106CHAPTER 1. COORDINATES AND VECTORSxyzOOPP′QQ′RR′−→vFigure 1.54:squareOPRQWe see from Figure1.54that the vectors−−→OP,−−→OQ,−→vobey the right-handrule, so havepositiveorientation.Given any four pointsA,B,C, andDinR3, we can form a “pyramid”built on the triangle△ABC, with a “peak” atD(Figure1.55). TheABCDFigure 1.55: Simplex△ABCDtraditional name for such a solid istetrahedron, but we will follow theterminology of combinatorial topology, calling this thesimplex22withverticesA,B,CandD, and denote it△ABCD; it isorientedwhen wepay attention to the order of the vertices. Just as for a triangle, the edges
This is the end of the preview.
access the rest of the document.