Posts Tagged development of analytic geometry
Geometry is the field of mathematics that deals with spatial relationships. It also relates to the deduction of properties, relationships of points, lines and angles. Like algebra, the earliest recorded uses of geometry can be traced back to ancient Babylonia, around 3000 BC. Early geometry was essentially a composite of empirical principals and discoveries concerning lengths, angles, areas, and volumes. Babylonians used it for surveying, construction, astronomy and various projects.
Though the Babylonians invented geometry, the Greeks perfected it. In mid 300 BC Euclidean geometry was developed through Euclid of Alexandria. Euclid, considered ‘the father of geometry,’ is a suspected student of the philosopher Plato. Euclid’s influence began with the release of his book, The Elements of Geometry. In The Elements of Geometry Euclid described geometry in a more fundamental form, later called Euclidean geometry.
Euclidean geometry defined fundamental geometric principles called axioms or postulates, and general quantitative principles, called common notions. Euclidean geometry sought to satisfy all of Euclid’s axioms. This form of math followed five main rules: any two points can be joined by a straight line, any fixed straight line can be extended in a straight line, a circle can be drawn with any center and any radius, all right angles are equal and the parallel postulate.
Geometry was also very important in ancient India and China. In 179 AD, Liu Hui, a 3rd century mathematician, wrote The Nine Chapters on the Mathematical Art. Hui’s book illustrated many geometric problems and solutions including surface areas for squares and circles, volumes of solids and three-dimensional shapes, and the Pythagorean theorem.
Modern geometry began in the 17th century with the development of analytic geometry and projective geometry. Analytical geometry was created by French philosopher, René Descartes and Pierre de Fermat. Analytical geometry refers to geometry with coordinates and equations. This form of math was not only necessary for the progression of geometry, but also formed the foundations for calculus and physics.
In the mid 1600s, French mathematician, Girard Desargues introduced projective geometry. Projective geometry is the study of geometry with the absence of measurement, focusing on the ways in which points align. This type of geometry is typically used to study geometric properties that are consistent under projective transformations. Read the rest of this entry »