Musings about Euclidean Space

The Geometry class taught in High School teaches you the basics of Euclidean Space. In two dimensions, two parallel lines will never intersect. Between any two points, there is a unique straight line.

We start by considering the equidistance of adjacent integers.

The distance between 6 and 7 is the same as the difference between 7 and 8. This is true for both the scientist working with centimeters and the engineer working with inches. This is one of the things alluded to when a mathematician talks about a space being flat.

How could it be anything else? Well, we create curvature when we try to graph the surface of Earth onto a piece of paper. The distortion shows up with Greenland looking much larger than Mexico even though the two areas are roughly the same size.