PLEASE HELP!!

Discussion Topic
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 Han the other? Describe the situation
and why you think analytical or Euclidean geometry is more applicable.

Based on my experiences so far, the approach to geometry that I prefer is: Euclidean Geometry. This is because the problems are easy to visualize since they are restricted to two-dimensional planes.

Which approach is easier to extend beyond two dimensions?

The approach that is easier to extend beyond two dimensions is Euclidean Geometry. Again, this is because of how it deals with shapes and visualization of the same.

Take for instance a triangle; it is easy to go from a two-dimensional equilateral triangle to a square pyramid.

What are some situations in which one approach to geometry would prove more beneficial than the other?

Analytical geometry is a superior technique for discovering objects (points, curves, and planes) based on their qualities in some situations than Euclidean geometry is in others (for example, when employing topography or building charts).

Learn more about Euclidean Geometry at;
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