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