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Could you elaborate on what Descartes did? He's known as the inventor of coordinate geometry, which seems to rely on the notion of number as the length of a lin
by civilized 5y ago
Could you elaborate on what Descartes did? He's known as the inventor of coordinate geometry, which seems to rely on the notion of number as the length of a line segment (two number lines placed perpendicular to one another uniquely identify any point on the plane). Are you talking about his work on algebra or other things?
- javajosh 5y agohttps://en.wikipedia.org/wiki/Ren%C3%A9_Descartes#Mathematical_legacy https://en.wikipedia.org/wiki/Ren%C3%A9_Descartes#Mathematic... I will look up the specific paper where he proposed that a squared number need not represent only an area, for example.
- civilized 5y agoAh, I get it now. Descartes suggested that the representation of numbers need not be dictated by the geometric interpretation of how they were calculated. For example, a^2 doesn't have to be represented as an area, even though geometrically it would be the area of a square.
- javajosh 5y agoThe "paper" was La Géométrie[1], originally published as an appendix(!) to another work, Discourses on the Method [2]. Not sure why all the downvotes. Oh well. 1 - https://en.wikipedia.org/wiki/La_G%C3%A9om%C3%A9trie https://en.wikipedia.org/wiki/La_G%C3%A9om%C3%A9trie 2 - https://en.wikipedia.org/wiki/Discourse_on_the_Method https://en.wikipedia.org/wiki/Discourse_on_the_Method