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- Published: November 11, 2022
- Updated: November 11, 2022
- Language: English
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At some point during a student’s standard educational career, often during high school, a coordinate system with be introduced for the purpose of graphing specific points on a plane and reproducing geometrical figures. Often times previous academic scaffolding will make this introduction seamless, and it will be assumed by many of the students that this charting grid system has always existed. It is important to note, however, that like most math concepts and systems that people use regularly, the coordinate grid hasn’t always existed.

It came to fruition because of Rene Descartes, a french philosopher and mathematician whose invention of the coordinate system was so revolutionary, it was named after him, and is today known as the Cartesian Coordinates System. During his fifty four years of life, Rene Descartes was quite the academic, spending much of his time attending school or writing books and developing complex theories and philosophies. He was a great thinker, and was naturally drawn to mathematics because of “ the certainty of its demonstrations” (Burton, p. 60)

Born in La Haye, Touraine, France in 1596, he was home schooled by his parents until the age of 8, when he was enrolled in a very illustrious school, the Jesuit College of La Fleche. He attended the Jesuit College for ten years before graduating at the age of 18. Descartes is known to have had a weakened immune system and delicate health during his childhood and was not expected to live a full life. Because of this, he was given some leniency at his school and was not always required to attend his classes, as well as being allowed to stay in bed each morning until he was ready to rise.

There is a story that one morning while lying in bed thinking and resting, a fly on the ceiling of his room got him thinking about tracking the fly’s movement and thus was the germinal idea of the coordinate system. Although this is most likely not entirely true, as there is no proof of its validity, it is interesting to think about what led to his development of such a complex idea. The base of the coordinate system is that any point in a plane can be defined by it’s position with relation to two fitted axes, or perpendicularly intersected lines that are on the same plane.

A point on this coordinate grid can be written by two locations, x and y and appears as (x, y) to plot the point on a grid. The perpendicular lines are called the x axis and the y axis, and the points are plotted directly in relation to these lines. Once his schooling was completed at the Jesuit College, he followed his fathers footsteps in getting a law degree from the University of Poiters, something he hadn’t originally intended to do.

Upon completion of his law degree he attended military school and enlisted in the Bavarian army. It is said that “ there is no evidence of any real soldiering on Descarte’s part, only years of leisure in which he had time to pursue his favorite studies” (Burton, p. 363) He finally settled down in Holland and gave up military life to further explore his passion for mathematics, and eventually publish a book that earned him the title of founder of analytic geometry.

Although Descartes had written books previously, the first one that he decided to publish was Discourse on the Method of Properly Conducting One’s Reason and of Seeking the Truth in the Sciences in 1637. This book was composed of three appendices; one on the subject of optics, one on meteorology, and most importantly for his contribution to the world, la geometrie (the geometry). Within the geometry section of this book was where Descartes wrote about what is today known as the Cartesian coordinate system.

It was the first time geometry and algebra had been combined, and the result was the first view into analytic geometry. The integration of algebra in the field of geometry through the use of the coordinate system opened up many new possibilities for mathematicians and students of mathematics. Using the coordinate system made it possible to exactly reproduce any geometric figure without ever actually seeing the figure. By plotting a set of points on a grid using Descartes coordinate system, any geometry student could easily replicate a shape.

For example, if one wanted to reproduce a quadrilateral (ABCD) and they were given the coordinates for vertices (A, B, C, D) as: (4, 2); (7, 7); (-3, 5); (-7, 3), that person could make that exact shape, without using any other tools. The ability to identify location with these numbers on a grid, allowed scientific data to be measured and displayed visually and exactly, which is why all science and engineering makes use of Cartesian coordinates. Rene Descartes made a significant impact on the scientific and mathematical world, through his coordinate system as well as many other philosophies and ideas.

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