The Beginning of Geometry
Geometry is derived from two Greek words— geo, meaning earth, and metria, meaning measure. Geometry is a branch of mathematics defined as the study of figures in a space of a given number of dimensions and of a given type.
In ancient times (2000 B.C.), the lengths, areas, and volumes of objects were derived by trial and error. This body of knowledge developed and used in construction, navigation, and surveying, as well as astronomy by the Babylonians and Egyptians and was passed to the Greeks. Among these Greek scholars was Euclid (300 BC), a mathematician and teacher often referred to as the "Father of Geometry," combined the geometric knowledge of his time with a more logical system. His famous book, Elements, presents geometry in an organized fashion.
Most of the theorems appearing in the Elements were not discovered by Euclid himself, but were the work of earlier Greek mathematicians such as Pythagoras, Hippocrates of Chios, Theaetetus of Athens, and Eudoxus of Cnidos. In this treatise (book), he organized a large body of known mathematics, including discoveries of his own, into the first formal system of mathematics—so as to demonstrate that they necessarily follow from five simple axioms or postulates. Euclid is also credited with devising a number of particularly ingenious proofs of previously discovered theorems.
The geometry that Euclid developed is known as the Euclidean Geometry—two-dimensional Euclidean geometry is called plane geometry (lines, polygons, and circles), and three-dimensional Euclidean geometry is called solid geometry (prisms, pyramids, and cylinders).
Non-Euclidean geometries are called hyperbolic geometry and elliptic geometry. Spherical geometry is a non-Euclidean two-dimensional geometry.
Geometry in Our Classroom
Third-year Geometry will cover the basic ideas of Euclidean Geometry, reasoning and writing proofs concerning angles, parallel lines, congruent triangles, and areas of polygons and volumes of solids. A flow chart of the concepts we will be handling can be viewed at A Journey with Geometry.
Why study the concepts of Euclidean Geometry and not those of non-Euclidean Geometry? Euclidean Geometry, or simply Geometry as we know it, has the most common applications in real-life—carpenters, draftsmen, architects, surveyors, engineers, including tailors and dressmakers, use Euclidean concepts in their professions.
In addition, the concepts of logical reasoning and deductive thinking found in high school geometry enable one's mind to solve abstract problems. Geometry prepares students to handle complex problems and helps them improve their reasoning abilities.
St. Augustine class, welcome to Third-Year Geometry.