What was the nature of the "triangle" consisting of Ike and Mamie and Ann, the wife and the secretary, one who ran his professional life, the other who ran his homelife?
If it is determined by three points, then the triangle consisting of those three points is not obtuse.
Conversely, if a graph has a cycle, then every chordal completion of the graph includes at least one triangle consisting of three consecutive vertices of the triangle, from which it follows that its treewidth is at least two.
It may help to visualise Carathéodory's theorem in 2 dimensions, as saying that we can construct a triangle consisting of points from P that encloses any point in P.
This particularly suits polyhedra that have equilateral triangular faces: Sonobe modules can replace each notional edge of the original deltahedron by the central diagonal fold of one unit and each equilateral triangle with a right-angle pyramid consisting of one half each of three units, without dangling flaps.
With the so-called "Magic triangle" consisting of players Krasimir Balakov, Giovane Elber, and Fredi Bobic, the team played a successful season and won the National Cup Final (DFB-Pokal).
Musicologists have sometimes classified music according to a trichotomic distinction such as Philip Tagg's "axiomatic triangle consisting of 'folk', 'art' and 'popular' musics".
Domestic triangles consisting of a husband, a wife and another man are common enough; the bridge equivalent is very rare indeed.
Set in Harlem during the 1920's, Toni Morrison's novel revolves around a triangle consisting of a discontented middle-aged black married couple and the young, seductive woman who disrupts their uneasy peace.
A ship's bearing was determined by settings of the astronomical triangle consisting of declination, latitude, altitude, hour angle, and azimuth.