Please help! Discussion Topic No
Earlier in this course, you explored Euclidean geometry, which is the study of flat space. This approach
follows the teachings of Euclid, in which he describes the relationships between points, lines, and
planes without any numerical measurement. You saw evidence of Euclidean geometry inside several
proofs and geometric constructions.
In contrast, the focus of this unit is understanding geometry using positions of points in a Cartesian
coordinate system. The study of the relationship between algebra and geometry was pioneered by the
French mathematician and philosopher René Descartes. In fact, the Cartesian coordinate system is
named after him. The study of geometry that uses coordinates in this manner is called analytical
geometry
It's clear that this course teaches a combination of analytical and Euclidean geometry. Based on your
experiences so far, which approach to geometry do you prefer? Why? Which approach is easier to
extend beyond two dimensions? What are some situations in which one approach to geometry would
prove more beneficial than the other? Describe the situation and why you think analytical or Euclidean
geometry is more applicable.
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