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It is a body of knowledge and practice
Mathematics
It was derived fromthe contributions of thinkers throughout the ages and across the globe
Mathematics
It gives us a way to understand patterns, to quantify relationships, and to predict the future
Mathematics
Math helps us understand the world —and we use the world to understand math.
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Use of mathematics to model situations or events in the world;
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Explanations of how the complexity and interrelatedness of situations or events in the world are reflected in the model;
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Data generated by the model to make and defend a decision; and
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A decision or conclusion supported by the mathematics within the context of a global community.
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The application of appropriate strategies to solve problems;
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The use of appropriate mathematical tools, procedures, and representations to solve the problem;
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The review and proof of a correct and reasonable mathematical solution given the context.
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The development, explanation, and justification of mathematical arguments, including concepts and procedures used
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Coherently and clear communication using correct mathematical language and visual representations;
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The expression of mathematical ideas using the symbols and conventions of mathematics.
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Patterns in nature are visible regular forms found in the natural world. The patterns can sometimes be modeled mathematically and they include symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes.
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In 1202,Introduced the Fibonacci number sequence. It turns out that simple equations involving the Fibonacci numbers can describe most of the complex spiral growth patterns found in nature.
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Belgian physicist Joseph Plateau (1801–1883) formulated the mathematical problem of the existence of a minimal surface with a given boundary, which is now named after him. He studied soap films intensively and formulated Plateau’s laws, which describe the structures formed by films in foams.
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The German psychologist (1810–1876) claimed that the golden ratio was expressed in the arrangement of plant parts, in the skeletons of animals and the branching patterns of their veins and nerves, as well as in the geometry of crystals.
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painted beautiful illustrations of marine organisms, in particular Radiolaria, emphasizing their symmetry to support his faux-Darwinian theories of evolution.
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The American photographer Wilson Bentley (1865–1931) took the first micrograph of a snowflake in 1885.
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pioneered the study of growth and formin his 1917 book.
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better known for his work on computing and codebreaking, wrote The Chemical Basis of Morphogenesis, an analysis of the mechanisms that would be needed to create patterns in living organisms, in the process called morphogenesis
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developed the L-system, a formal grammar which can be used to model plant growth patterns in the style of fractals. L-systems have an alphabet of symbols that can be combined using production rules to build larger strings of symbols, and a mechanism for translating the generated strings into geometric structures
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Symmetry is pervasive in living things. Animals mainly have bilateral or mirror symmetry, as do the leaves of plants and some flowers such as orchids. • Plants often have radial or rotational symmetry, as do many flowers and some groups of animals such as sea anemones. • Rotational symmetry is also found at different scales among non-living things including the crown-shaped splash pattern formed when a drop falls into a pond, and both the spheroidal shape and rings of a planet like Saturn.
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are infinitely self-similar, iterated mathematical constructs having fractal dimension. Infinite iteration is not possible in nature so all ‘fractal’ patterns are only approximate.
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are common in plants and in some animals, notably molluscs.
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are sinuous bends in rivers or other channels, which form as a fluid, most often water, flows around bends. As soon as the path is slightly curved, the size and curvature of each loop increases as helical flow drags material like sand and gravel across the river to the inside of the bend. The outside of the loop is left clean and unprotected, so erosion accelerates, further increasing the meandering in a powerful positive feedback loop.
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are disturbances that carry energy as they move. Mechanical waves propagate through a medium – air or water, making it oscillate as they pass by
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Dunes may form a range of patterns including crescents, very long straight lines, stars, domes, parabolas, and longitudinal or Seif (‘sword’) shapes.
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A soap bubble forms a sphere, a surface with minimal area — the smallest possible surface area for the volume enclosed
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are patterns formed by repeating tiles all over a flat surface.
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are linear openings that formin materials to relieve stress.
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Leopards and ladybirds are spotted; angelfish and zebras are striped. • These patterns have an evolutionary explanation: they have functions which increase the chances that the offspring of the patterned animal will survive to reproduce. • One function of animal patterns is camouflage; for instance, a leopard that is harder to see catches more prey
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