three points — and there exists a unique transformation (a projectivity) that maps the original triangle's vertices to those intersection points while respecting the triangle's structure. It appears in textbooks under this playful name because the diagram resembles the Starfleet insignia from Star Trek. The post is a personal, anecdotal reflection more than a technical proof — Cook recalls sharing an office with the book's author and discovering the nickname by flipping through the table of contents.