IN MATH: 1. adj. refering to rectangular coordinate system created by Rene Descartes, mathematician and philosopher. EX. The Cartesian coordinates of point A are (2,4).
IN ENGLISH: 1. as defined above.
APPLICATION: See list 230.
Above, the picture of Descarte was first published in 1995. The web version appeared in 2005. At the right, Descarte is depicted in 2021. The picture has changed, but, so has the "history." The former appears in a dictionary for those just beginning to study algebra, analytic geometry, graphing, functions -- it is simple. The latter appears in a Geometer's® Sketch Pad for those studying precalc, and calc, and any other interested party -- it is more complicated.
Years ago, stories of the fly on Descarte's ceiling and Newton's falling apple were told. Now, some support the stories but others do not. Information availability and volume has increased (in evidence, compare the two Descartes).
The history presented is elaborations on the content of each headshot w/thumbnail info. Sources are provided, but with links rather than academic citations.
Ancient Computing Devises Used Digitally (text format) and 50+ Centuries of Computation in a 21st-Century Format (lecture format) are other math history pages unrelated to this material.
|Analytic Geometry & Graphing Functions
Years ago we credited Descartes with the coordinate plane. Descartes in Latin is Cartesius [Descartes 1]. Now we elaborate a bit more, witness the players shown above.
Though Galileo [analytic 1] was working on the same thing, while Fermat and Descartes worked independently, credit is given to Fermat and Descartes -- based first publication date and evidence of private, unpublished work. Each also developed the idea of and computed derivatives before calculus was "invented," but Newton and Leibniz are given credit for calculus.
Note in the image that these men also worked on other things. Fermat was better known for Fermat's Last Theorem [Fermat 1] and Descartes for "I think, therefore I am" [Descartes 2].
Leibniz and van Schooten also worked on other things. Leibniz discovered calculus!
van Schooten taught and translated and edited Descartes' La Geometrie [Descartes 1] when he introduced the use of two axes. It has a horizontal base line AB, but no axes. The translation into Latin made it available to more people. The axes made it easier for all.
2graphs.gsp -- graphs and functions sketch pad
Precalc Functions in Sketch Pad Format
(if you do not wish to use 2graphs.gsp or fX.f'X.f''X.intX.gsp
ReimannSums.gsp animates partitions, boxes, Reimann sums, then area under (or between) curve(s), and plotting an antiderivative by using the sums.
limit -- history, symbols, by definition, by epsilon-delta, by approach
fX.f'X.f''X.intX.gsp -- derivatives, be definition (limit of the difference quotient), br tangent, by trace, antiderivative by plotting sums of sums, history