Notes are on my GitHub! github.com/rorg314/WHYBmaths
In this video we will explore the Euclidean geometry defined by the Euclidean line element. By considering the (finite) interval as measured from the origin this conveniently allows us to simply represent the interval by the corresponding coordinate value of the endpoint of the interval (i.e delta x = x - 0 ). This allows us to consider the Euclidean line element in the form s^2 = x^2 + y^2, and thus consider the points (x, y) on which s^2 is constant. Here we see these are simply circles in R^2 (n-spheres in R^n), which agrees with our usual Euclidean intuition. I then briefly begin to discuss how the invariance of the line element can be used when comparing coordinates on such a figure, i.e by comparing the intersection of the curves of constant s with each coordinate axis - we will see how this is incredibly useful in the Minkowski version of this diagram!

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