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Three spin-off games accompany the main series: Geometry Dash Meltdown, Geometry Dash World and Geometry Dash SubZero. Geometry Dash Lite is a free version of the main game that includes fewer levels, displays advertisements, and lacks the level editor and most online features, along with various unlockable characters.
Nikolai Ivanovich Lobachevsky (Russian: Никола́й Ива́нович Лобаче́вский, IPA: [nʲɪkɐˈlaj ɪˈvanəvʲɪtɕ ləbɐˈtɕefskʲɪj] ⓘ; 1 December [O.S. 20 November] 1792 – 24 February [O.S. 12 February] 1856) was a Russian mathematician and geometer, known primarily for his work on hyperbolic geometry, otherwise known as Lobachevskian geometry, and also for ...
The game is using the alternate binary tiling of the hyperbolic plane. HyperRogue is a turn-based game in which the player controls one character exploring a world based on hyperbolic geometry, with cells arranged as a truncated order-7 triangular tiling by default (with a few exceptions).
Hungarian mathematics began its rise to prominence in the early 1800s with János Bolyai, one of the creators of non-Euclidean geometry, and his father Farkas Bolyai. Though they were largely ignored during their lifetimes, János Bolyai's groundbreaking work on hyperbolic geometry would later be recognized as foundational to modern mathematics.
Nikolai Ivanovich Lobachevsky (1792–1856) – hyperbolic geometry, a non-Euclidean geometry Michel Chasles (1793–1880) – projective geometry Germinal Dandelin (1794–1847) – Dandelin spheres in conic sections
Compared to Euclidean geometry, hyperbolic geometry presents many difficulties for a coordinate system: the angle sum of a quadrilateral is always less than 360°; there are no equidistant lines, so a proper rectangle would need to be enclosed by two lines and two hypercycles; parallel-transporting a line segment around a quadrilateral causes ...
Many other mathematical objects have their origin in the hyperbola, such as hyperbolic paraboloids (saddle surfaces), hyperboloids ("wastebaskets"), hyperbolic geometry (Lobachevsky's celebrated non-Euclidean geometry), hyperbolic functions (sinh, cosh, tanh, etc.), and gyrovector spaces (a geometry proposed for use in both relativity and ...
János Bolyai (Hungarian: [ˈjaːnoʃ ˈboːjɒi]; 15 December 1802 – 27 January 1860) or Johann Bolyai, [2] was a Hungarian mathematician who developed absolute geometry—a geometry that includes both Euclidean geometry and hyperbolic geometry. The discovery of a consistent alternative geometry that might correspond to the structure of the ...