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What is a synonym for ordered pairs?

One such synonym would be coordinates, which is also the proper way of naming the ordered pairs on a Cartesian coordinate plane.


What is the implication and criticism of Cartesian dualism?

Cartesesian Dualism is seeing immaterial 'mind' as superior over body. It leads to accepting immaterial 'understanding' as possible, knowing what is 'good' without experience. That way the Pope can say: sex without condom is not cause of AIDS. Western Society is based on Cartesian Dualism. Quite opposed to 'neurology': "everything is physical"


What does origin mean in the MATH way?

The point in a Cartesian coordinate system where the axes intersect. On a 2-D graph, for example, this is where x and y equal zero. also the point (0,0) on a graph


Who thought of the Cartesian plane?

The Cartesian plane is named after the French mathematician and philosopher René Descartes, who introduced the concept in his work "La Géométrie" published in 1637. Descartes developed the idea of using a coordinate system to represent geometric shapes algebraically, which laid the groundwork for analytical geometry. His innovation allowed for the visualization of algebraic equations as geometric figures, fundamentally changing mathematics and paving the way for future developments in various fields.


Given three points in polar notation what are the polar coordinates of a point equidistant from the three given points and can this point be found without converting to Cartesian coordinates?

Technically, yes. But, the equations involved are complicated to the point that it would be a fraction of the difficulty of converting. Also, the equations are essentially the Cartesian equations with the conversions built in, so you might as well convert them to start with. However, if you insist on not converting, write out the entire process with all 4 points of interest in Cartesian coordinates. From beginning to end. Find the final equations needed and insert the conversion factors and simplify from there. To the best of my knowledge (and I did quite a bit of digging) there isn't a simply way of doing it. - Sorry.