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It is said that he was ill and in bed. He looked up at the ceiling where he noticed a fly. He figured out that knowing the distances from a corner of the ceiling along the two adjacent sides of the ceiling will uniquely identify its location. So, if the corner of the ceiling was the origin and the two adjacent sides were the axes, you have the Cartesian plane.

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The story is that he was ill and lying in bed. He watched an insect crawling on the rectangular ceiling and worked out that he could identify the exact location of the insect using only two numbers. These would represent the distance from any corner of the ceiling along two perpendicular directions.

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Q: How did Descartes think of the coordinate planes?
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