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According to the Twelfth Doctor, feigning surprise at the TARDIS' dimensional transcendentalism, three-dimensional Euclidean geometry had just been "torn up, thrown in the air, and snogged to death". (TV: The Husbands of River Song)

The "warped physics of hyperspace" were outside of Euclidean space. (PROSE: Uranus)

Euclidean geometry was distinguished from non-Euclidean geometry, (PROSE: Shadow of the Times Before, The Book of the Enemy) which characterised the intersections of space and time within the Time Vortex. (PROSE: Cat's Cradle: Witch Mark)

Once, while visiting ancient Athens with the Seventh Doctor, Melanie Bush corrected Euclid's geometry, much to his annoyance. (AUDIO: Mask of Tragedy)

Behind the scenes Edit

Euclidean geometry is a specific mathematical conception of geometry consisting of five axioms. Most famously the ancients took the first four to be definitional and would attempt to justify the parallel postulate, leading to non-Euclidean geometry. However, modern work has shown that this is not the only axiom that can be coherently denied given the proper approach.

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