{"/e/geometry-and-topology/angle/": {"t": "Angle", "s": "A geometric figure formed by two lines meeting at a point."}, "https://codexery.com/greek-inventions/e/greek-inventions/euclidean-geometry/": {"t": "Euclidean geometry", "s": "Ancient Greek mathematician who systematized geometry in Elements."}, "/e/geometry-and-topology/metric-space/": {"t": "Metric space", "s": "A set with a distance function between its points."}, "/e/geometry-and-topology/affine-transformation/": {"t": "Affine transformation", "s": "A transformation preserving lines and parallelism in affine spaces."}, "/e/geometry-and-topology/affine-space/": {"t": "Affine space", "s": "Geometric structure preserving parallelism and ratios, not distances."}, "https://codexery.com/set-theory-logic/e/set-theory-and-logic/ordered-pair/": {"t": "Ordered pair", "s": "Ordered pair: a fundamental mathematical object with order significance."}, "/e/geometry-and-topology/manifold/": {"t": "Manifold", "s": "A topological space locally resembling Euclidean space near each point."}, "https://codexery.com/scientists-and-mathematicians/e/scientists-and-mathematicians/leonhard-euler/": {"t": "Leonhard Euler", "s": "Swiss polymath who founded graph theory and topology, introduced key mathematical notation, and was the most prolific mathematician of the 18th century."}, "https://codexery.com/mathematicians/e/mathematicians/felix-klein/": {"t": "Felix Klein", "s": "German mathematician known for the Erlangen program and the Klein bottle.", "i": "https://codexery.com/mathematicians/img/mathematicians/felix-klein.webp", "c": "via Wikipedia: Felix Klein · see source"}, "https://codexery.com/mathematicians/e/mathematicians/hermann-weyl/": {"t": "Hermann Weyl", "s": "Universal mathematician who bridged pure mathematics and theoretical physics.", "i": "https://codexery.com/mathematicians/img/mathematicians/hermann-weyl.webp", "c": "via Wikipedia: Hermann Weyl · see source"}, "https://codexery.com/mathematicians/e/mathematicians/h-s-m-coxeter/": {"t": "H. S. M. Coxeter", "s": "British-Canadian geometer and mathematician, a leading figure in 20th-century geometry."}, "https://codexery.com/geometry-and-shapes/e/geometry-and-shapes/rotation-mathematics/": {"t": "Rotation (mathematics)", "s": "A geometric motion preserving at least one point."}, "https://codexery.com/historical-figures/e/notable/david-hilbert/": {"t": "David Hilbert", "s": "German mathematician and philosopher of mathematics"}, "https://codexery.com/algebra/e/algebra/representation-theory/": {"t": "Representation theory", "s": "Studies algebraic structures via linear transformations."}, "https://codexery.com/geometry-and-shapes/e/geometry-and-shapes/three-dimensional-space/": {"t": "Three-dimensional space", "s": "Three coordinates define a point in space."}, "https://codexery.com/classical-mechanics-and-dynamics/e/classical-mechanics-and-dynamics/kinematics/": {"t": "Kinematics", "s": "Subfield of physics and geometry describing motion without forces."}, "https://codexery.com/classical-mechanics/e/classical-mechanics/velocity/": {"t": "Velocity", "s": "A vector measure of speed with direction."}, "https://codexery.com/geometry-and-shapes/e/geometry-and-shapes/shear-mapping/": {"t": "Shear mapping", "s": "An affine transformation displacing points proportionally to signed distance."}, "https://codexery.com/geometry-and-shapes/e/geometry-and-shapes/parallel-geometry/": {"t": "Parallel (geometry)", "s": "Parallel lines are coplanar lines that never meet."}, "https://codexery.com/geometry-and-shapes/e/geometry-and-shapes/similarity-geometry/": {"t": "Similarity (geometry)", "s": "Two objects are similar if they have the same shape."}, "https://codexery.com/combinatorics/e/combinatorics/bijection/": {"t": "Bijection", "s": "A function pairing each element of two sets exactly once.", "i": "https://codexery.com/combinatorics/img/combinatorics/bijection.webp", "c": "Schapel · Public domain"}, "https://codexery.com/sets-and-logic/e/sets-and-logic/set-mathematics/": {"t": "Set (mathematics)", "s": "A set is a collection of different things, typically mathematical objects."}, "https://codexery.com/design-digital-arts/e/design-and-digital-arts/computer-graphics/": {"t": "Computer graphics", "s": "Computer graphics generates and manipulates images using computers."}, "https://codexery.com/algebra/e/algebra/rank-linear-algebra/": {"t": "Rank (linear algebra)", "s": "Rank measures the dimension of a matrix's column or row space."}, "https://codexery.com/historical-figures/e/notable/carl-friedrich-gauss/": {"t": "Carl Friedrich Gauss", "s": "German mathematician, astronomer, geodesist, and physicist"}, "https://codexery.com/geometry-and-shapes/e/geometry-and-shapes/plane-geometry/": {"t": "Plane (geometry)", "s": "Two-dimensional Euclidean space with distance and angle."}, "/e/geometry-and-topology/analytic-geometry/": {"t": "Analytic geometry", "s": "Study of geometry using a coordinate system."}, "/e/geometry-and-topology/cohomology/": {"t": "Cohomology", "s": "Algebraic invariants encoding obstructions to global properties."}, "/e/geometry-and-topology/differential-geometry/": {"t": "Differential geometry", "s": "Study of smooth shapes and spaces using calculus and algebra."}, "https://codexery.com/historical-figures/e/notable/alexander-grothendieck/": {"t": "Alexander Grothendieck", "s": "German-born French mathematician and leading figure in modern algebraic geometry"}, "https://codexery.com/topology-and-abstract-spaces/e/topology-and-abstract-spaces/sheaf-mathematics/": {"t": "Sheaf (mathematics)", "s": "Tool for tracking local data on topological spaces."}, "https://codexery.com/algebra/e/algebra/polynomial/": {"t": "Polynomial", "s": "A mathematical expression of variables and coefficients using addition and multiplication."}, "https://codexery.com/geometry-and-shapes/e/geometry-and-shapes/sphere/": {"t": "Sphere", "s": "A sphere is a set of points equidistant from a center in 3D space."}, "https://codexery.com/algebra/e/algebra/polynomial-ring/": {"t": "Polynomial ring", "s": "Ring formed from polynomials with coefficients in another ring."}, "/e/geometry-and-topology/topological-space/": {"t": "Topological space", "s": "A set with a structure defining closeness without distance."}, "https://codexery.com/algebra/e/algebra/rational-function/": {"t": "Rational function", "s": "Ratio of two polynomial functions, fundamental in algebra and analysis."}, "https://codexery.com/set-theory-and-foundations/e/set-theory-and-foundations/complement-set-theory/": {"t": "Complement (set theory)", "s": "Set of elements not in a given set."}, "https://codexery.com/set-theory-logic/e/set-theory-and-logic/quantifier-elimination/": {"t": "Quantifier elimination", "s": "Quantifier elimination is a concept of simplification used in mathematical logic, model theory, and theoretical computer science."}, "https://codexery.com/inventors/e/great-inventors/archimedes/": {"t": "Archimedes", "s": "Ancient Greek mathematician, physicist, engineer, astronomer, and inventor of Syracuse."}, "https://codexery.com/scientists-and-mathematicians/e/scientists-and-mathematicians/apollonius-of-perga/": {"t": "Apollonius of Perga", "s": "Ancient Greek geometer who defined conic sections."}, "https://codexery.com/historical-figures/e/scientists/ren-descartes/": {"t": "René Descartes", "s": "Father of modern philosophy and analytic geometry"}, "/e/geometry-and-topology/homology-mathematics/": {"t": "Homology (mathematics)", "s": "Homology studies invariants via chain complexes and cycles."}, "https://codexery.com/topology-and-abstract-spaces/e/topology-and-abstract-spaces/fundamental-group/": {"t": "Fundamental group", "s": "A homotopy invariant group of loops in a topological space."}, "https://codexery.com/languages-and-dialects/e/languages-and-dialects/greek-language/": {"t": "Greek language", "s": "Greek is the world's oldest recorded living language."}, "/e/geometry-and-topology/torus/": {"t": "Torus", "s": "A surface of revolution shaped like a doughnut."}, "https://codexery.com/topology-and-abstract-spaces/e/topology-and-abstract-spaces/klein-bottle/": {"t": "Klein bottle", "s": "A one-sided surface with no boundary."}, "https://codexery.com/set-theory-logic/e/set-theory-and-logic/natural-transformation/": {"t": "Natural transformation", "s": "A morphism of functors preserving categorical structure."}, "https://codexery.com/mathematics-and-cryptography/e/mathematics-and-cryptography/samuel-eilenberg/": {"t": "Samuel Eilenberg", "s": "Co-founder of category theory and homological algebra"}, "/e/geometry-and-topology/coordinate-system/": {"t": "Coordinate system", "s": "A system using numbers to determine positions in space."}, "https://codexery.com/economic-concepts/e/economic-concepts/economics/": {"t": "Economics", "s": "Social science studying production, distribution, and consumption of goods and services.", "i": "https://codexery.com/economic-concepts/img/economic-concepts/economics.webp", "c": "Pk0001 · CC BY-SA 4.0"}, "/e/geometry-and-topology/algebraic-geometry/": {"t": "Algebraic geometry", "s": "Branch of mathematics studying zeros of polynomial equations."}, "https://codexery.com/authors-poets/e/authors-and-poets/omar-khayyam/": {"t": "Omar Khayyam", "s": "Persian poet and polymath who revolutionized algebra and astronomy."}, "https://codexery.com/scientists-and-mathematicians/e/scientists-and-mathematicians/pierre-de-fermat/": {"t": "Pierre de Fermat", "s": "Mathematician and magistrate who pioneered analytic geometry, probability, and number theory."}, "https://codexery.com/languages-and-dialects/e/languages-and-dialects/french-language/": {"t": "French language", "s": "A Romance language of the Indo-European family, descended from Vulgar Latin and shaped by Celtic and Frankish influences."}, "https://codexery.com/languages/e/languages/latin/": {"t": "Latin", "s": "A classical language of the Italic branch, Latin evolved into the Romance languages and remained a key scholarly tongue into the early 19th century."}, "https://codexery.com/sets-and-logic/e/sets-and-logic/subset/": {"t": "Subset", "s": "A set whose elements all belong to another set."}, "https://codexery.com/algebra/e/algebra/quadratic-equation/": {"t": "Quadratic equation", "s": "A second-degree polynomial equation with at most two solutions."}, "https://codexery.com/algebra/e/algebra/quadratic-function/": {"t": "Quadratic function", "s": "A polynomial function of degree two, graphed as a parabola."}, "https://codexery.com/geometry-and-shapes/e/geometry-and-shapes/tangent/": {"t": "Tangent", "s": "The line that just touches a curve at a point."}, "https://codexery.com/units-measurement/e/units-and-measurement/unit-of-measurement/": {"t": "Unit of measurement", "s": "Standardized quantities enabling consistent measurement across time and place."}, "https://codexery.com/metrology/e/metrology/international-system-of-quantities/": {"t": "International System of Quantities", "s": "The standard system of quantities underlying the SI, codified in ISO/IEC 80000."}, "https://codexery.com/units-measurement/e/units-and-measurement/international-system-of-units/": {"t": "International System of Units", "s": "The modern metric system used worldwide for measurement."}, "https://codexery.com/metrology/e/metrology/dimensional-analysis/": {"t": "Dimensional analysis", "s": "Method for analyzing physical dimensions of quantities."}, "https://codexery.com/transportation/e/transportation/navigation/": {"t": "Navigation", "s": "The art and science of directing movement from one place to another."}, "https://codexery.com/lines-hemispheres/e/lines-and-hemispheres/azimuth/": {"t": "Azimuth", "s": "Horizontal angle from north used in navigation and astronomy."}, "https://codexery.com/historical-figures/e/notable/euclid/": {"t": "Euclid", "s": "Ancient Greek mathematician, author of the Elements."}, "https://codexery.com/philosophers-thinkers/e/philosophers-and-thinkers/thales-of-miletus/": {"t": "Thales of Miletus", "s": "Pre-Socratic philosopher, first to use natural reason over myth."}, "https://codexery.com/geometry-and-shapes/e/geometry-and-shapes/shape/": {"t": "Shape", "s": "Geometric information remaining after removing location, scale, orientation, and reflection."}, "https://codexery.com/classical-mechanics-and-dynamics/e/classical-mechanics-and-dynamics/rotation/": {"t": "Rotation", "s": "Rotational motion leaves at least one point unchanged."}, "https://codexery.com/geometry-and-shapes/e/geometry-and-shapes/polygon/": {"t": "Polygon", "s": "A plane figure of connected line segments forming a closed chain."}, "https://codexery.com/geometry-and-shapes/e/geometry-and-shapes/polyhedron/": {"t": "Polyhedron", "s": "Three-dimensional figures with flat faces, straight edges, and vertices."}, "https://codexery.com/algebra/e/algebra/real-valued-function/": {"t": "Real-valued function", "s": "A function that assigns a real number to each domain element."}, "/e/geometry-and-topology/connected-space/": {"t": "Connected space", "s": "A topological space that cannot be split into two disjoint open subsets."}, "/e/geometry-and-topology/compact-space/": {"t": "Compact space", "s": "Compactness makes a space behave like a finite set."}, "https://codexery.com/set-theory-logic/e/set-theory-and-logic/operation-mathematics/": {"t": "Operation (mathematics)", "s": "A function combining elements of a set into another element."}, "https://codexery.com/set-theory-and-foundations/e/set-theory-and-foundations/axiom/": {"t": "Axiom", "s": "A foundational statement accepted as true without proof."}, "https://codexery.com/geometry-and-shapes/e/geometry-and-shapes/spherical-coordinate-system/": {"t": "Spherical coordinate system", "s": "A system using distance and two angles to locate points in space."}, "https://codexery.com/historical-eras/e/historical-eras/hellenistic-period/": {"t": "Hellenistic period", "s": "Era of Greek cultural expansion after Alexander the Great's conquests."}, "https://codexery.com/geometry-and-shapes/e/geometry-and-shapes/volume/": {"t": "Volume", "s": "Volume quantifies three-dimensional space and container capacity."}, "https://codexery.com/combinatorics/e/combinatorics/pigeonhole-principle/": {"t": "Pigeonhole principle", "s": "If n items go into m boxes and n > m, one box holds more."}, "https://codexery.com/scientists-and-mathematicians/e/scientists-and-mathematicians/karl-weierstrass/": {"t": "Karl Weierstrass", "s": "Father of modern analysis"}, "https://codexery.com/mathematicians/e/mathematicians/henri-lebesgue/": {"t": "Henri Lebesgue", "s": "French mathematician who revolutionized integration theory.", "i": "https://codexery.com/mathematicians/img/mathematicians/henri-lebesgue.webp", "c": "via Wikipedia: Henri Lebesgue · see source"}, "https://codexery.com/topology-and-abstract-spaces/e/topology-and-abstract-spaces/topology/": {"t": "Topology", "s": "Study of properties preserved under continuous deformations."}, "https://codexery.com/sets-and-logic/e/sets-and-logic/empty-set/": {"t": "Empty set", "s": "The unique set containing no elements."}, "https://codexery.com/mathematicians/e/mathematicians/felix-hausdorff/": {"t": "Felix Hausdorff", "s": "Founder of modern topology and pioneer of set theory", "i": "https://codexery.com/mathematicians/img/mathematicians/felix-hausdorff.webp", "c": "via Wikipedia: Felix Hausdorff · see source"}, "https://codexery.com/set-theory-logic/e/set-theory-and-logic/partition-of-a-set/": {"t": "Partition of a set", "s": "Grouping elements into non-empty, disjoint subsets that cover the whole set."}, "https://codexery.com/crystallography/e/crystallography/crystal-structure/": {"t": "Crystal structure", "s": "Ordered arrangement of particles in crystalline materials.", "i": "https://codexery.com/crystallography/img/crystallography/crystal-structure.webp", "c": "Biochemlife · CC BY-SA 4.0"}, "https://codexery.com/classical-mechanics-and-dynamics/e/classical-mechanics-and-dynamics/frame-of-reference/": {"t": "Frame of reference", "s": "Abstract coordinate system for describing physical space and motion."}, "https://codexery.com/set-theory-and-foundations/e/set-theory-and-foundations/axiom-of-choice/": {"t": "Axiom of choice", "s": "Given any collection of non-empty sets, one can identify another set containing one element chosen from each set, even if the collection is infinite."}, "https://codexery.com/algebra/e/algebra/ring-mathematics/": {"t": "Ring (mathematics)", "s": "Algebraic structure with two binary operations, generalizing integer arithmetic."}, "https://codexery.com/set-theory-and-foundations/e/set-theory-and-foundations/cardinality/": {"t": "Cardinality", "s": "Fundamental concept defining the size of sets."}, "https://codexery.com/set-theory-and-foundations/e/set-theory-and-foundations/cardinal-number/": {"t": "Cardinal number", "s": "A number measuring the size of a set."}, "https://codexery.com/probability-statistics/e/probability-and-statistics/probability-distribution/": {"t": "Probability distribution", "s": "Mathematical description of probabilities for random phenomena.", "i": "https://codexery.com/probability-statistics/img/probability-and-statistics/probability-distribution.webp", "c": "Incnis Mrsi ( talk ) · Public domain"}, "https://codexery.com/sets-and-logic/e/sets-and-logic/set-theory/": {"t": "Set theory", "s": "The branch of mathematical logic that studies sets, founded by Georg Cantor in the 1870s."}, "https://codexery.com/set-theory-logic/e/set-theory-and-logic/power-set/": {"t": "Power set", "s": "The set of all subsets of a given set."}, "https://codexery.com/card-games/e/card-games/standard-52-card-deck/": {"t": "Standard 52-card deck", "s": "The most common playing card deck used worldwide."}, "https://codexery.com/set-theory-and-foundations/e/set-theory-and-foundations/axiom-of-pairing/": {"t": "Axiom of pairing", "s": "Any two objects have a pair."}, "https://codexery.com/set-theory-and-foundations/e/set-theory-and-foundations/axiom-of-power-set/": {"t": "Axiom of power set", "s": "Axiom ensuring every set has a power set."}, "https://codexery.com/set-theory-and-foundations/e/set-theory-and-foundations/axiom-schema-of-specification/": {"t": "Axiom schema of specification", "s": "Axiom schema that asserts any definable subclass of a set is itself a set."}, "https://codexery.com/sets-and-logic/e/sets-and-logic/universe-mathematics/": {"t": "Universe (mathematics)", "s": "A universe is a collection that contains all entities one wishes to consider in a given situation."}, "/e/geometry-and-topology/knot-theory/": {"t": "Knot theory", "s": "Mathematical study of knots as embeddings of circles in space."}, "https://codexery.com/classical-mechanics-and-dynamics/e/classical-mechanics-and-dynamics/fluid-mechanics/": {"t": "Fluid mechanics", "s": "Branch of physics studying fluids and forces on them."}, "https://codexery.com/topology-and-abstract-spaces/e/topology-and-abstract-spaces/homotopy/": {"t": "Homotopy", "s": "A continuous deformation between two functions in topology."}, "/e/geometry-and-topology/algebraic-topology/": {"t": "Algebraic topology", "s": "Branch of mathematics using algebra to study topological spaces."}, "/e/geometry-and-topology/cartesian-product/": {"t": "Cartesian product", "s": "Set of all ordered pairs from two sets."}, "https://codexery.com/combinatorics/e/combinatorics/permutation/": {"t": "Permutation", "s": "A bijection rearranging a set's elements into a new order."}, "https://codexery.com/algebra/e/algebra/normal-subgroup/": {"t": "Normal subgroup", "s": "Subgroup invariant under conjugation by group elements."}, "https://codexery.com/mathematics-and-cryptography/e/mathematics-and-cryptography/vladimir-arnold/": {"t": "Vladimir Arnold", "s": "Soviet and Russian mathematician (source does not provide details about Arnold)."}, "https://codexery.com/topology-and-abstract-spaces/e/topology-and-abstract-spaces/m-bius-strip/": {"t": "Möbius strip", "s": "A non-orientable surface with one side and one boundary."}, "https://codexery.com/geometry-and-shapes/e/geometry-and-shapes/unit-circle/": {"t": "Unit circle", "s": "A circle of radius 1, central to trigonometry and complex analysis."}, "https://codexery.com/topology-and-abstract-spaces/e/topology-and-abstract-spaces/covering-space/": {"t": "Covering space", "s": "A space that locally projects multiple copies onto a base space."}, "https://codexery.com/mathematicians/e/mathematicians/henri-poincar/": {"t": "Henri Poincaré", "s": "French polymath and last universalist mathematician.", "i": "https://codexery.com/mathematicians/img/mathematicians/henri-poincar.webp", "c": "via Wikipedia: Henri Poincaré · see source"}, "https://codexery.com/cities/e/landmark-cities/moscow/": {"t": "Moscow", "s": "Capital of Russia, largest city in Europe, and a historic center of power and culture."}, "https://codexery.com/planets-and-dwarf-planets/e/planets-and-dwarf-planets/earth/": {"t": "Earth", "s": "The only known planet with liquid surface water and life."}, "https://codexery.com/scientists-and-mathematicians/e/scientists-and-mathematicians/nikolai-lobachevsky/": {"t": "Nikolai Lobachevsky", "s": "The Copernicus of Geometry who pioneered hyperbolic geometry."}, "https://codexery.com/science-and-technology/e/science-and-technology/natural-science/": {"t": "Natural science", "s": "Empirical study of natural phenomena through observation and experimentation."}, "https://codexery.com/historical-figures/e/notable/albert-einstein/": {"t": "Albert Einstein", "s": "Theoretical physicist who developed relativity and E=mc²"}, "https://codexery.com/particle-and-nuclear-physics/e/particle-and-nuclear-physics/quantum-field-theory/": {"t": "Quantum field theory", "s": "Framework combining field theory, relativity, and quantum mechanics."}, "https://codexery.com/science-measurement/e/science-and-measurement/machine-learning/": {"t": "Machine learning", "s": "Statistical algorithms that learn from data without explicit programming."}, "https://codexery.com/scientists-and-mathematicians/e/scientists-and-mathematicians/eratosthenes/": {"t": "Eratosthenes", "s": "Ancient Greek polymath who first measured Earth's circumference."}, "https://codexery.com/ancient-greek-astronomers/e/ancient-greek-astronomers/ptolemy/": {"t": "Ptolemy", "s": "Greco-Roman scholar who authored the Almagest and Geography."}, "https://codexery.com/ancient-classical-texts/e/ancient-and-classical-texts/geography-ptolemy/": {"t": "Geography (Ptolemy)", "s": "A 2nd-century gazetteer and atlas foundational to later cartography."}, "https://codexery.com/historical-figures/e/notable/isaac-newton/": {"t": "Isaac Newton", "s": "English polymath who formulated laws of motion and universal gravitation."}, "https://codexery.com/historical-figures/e/notable/gottfried-wilhelm-leibniz/": {"t": "Gottfried Wilhelm Leibniz", "s": "German polymath and co-creator of calculus"}, "https://codexery.com/other-geographic-features/e/other-geographic-features/mercator-projection/": {"t": "Mercator projection", "s": "Gerardus Mercator's 1569 cylindrical map projection, built so sailors could steer by straight lines.", "i": "https://codexery.com/other-geographic-features/img/other-geographic-features/mercator-projection.webp", "c": "via Wikipedia: Mercator projection · see source"}, "https://codexery.com/algebra/e/algebra/quadratic-form/": {"t": "Quadratic form", "s": "A homogeneous polynomial of degree two in several variables."}, "https://codexery.com/scientists-and-mathematicians/e/scientists-and-mathematicians/bernhard-riemann/": {"t": "Bernhard Riemann", "s": "German mathematician who revolutionized analysis, geometry, and number theory"}, "/e/geometry-and-topology/affine-geometry/": {"t": "Affine geometry", "s": "Geometry without distance or angle, focusing on parallelism."}, "https://codexery.com/set-theory-logic/e/set-theory-and-logic/recursion/": {"t": "Recursion", "s": "A process defined by reference to a simpler version of itself."}, "https://codexery.com/historical-figures/e/notable/benoit-mandelbrot/": {"t": "Benoit Mandelbrot", "s": "The father of fractals who found order in roughness"}, "https://codexery.com/mythological-creatures/e/mythological-creatures/homunculus/": {"t": "Homunculus", "s": "A miniature artificial human from alchemy and folklore."}, "https://codexery.com/historical-figures/e/notable/georg-cantor/": {"t": "Georg Cantor", "s": "Founder of set theory and transfinite numbers"}, "https://codexery.com/set-theory-and-foundations/e/set-theory-and-foundations/cantor-set/": {"t": "Cantor set", "s": "A fractal set of points on a line, built by repeatedly removing middle thirds, with surprising properties of uncountability and zero measure."}, "https://codexery.com/mathematics-and-cryptography/e/mathematics-and-cryptography/wac-aw-sierpi-ski/": {"t": "Wacław Sierpiński", "s": "Mathematician mentioned in the Mathemalchemy installation."}, "https://codexery.com/complexity-theory/e/complexity-theory/np-hardness/": {"t": "NP-hardness", "s": "Problems at least as hard as the hardest in NP."}, "https://codexery.com/complexity-theory/e/complexity-theory/time-complexity/": {"t": "Time complexity", "s": "A measure of algorithm running time as input size grows."}, "https://codexery.com/topology-and-abstract-spaces/e/topology-and-abstract-spaces/euler-characteristic/": {"t": "Euler characteristic", "s": "Topological invariant describing shape regardless of bending."}, 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cannot be superposed on its mirror image.", "i": "https://codexery.com/organic-chemistry-and-reaction-mechanism/img/organic-chemistry-and-reaction-mechanisms/chirality-chemistry.webp", "c": "Wikimedia Commons · Public domain"}, "https://codexery.com/mathematical-logic-and-computation/e/mathematical-logic-and-computation/algorithm/": {"t": "Algorithm", "s": "A finite sequence of logical instructions for solving problems."}, "https://codexery.com/geometry-and-shapes/e/geometry-and-shapes/surface-topology/": {"t": "Surface (topology)", "s": "A surface is a two-dimensional topological manifold."}, "https://codexery.com/medical-tests/e/medical-tests/ct-scan/": {"t": "CT scan", "s": "Cross-sectional X-ray imaging for detailed internal views."}, "https://codexery.com/mechanics-and-fluid-dynamics/e/mechanics-and-fluid-dynamics/hamiltonian-mechanics/": {"t": "Hamiltonian mechanics", "s": "Reformulation of Lagrangian mechanics using generalized momenta."}, 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