Patterns in naturePatterns in nature are visible regularities of form found in the natural world. These patterns recur in different contexts and can sometimes be modelled mathematically. Natural patterns include symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes. Early Greek philosophers studied pattern, with Plato, Pythagoras and Empedocles attempting to explain order in nature. The modern understanding of visible patterns developed gradually over time.
MathematicsMathematics is a field of knowledge concerned with abstract concepts such as numbers, geometric shapes, sets, functions, and probabilities. It uses logical reasoning and proof to study and establish their properties, often expressed as theorems, formulas, and equations. Mathematics is used to model and solve problems in science, engineering, technology, economics, and everyday life.
FractalGeometryProjecting a sphere to a plane Branches Euclidean Non-Euclidean Elliptic Spherical Hyperbolic Non-Archimedean geometry Projective Affine Synthetic Analytic Algebraic Arithmetic Diophantine Differential Riemannian Symplectic Discrete differential Complex Finite Discrete/Combinatorial Digital Convex Computational Fractal Incidence Noncommutative geometry Noncommutative algebraic geometry ConceptsFeaturesDimension Straightedge and compass constructions Angle Polytope Centroid Diagonal Orthogonality (Perpendicular) Parallel Vertex Congruence Similarity Symmetry Zero-dimensional Point One-dimensional Line Line segment Ray Curve Geodesic Length Two-dimensional Surface Plane Area Polygon Simple Convex Concave Star Regular Reuleaux Triangle Centers Altitude Hypotenuse Pythagorean theorem Circular Reuleaux Hyperbolic Ideal Spherical Quadrilateral Parallelogram Rectangle Square Rhombus Rhomboid Trapezoid Kite Circle Radius Diameter Circumference Disk Area Three-dimensional Surface area Volume Polyhedron Platonic Solid Tetrahedron Reuleaux cuboid Cube Octahedron Dodecahedron Icosahedron Pyramid Star Toroidal Ideal Solid of revolution Sphere Great circle Cylinder Cone Four - other-dimensional 4-polytope Simplex 5-cell Hypercube Tesseract n-sphere Geometers by name Aida Aryabhata Ahmes Alhazen Apollonius Archimedes Atiyah Baudhayana Bolyai Brahmagupta Cartan Chern Coxeter Descartes Euclid Euler Gauss Gromov Hilbert Huygens Jyeṣṭhadeva Kātyāyana Khayyám Klein Lobachevsky Manava Minkowski Minggatu Pascal Pythagoras Parameshvara Poincaré Riemann Sakabe Sijzi al-Tusi Veblen Virasena Yang Hui al-Yasamin Zhang List of geometers by period BCE Ahmes Baudhayana Manava Pythagoras Euclid Archimedes Apollonius 1–1400s Zhang Kātyāyana Aryabhata Brahmagupta Virasena Alhazen Sijzi Khayyám al-Yasamin al-Tusi Yang Hui Parameshvara 1400s–1700s Jyeṣṭhadeva Descartes Pascal Huygens Minggatu Euler Sakabe Aida 1700s–1900s Gauss Lobachevsky Bolyai Riemann Klein Poincaré Hilbert Minkowski Cartan Veblen Coxeter Chern Present day Atiyah Gromov vteInfinitely detailed mathematical structure Sierpiński carpet - infinite perimeter and zero area Highly magnified area on the boundary of the Mandelbrot set The Mandelbrot set: its boundary is a fractal curve with Hausdorff dimension 2.
WallpaperWallpaper is used in interior decoration to cover the interior walls of domestic and public buildings. It is usually sold in rolls and is applied onto a wall using wallpaper paste. Wallpapers can come plain as "lining paper" to help cover uneven surfaces and minor wall defects, "textured", plain with a regular repeating pattern design, or with a single non-repeating large design carried over a set of sheets.
NatureNature, in the broadest sense, is the physical world or universe. In this general sense nature refers to the laws, elements and phenomena of the physical world, including life. Although humans are part of nature, human activity or humans as a whole are often described as at times at odds, or outright separate and even superior to nature.
ShapeA shape is a graphical representation of an object's form or its external boundary, outline, or external surface. It is distinct from other object properties, such as color, texture, or material type. In geometry, shape excludes information about the object's position, size, orientation and chirality. A figure is a representation including both shape and size (as in, e.g., figure of the Earth).
Chaos theoryField of mathematics and science based on non-linear systems and initial conditionsA plot of the Lorenz attractor for values r = 28, σ = 10, b = 8/3A plot of the 3D Lorenz attractorAn animation of a double-rod pendulum at an intermediate energy showing chaotic behavior. Starting the pendulum from a slightly different initial condition would result in a vastly different trajectory.GeometryBranch of mathematics GeometryProjecting a sphere to a plane Branches Euclidean Non-Euclidean Elliptic Spherical Hyperbolic Non-Archimedean geometry Projective Affine Synthetic Analytic Algebraic Arithmetic Diophantine Differential Riemannian Symplectic Discrete differential Complex Finite Discrete/Combinatorial Digital Convex Computational Fractal Incidence Noncommutative geometry Noncommutative algebraic geometry ConceptsFeaturesDimension Straightedge and compass constructions Angle Polytope Centroid Diagonal Orthogonality (Perpendicular) Parallel Vertex Congruence Similarity Symmetry Zero-dimensional Point One-dimensional Line Line segment Ray Curve Geodesic Length Two-dimensional Surface Plane Area Polygon Simple Convex Concave Star Regular Reuleaux Triangle Centers Altitude Hypotenuse Pythagorean theorem Circular Reuleaux Hyperbolic Ideal Spherical Quadrilateral Parallelogram Rectangle Square Rhombus Rhomboid Trapezoid Kite Circle Radius Diameter Circumference Disk Area Three-dimensional Surface area Volume Polyhedron Platonic Solid Tetrahedron Reuleaux cuboid Cube Octahedron Dodecahedron Icosahedron Pyramid Star Toroidal Ideal Solid of revolution Sphere Great circle Cylinder Cone Four - other-dimensional 4-polytope Simplex 5-cell Hypercube Tesseract n-sphere Geometers by name Aida Aryabhata Ahmes Alhazen Apollonius Archimedes Atiyah Baudhayana Bolyai Brahmagupta Cartan Chern Coxeter Descartes Euclid Euler Gauss Gromov Hilbert Huygens Jyeṣṭhadeva Kātyāyana Khayyám Klein Lobachevsky Manava Minkowski Minggatu Pascal Pythagoras Parameshvara Poincaré Riemann Sakabe Sijzi al-Tusi Veblen Virasena Yang Hui al-Yasamin Zhang List of geometers by period BCE Ahmes Baudhayana Manava Pythagoras Euclid Archimedes Apollonius 1–1400s Zhang Kātyāyana Aryabhata Brahmagupta Virasena Alhazen Sijzi Khayyám al-Yasamin al-Tusi Yang Hui Parameshvara 1400s–1700s Jyeṣṭhadeva Descartes Pascal Huygens Minggatu Euler Sakabe Aida 1700s–1900s Gauss Lobachevsky Bolyai Riemann Klein Poincaré Hilbert Minkowski Cartan Veblen Coxeter Chern Present day Atiyah Gromov vte Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures.
ScienceSystematic endeavour to gain knowledgeScience is a systematic discipline that builds and organises knowledge in the form of testable explanations about nature and society. It is driven by the scientific method: an empirical cycle that typically involves making observations, producing hypotheses, testing them with evidence, and drawing conclusions.
SenseA sense is a biological system used by an organism for sensation, the process of gathering information about the surroundings through the detection of stimuli. During sensation, sense organs collect various stimuli (such as a sound or smell) for transduction, meaning transformation into a form that can be understood by the brain. Sensation and perception are fundamental to nearly every aspect of an organism's cognition, behavior and thought.
AbstractionAbstraction is the process of generalizing rules and concepts from specific examples, literal (real or concrete) signifiers, first principles, or other methods. The result of the process, an abstraction, is a concept that acts as a common noun for all subordinate concepts and connects any related concepts as a group, field or category. Abstractions and levels of abstraction play an important role in the theory of general semantics originated by Alfred Korzybski.
LanguageStructured system of communicationA mural in Teotihuacan, Mexico (c. 2nd century) depicting a person emitting a speech scroll from his mouth, symbolizing speechA Cuneiform tabletChildren of deaf adults using American Sign LanguageBraille, a tactile writing systemLanguage is a structured system of communication that consists of grammar and vocabulary.
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