Fundamentos de la geometría: desde figuras básicas hasta formas complejas

Geometry is an ancient branch of mathematics devoted to the study of shapes, spaces, sizes, distances, angles, dimensions, and their properties. It has its roots in Ancient Greece from around the fifth century BC. One of the earliest known constructions was by Thales of Miletus who erected a pyramid on the island of Samos using the height of the Great Pyramid as his guide. Today geometry can range anywhere from basic two dimensional shapes like squares and circles all the way up to complex four-dimensional shapes like cubes and spheres. In everyday life, you might encounter geometry when measuring your home's floor area or calculating the surface area of a box containing goods. Different areas of interest within this field include Euclidean geometry where points, lines, planes exist; topology which deals with properties that remain constant regardless of how much a shape changes; vector geometry which involves measurements and direction; and algebraic geometry which combines both algebra and geometry. Overall, geometry provides us with tools to understand our physical world through measurement and spatial reasoning, making it a fundamental subject in many fields of science and engineering today.