Ruler and compass constructions.

Ruler Ruler and compass constructions Geometry Measuring tools and compass constructions have long been important in mathematics. In geometry, a ruler and compass construction refers to a geometric construction that uses only an unmarked ruler and a compass. The ancient construction problems of squaring the circle, duplicating the cube, and trisecting the angle were unsolved until they were proved impossible by algebraic techniques. Early tile makers and architects were also interested in these constructions. Aside from historical considerations, limiting constructions to these two tools is important because the restrictions generate a variety of rich problems. In the twenty-first century, dynamic geometry software programs allow students, teachers, and researchers to explore, save, and share constructions.