Geometry and geometry education.

The Geometry Education word “geometry” is derived from the ancient Greek words geo (Earth) and metron (a measure). In addition to its practical origins, it is also associated with the language and theory of geometric figures, spaces, and forms. Ancient and medieval civilizations from all around the world contributed to the development of geometric concepts, including mathematicians in Babylonia, Egypt, China, India, Mesoamerica, Greece, and the Islamic and Arabic world. At times, the prominence of geometry has declined, such as in Western Europe during the Middle Ages and in certain research areas and undergraduate courses in North America in the twentieth century. Some curricular concepts that were once the focus of investigations have declined in relevance, such as spherical trigonometry, having been replaced in curricula by new fields or notions. Geometry research and education continue to evolve in response to changing emphases. At the beginning of the twenty-first century, students explore the properties of geometric objects and transformations. They learn about deductive geometry, coordinate geometry, and algebraic connections. Visualization and geometric history and applications are also a focus. Some of the curricular topics have been fundamental for millennia, like the Pythagorean Theorem, named for Pythagoras of Samos (c. 569–475 b.c.e.), while others, like vertex-edge graphs, are relatively recent inclusions.