If we were to live in an exact Euclidean space, our understanding of the world would be significantly different. In an exact Euclidean space, the fundamental principles of geometry would govern every aspect of our environment.
One of the most noticeable differences would be the straightness of lines. In Euclidean space, lines would be perfectly straight, never deviating from their path. This would affect everything from the layout of buildings and roads to the behavior of light and sound.
Furthermore, in an exact Euclidean space, the angles of triangles would always add up to 180 degrees, and the ratios of the sides of similar triangles would always be the same. This would have a profound impact on the way we measure and calculate distances, as well as the design of structures and objects.
Overall, living in an exact Euclidean space would require a complete reimagining of our understanding of the world around us. While it may seem like a purely hypothetical concept, the principles of Euclidean geometry have greatly influenced our understanding of the physical world and continue to shape the way we think about space and dimension.