Euclid's axioms describe the geometry of shapes and curves in simple mathematical spaces which are called *flat*. When one considers more complex spaces, these axioms are no longer adequate. I illustrate this by looking at the special case where the mathematical space is a *two-sheet hyperboloid*.
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I talk about the mathematics describing what happens when a massive objects is accelerated at a steady rate and how it behaves when its velocity approaches that of light using the principles of special relativity.