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Euclidean space was introduced by ancient Greeks as an abstraction of our physical space. Their great innovation, appearing in Euclid's Elements was to build and prove all geometry by starting from a few very basic properties, which are abstracted from the physical world, and cannot be mathematically proved because of the lack of more basic tools.
The tilde (/ ˈ t ɪ l d ə /, also / ˈ t ɪ l d,-d i,-d eɪ /) [1] is a grapheme ˜ or ~ with a number of uses. The name of the character came into English from Spanish tilde, which in turn came from the Latin titulus, meaning 'title' or 'superscription'. [2]