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Analytic Geometry
alejandroel
Created on August 15, 2023
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Transcript
Analytic Geometry
introduction
worldhistory.com
René Descartes (1596-1650) was a French mathematician, natural scientist, and philosopher, best known by the phrase 'Cogito ergo sum' ('I think therefore I am'). He published works on optics, coordinate geometry, physiology, and cosmology, however, he is mostly remembered as the "father of modern philosophy".
Historical background
French philosopher, mathematician and physicist.
René Descartes
sciencephoto.com
Matemáticas III, Patricia Ibañez Carrasco
With his famous work "Discourse on the Method" (1637), in whose section "Géometrie", details geometric instructions for solving quadratic equations, then describes the application of algebra to certain geometric problems.
Discourse on the Method
https://www.media4math.com/
Matemáticas III, Patricia Ibañez Carrasco
Almost all the "Géometrie" is dedicated to the relationship between the algebra and geometry, with help of the coordinate system, just what we currently call "Analitic Geometry".
An ordered pair is a composition of the x coordinate (abscissa) and the y coordinate (ordinate), having two values written in a fixed order within parentheses. It helps to locate a point on the Cartesian plane.
Ordered Pairs
https://www.splashlearn.com/
In the Cartesian plane, we define a two-dimensional space with two perpendicular reference lines, namely x-axis and y-axis. The point where the two lines meet at “0” is the origin. To comprehend it better, let’s take an example. Plot the point “P” with coordinates 6, 4. As per the definition of ordered pair, the point P will be written as: P = (6, 4). The first number in the ordered pair shows the distance from “x” axis which is 6. The second number in the ordered pair shows the distance from “y” axis which is 4.
https://www.splashlearn.com/
To mark the point on the Cartesian plane, start from the origin. Take 6 steps towards the “x” axis (towards right) starting from the origin. From here, take 4 steps towards the “y” axis (upwards).
https://www.splashlearn.com/
As the name “ordered pair” suggests, the order in which values are written in a pair is very important. The ordered pair (6, 4) is different from the pair (4, 6). Both represent two different points as shown.