Earlier in this course, you explored Euclidean geometry, which is the study of flat space. This approach follows the teachings o
f 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.
I prefer the Euclidian approach. Euclidian geometry is easier to relate to more common experiences or things that happen in real life. On the other hand analytical geometry is more complex and is used in more mathematical problems.
