# Rene Descartes And Analytical Geometry

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Analytical geometry is the study of geometry using a coordinate system. It is simply concerned with defining and representing geometrical shapes in a numerical way and extracting numerical information from shapes, numerical definitions and representations. Analytical geometry can also be referred to as coordinate geometry or Cartesian geometry. Rene Descartes (1596-1650) invented analytic geometry. He was a French philosopher and mathematician. One day, Descartes noticed a fly crawling around on the ceiling. He watched the fly for a long time. He wanted to know how to tell someone else where the fly was. Finally he realized that he could describe the position of the fly by its distance from the walls of the room. When he got out of bed, Descartes…show more content…
It can be used in Euclidean Geometry. Euclidean Geometry uses concepts from Analytical geometry to find the length of lines in a triangle, for example by using Pythagoras theorem, it also uses certain aspects of analytical geometry with regards to secants of a circle. Formulas in Analytical geometry are also used for concepts in two dimensions like points, directions, lines, triangles, polygons, conic sections, and general quadratic equations. Inverse functions also use analytical geometry as the use of co-ordinates are used; the Cartesian plane is put to use. We also use Analytical geometry to find the shortest distance between two points. Engineering and architecture also use analytical geometry. Engineers and architects use it to represent points, lines, shapes, and surfaces as algebraic expressions. This allows them to execute the calculations required to design a complex structure like a bridge. Geography and cartography also use analytic geometry for locating places and points on a topographical map. The concept of longitude and latitude is also based on analytical geometry thus it is used for navigation. Scientists use analytical geometry to analyse results of experimental data. In any scientific experiment, data collected for the dependent and independent variable is plotted on a graph which uses Cartesian co-ordinates. The independent variable is plotted on the x-axis and the…show more content…
n.d. everything in maths and science. http://everythingmaths.co.za/maths/grade-11/04-analytical-geometry. (29 May 2015) Section B Mathematical Formulae There are many mathematical formulae used to solve problems in the field of mathematics and other fields which include physics and engineering. S_(n=n/2 (2a+(n-1)d) ) Sn=sum ; n= number of terms ; a= first term ; d= difference The formula is used sequences and series. It is used to calculate the sum of terms in an arithmetic series. it can be used to calculate the sum of money, sticks, and other items after a number of days, months and years. It can also help give an overall view of a certain situation and can determine, for example, if a company is undergoing a loss or profit. Example A ladder has 50 rungs. The bottom rung is 1m long. Each rung is 12.5mm shorter than the rung beneath it. Determine the total length of the wood required to make 50 rungs. Solution: S_(n=n/2 (2a+(n-1)d) ) Come up with a sequence Sequence: 1; 0,9875; 0,975; 0,9625 Find the difference: Difference=0,9875-1= -0,0125 Substitute in the formula: T_n=a+(n-1)d 1 + (n-1) (-0,0125) 1 + -0,0125n + 0,0125 T_n= -0,0125n+0,0125 S_50= 50/2 ⌊2(1)+(50-1)(