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.