Analytic geometry or_the_origin_of_the_gps
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Analytic Geometry or the origin of the GPS There is a long-standing myth that describes how the French mathematician René Descartes (1596 - 1650) (pronounced "day CART") discovered analytic geometry. He was lying in bed when he saw a fly crawling on the ceiling. Being a creative mathematician, he wondered if he could plot the fly’s path on a geometric plane. Grabbing a sheet of paper, he drew a graph of the ceiling. He drew a horizontal line called the x axis and a vertical line called the y axis. He marked numbers on these axes like those of a ruler. Then he took the point where the axes met and called it the origin. With growing excitement, he watched the fly land on point after point and realized that every point could be described with a pair of numbers: its distance from the x axis and its distance from the y axis. He proposed further that curves and lines could be described by equations using this technique, thus being the first to link algebra and geometry. This was an innovation that enabled mathematicians to solve complex problems and invent new forms of mathematics such as calculus, which laid the foundation for modern science and technology. In honour of his work, the coordinates of a point are often referred to as its Cartesian coordinates, and the coordinate plane as the Cartesian Coordinate Plane. Vocabulary: Myth: mite Fly: mosca Crawl: arrossegar-se Ceiling: sostre Plot: traçar Path: camí Grab: agafar Sheet: full Thus: així Link: relacionar Enable: permetre Refer to: referir-se a Answer the following questions: 1. Which parts of mathematics joined Descartes together? 2. Can you explain the meaning of ’analytic geometry’? 3. What are the coordinates of a point? 4. What are the coordinates of the origin? PC2 Ensenyament - Aprenentatge Pla lector Mates 2n ESO Analytic Geometry Versió Abril 2014 Elaborat : Departament de Matemàtiques Pàgina 1 de 4
Transcript of Analytic geometry or_the_origin_of_the_gps
Analytic Geometry or the origin of the GPS
There is a long-standing myth that describes how the French mathematician René Descartes (1596 - 1650) (pronounced "day CART") discovered analyticgeometry. He was lying in bed when he saw a fly crawling on the ceiling. Being a creative mathematician, he wondered if he could plot the fly’s path on a geometric plane. Grabbing a sheet of paper, he drew a graph of the ceiling. He drew a horizontal line called the x axis and a vertical line called the y axis. He marked numbers on these axes like those of a ruler. Then he took the point where the axes met and called it the origin. With growing excitement, he watched the fly land on point after point and realized that every point could be described with a pair of numbers: its distance from the x axis and its distance from the y axis.He proposed further that curves and lines could be described by equations using this technique, thus being the first to link algebra and geometry. This was an innovation that enabled mathematicians to solve complex problems and invent new forms of mathematics such as calculus, which laid the foundation for modern science and technology.In honour of his work, the coordinates of a point are often referred to as its Cartesian coordinates, and the coordinate plane as the Cartesian Coordinate Plane.
Vocabulary:Myth: miteFly: moscaCrawl: arrossegar-seCeiling: sostrePlot: traçarPath: camíGrab: agafarSheet: fullThus: aixíLink: relacionarEnable: permetreRefer to: referir-se a
Answer the following questions:
1. Which parts of mathematics joined Descartes together?
2. Can you explain the meaning of ’analytic geometry’?
3. What are the coordinates of a point?
4. What are the coordinates of the origin?
PC2 Ensenyament - Aprenentatge Pla lector Mates 2n ESO Analytic Geometry Versió Abril 2014
Elaborat : Departament de Matemàtiques
Pàgina 1 de 4
5. The street map shows the location of Maria’s house (M), Bob’s house (B), Anthony’s house (A), and their school (S).
Write a set of directions showing how each of them get home from school.For example, to go to school, Anthony would go one block W and then three blocks S ( or three blocks S and then one block W ).
6. Can you find another example in the real world that uses the Cartesian coordinates?
Conclusions and a little more:
coordinates (x,y) ,also called coordinate pairs or ordered pairs, are two numbers which describe the location of a point on a graph
x-axis is the horizontal axis of a graph
y-axis is the vertical axis of a graph
x-coordinate is the first number in the pair. It tells you how far along the x-axis to move
y-coordinate is the second number in the pair. It tells you how far up or down the y-axis to move
origin (0,0) is the point where the two axes meet. The x-axis and the y-axis divide a plane into four quadrants
PC2 Ensenyament - Aprenentatge Pla lector Mates 2n ESO Analytic Geometry Versió Abril 2014
Elaborat : Departament de Matemàtiques
Pàgina 2 de 4
to plot is to mark the position on a graph using the two coordinates, e.g. The coordinates are (3,4)
the plural of axis is axes
Let’s see with a simple game if everything is clear:
PC2 Ensenyament - Aprenentatge Pla lector Mates 2n ESO Analytic Geometry Versió Abril 2014
Elaborat : Departament de Matemàtiques
Pàgina 3 de 4
PC2 Ensenyament - Aprenentatge Pla lector Mates 2n ESO Analytic Geometry Versió Abril 2014
Elaborat : Departament de Matemàtiques
Pàgina 4 de 4
Crossword clues:Across3. The name of the point (0,0)4. The name of the vertical line through the point (0,0)5. The name for straight-line graphs6. The plural of axis
Down1. The name for a point or ordered
pair on a graph2. The name for a graph with a curve
