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Math - The Fly on the Ceiling

Updated: Jan 2, 2022

By : Gail Murzello

The coordinate system we commonly use is called the Cartesian system, after the French mathematician René Descartes (1596-1650), who developed it in the 17th century.

The Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length.

A few common examples of coordinate geometry in our daily lives include, mapping of distances for navigation of ships and air crafts, for techniques like x-rays, ultrasounds, MRIs, and nuclear imaging require the reconstruction of shapes of organs, bones, and tumours as well as for GPS.Tracking coordinate geometry helps GPS to track transportation accidents and carry out rescue operations. The coordinate geometry also aids in enhancing flight security weather forecasting, earthquake monitoring, and environmental protection. Moreover, various facets of military operations are equipped with GPS.

The story of how this system was discovered was a rather unusual one. Legend has it that Descartes, who liked to stay in bed until late, was watching a fly on the ceiling from his bed. He wondered how to best describe the fly's location and decided that one of the corners of the ceiling could be used as a reference point.

Imagine the ceiling as a rectangle drawn on a piece of paper. Take the left bottom corner as the reference point, you can specify the location of the fly by measuring how far you need to go in the horizontal direction and how far you need to go in the vertical direction to get to it.These two number are the fly's coordinates. Every pair of coordinates specifies a unique point on the ceiling and every point on the ceiling comes with a unique pair of coordinates.

Réne watched the fly on the ceiling. When it landed, he counted the lines over to that spot. He wrote down the number of lines: 2. Then he counted the lines up to that spot. He wrote down the number: 5. Together, the two numbers - 2 and 5 - told him exactly where the fly was!”

A quote from the book - The fly on the ceiling by Doctor Julie Glass published on 19 May 1998.

Descartes' coordinate system created a link between algebra and geometry. Geometric shapes, such as circles, could now be described algebraically using the coordinates of the points that make up the shapes.

Descartes produced many other works in mathematics, science and philosophy. You might have heard of his famous quote, "I think, therefore I am". And he would undoubtedly have gone on to produce more, had he not died at the relatively young age of 53. René Descartes is often credited with being the “Father of Modern Philosophy.” This title is justified due both to his break with the traditional Scholastic-Aristotelian philosophy prevalent at his time and to his development and promotion of the new, mechanistic sciences.

137 views2 comments


Very well written keep it up Gail😘


Dec 27, 2021

Cool write up Gail! I wonder what Euler would say to Descarte combining algebra and geometry!

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