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Patterns 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. [ 1 ]
A pattern is a regularity in the world, in human-made design, [1] or in abstract ideas. As such, the elements of a pattern repeat in a predictable manner. A geometric pattern is a kind of pattern formed of geometric shapes and typically repeated like a wallpaper design.
Physicist Max Tegmark argued that the effectiveness of mathematics in describing external physical reality is because the physical world is an abstract mathematical structure. [ 8 ] [ 15 ] This theory, referred to as the mathematical universe hypothesis , mirrors ideas previously advanced by Peter Atkins . [ 16 ]
Possibly as a result of this unique property, the spira mirabilis has evolved in nature, appearing in certain growing forms such as nautilus shells and sunflower heads. Jacob Bernoulli wanted such a spiral engraved on his headstone along with the phrase " Eadem mutata resurgo " ("Although changed, I shall arise the same."), but, by error, an ...
The "nature" of the objects defined this way is a philosophical problem that mathematicians leave to philosophers, even if many mathematicians have opinions on this nature, and use their opinion—sometimes called "intuition"—to guide their study and proofs.
Number systems have progressed from the use of fingers and tally marks, perhaps more than 40,000 years ago, to the use of sets of glyphs able to represent any conceivable number efficiently. The earliest known unambiguous notations for numbers emerged in Mesopotamia about 5000 or 6000 years ago.
A model for the pattern of florets in the head of a sunflower [13] was proposed by H. Vogel. This has the form =, = where n is the index number of the floret and c is a constant scaling factor, and is a form of Fermat's spiral.
Cast metal vessels lacked the inherent rotational symmetry of wheel-made pottery, but otherwise provided a similar opportunity to decorate their surfaces with patterns pleasing to those who used them. The ancient Chinese, for example, used symmetrical patterns in their bronze castings as early as the 17th century BC. Bronze vessels exhibited ...