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Questions and Answers
What is a Cartesian coordinate system?
What is a Cartesian coordinate system?
A coordinate system that specifies each point uniquely by a pair of real numbers called coordinates
What is the point where the two axes meet called?
What is the point where the two axes meet called?
The origin
Who is the Cartesian coordinate system named after?
Who is the Cartesian coordinate system named after?
René Descartes
What can be described using the Cartesian coordinate system?
What can be described using the Cartesian coordinate system?
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Who independently discovered the concept of Cartesian coordinates?
Who independently discovered the concept of Cartesian coordinates?
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Who used constructions similar to Cartesian coordinates before Descartes and Fermat?
Who used constructions similar to Cartesian coordinates before Descartes and Fermat?
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Who translated Descartes' work into Latin, leading to further developments?
Who translated Descartes' work into Latin, leading to further developments?
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What role did the Cartesian coordinate system play in the development of calculus?
What role did the Cartesian coordinate system play in the development of calculus?
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What is the significance of the Cartesian coordinate system in the development of mathematics?
What is the significance of the Cartesian coordinate system in the development of mathematics?
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What is the purpose of the coordinate axes in a Cartesian coordinate system?
What is the purpose of the coordinate axes in a Cartesian coordinate system?
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How did the Cartesian coordinate system influence the development of vector spaces?
How did the Cartesian coordinate system influence the development of vector spaces?
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What was the contribution of Pierre de Fermat to the development of Cartesian coordinates?
What was the contribution of Pierre de Fermat to the development of Cartesian coordinates?
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What was the significance of the translation of Descartes' work into Latin in 1649?
What was the significance of the translation of Descartes' work into Latin in 1649?
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How did the Cartesian coordinate system impact the development of geometry?
How did the Cartesian coordinate system impact the development of geometry?
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What was the role of Frans van Schooten and his students in the development of the Cartesian coordinate system?
What was the role of Frans van Schooten and his students in the development of the Cartesian coordinate system?
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What is the relationship between the Cartesian coordinate system and the concept of algebra?
What is the relationship between the Cartesian coordinate system and the concept of algebra?
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Study Notes
Cartesian Coordinate System
- A coordinate system that specifies each point uniquely by a pair of real numbers called coordinates.
- Coordinates are the signed distances to the point from two fixed perpendicular oriented lines, called coordinate lines, coordinate axes or just axes.
- The point where the axes meet is called the origin and has (0, 0) as coordinates.
History of Cartesian Coordinates
- Named after René Descartes, who invented the system in the 17th century.
- Descartes' invention revolutionized mathematics by allowing the expression of geometric problems in terms of algebra and calculus.
- Published in 1637 while Descartes was resident in the Netherlands.
- Independently discovered by Pierre de Fermat, who also worked in three dimensions.
- French cleric Nicole Oresme used constructions similar to Cartesian coordinates before Descartes and Fermat.
Development of the Cartesian Coordinate System
- Initially, Descartes and Fermat used a single axis with a variable length measured in reference to it.
- The concept of using a pair of axes was introduced later, after Descartes' La Géométrie was translated into Latin in 1649.
- Frans van Schooten and his students introduced several concepts to clarify Descartes' ideas.
Impact of Cartesian Coordinate System
- Played a fundamental role in the development of calculus by Isaac Newton and Gottfried Wilhelm Leibniz.
- The two-coordinate description of the plane was generalized into the concept of vector spaces.
- Led to the development of other coordinate systems, such as polar, spherical, and cylindrical coordinates.
Cartesian Coordinate System
- A coordinate system that specifies each point uniquely by a pair of real numbers called coordinates.
- Coordinates are the signed distances to the point from two fixed perpendicular oriented lines, called coordinate lines, coordinate axes or just axes.
- The point where the axes meet is called the origin and has (0, 0) as coordinates.
History of Cartesian Coordinates
- Named after René Descartes, who invented the system in the 17th century.
- Descartes' invention revolutionized mathematics by allowing the expression of geometric problems in terms of algebra and calculus.
- Published in 1637 while Descartes was resident in the Netherlands.
- Independently discovered by Pierre de Fermat, who also worked in three dimensions.
- French cleric Nicole Oresme used constructions similar to Cartesian coordinates before Descartes and Fermat.
Development of the Cartesian Coordinate System
- Initially, Descartes and Fermat used a single axis with a variable length measured in reference to it.
- The concept of using a pair of axes was introduced later, after Descartes' La Géométrie was translated into Latin in 1649.
- Frans van Schooten and his students introduced several concepts to clarify Descartes' ideas.
Impact of Cartesian Coordinate System
- Played a fundamental role in the development of calculus by Isaac Newton and Gottfried Wilhelm Leibniz.
- The two-coordinate description of the plane was generalized into the concept of vector spaces.
- Led to the development of other coordinate systems, such as polar, spherical, and cylindrical coordinates.
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Description
A coordinate system that uniquely specifies each point by a pair of real numbers. It includes the origin, axes, and coordinates.
