Locus (1963)

Discusses the concept of “locus” in geometry, which refers to the set of all positions a point may occupy under certain conditions. It outlines five basic locus theorems, illustrated through various examples, including the location of an illegal radio transmitter, the arrangement of cards in a cheering section, and geometric shapes like circles and lines. The theorems include: 1) points at a distance from a point form a circle, 2) points at a distance from a line form parallel lines, 3) points equidistant from two points form a perpendicular bisector, 4) points equidistant from two parallel lines form a line midway between them, and 5) points equidistant from two intersecting lines form angle bisectors. The text emphasizes the application of these concepts in solving geometric problems. Keywords: locus, geometry, theorems, distance, points, circle, parallel lines, perpendicular bisector, equidistant, intersecting lines, radio transmitter, cheering section, geometric shapes, conditions, intersection.