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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.

Sagot :

Answer:

Step-by-step explanation:

Instead of working with the plane, we work with a spear in spiritual geometry, therefore all of the plane's notions are the same as the spear's. Three lines would be required to draw a triangle. We can't adjust the size of these circles to make a triangle bigger. So, in this situation, a line is defined as what I would term a "great circle," meaning it is always the same size as the sphere's radius. As a result, even if we only moved one of them, the angles of the others would shift.

both of the approaches are going fine for me so far. all of the subjects that I've learned have been easy-going and easy to understand. if I had to choose which one was easier for me, I would choose Euclidean. Mostly because it's easier than Analytical as well as it's not hard to solve for the data that was given to me. With Analytical, it's harder to establish a correspondence between geometric curves and algebraic equations.

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