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swampwiz
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What's the difference between Euclidean & Cartesian space?
One exists, the other doesn't.swampwiz said:What's the difference between Euclidean & Cartesian space?
I've never heard the term "Cartesian space," but if I search for it on the web, I find some hits. More often I see "Cartesian coordinates."swampwiz said:What's the difference between Euclidean & Cartesian space?
Better than what had happened to me here on PF. I innocently abbreviated orthonormal system ...jedishrfu said:Most likely authors are conflating the terms of Cartesian space to mean Cartesian coordinates in a Euclidean space.
Euclidean space is a mathematical concept used to describe the three-dimensional world we live in. It is a type of space where the distance between any two points is defined by the Pythagorean theorem.
Cartesian space, also known as Cartesian coordinate system, is a mathematical concept that uses a set of coordinates to locate points in a two-dimensional or three-dimensional space. It is named after the French mathematician and philosopher René Descartes.
The main difference between Euclidean and Cartesian space is the way they measure distance. Euclidean space uses the Pythagorean theorem to calculate distance, while Cartesian space uses a coordinate system.
Both Euclidean and Cartesian space are used in real-life applications. Euclidean space is commonly used in physics, engineering, and geometry, while Cartesian space is used in computer graphics, navigation systems, and mapping.
Yes, Euclidean and Cartesian space can be converted into each other. This is because they are different mathematical representations of the same physical space. For example, in two dimensions, a point in Euclidean space can be represented as (x,y) in Cartesian space, and vice versa.