Coordinate Geometry(Intro)

Coordinate Geometry

Today my post is going to concentrate on Introduction to Coordinate Geometry and its applications and in future posts, I’ll discuss in detail about various theorems and results in Coordinate Geometry.

Prelude

Coordinate geometry is the branch of geometry using the coordinate system, i.e., using x, y, z axes. It is also known as Analytical Geometry or Cartesian Geometry. Coordinate Geometry led to the development of Calculus (both integral and differential) that we know today. Let’s see its beginning.

Beginning

Coordinate Geometry was first developed by the French Mathematician Rene Descartes. There’s a small story associated with the development of this field. One day Descartes was lying on his bed and pondering about a problem. Suddenly, he got distracted by a fly sitting on the roof tile of his house. Being a mathematician, that scene got registered differently in his mind. This was the birth of coordinate geometry.  Descartes imagined it as follows- the roof of the house as the plane and the sides of the tile as the axes and the fly as a point on the plane.

After the development of coordinate geometry, it became more popular than the conventional Euclidean geometry used till that day. The reason is very simple. Using Coordinate Geometry, most of the theorems and results from Euclidean geometry could be proved very easily and also, using Coordinate geometry, it was much simpler to deal with non-regular shapes like ellipse, parabola, hyperbola etc. compared to Euclidean geometry. With Coordinate geometry tools, one can easily prove or explain any concept in Calculus which is the foundation of science.

Applications

Applications of coordinate geometry are almost immeasurable. It has uses in all domains of our lives. Be it economics, finance, medicine, etc. Though it has so many applications, it’s extensively used in avionics, space flight technology, Astronomy, Kinematics and Mechanics. Its use in physics (mainly in kinematics and mechanics) led to the development of closely associated fields called tensors and vectors (about which we’ll discuss in detail in another season).

It’s quite fascinating that a fly literally changed the way Mathematics was studied and it brought Science more closer to Mathematics. That is the beauty of Coordinate Geometry.