** Mathematics** is the study of

Fractals arise in surprising places, in this case, the famous Image credit: |

A ** fractal** is "a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole". The term was coined by

A fractal as a

- It has a fine structure at arbitrarily small scales.
- It is too irregular to be easily described in traditional Euclidean geometric language.
- It is
self-similar (at least approximately orstochastically ). - It has a
Hausdorff dimension which is greater than itstopological dimension (although this requirement is not met by space-filling curves such as theHilbert curve ). - It has a simple and recursive definition.

Because they appear similar at all levels of magnification, fractals are often considered to be infinitely complex (in informal terms). Natural objects that approximate fractals to a degree include clouds, mountain ranges, lightning bolts, coastlines, and snow flakes. However, not all self-similar objects are fractals—for example, the

A ** Klein bottle** is an example of a closed

- ...the
Piphilology record (memorizing digits ofPi ) is 70000 as of Mar 2015? - ...that
Auction theory was successfully used in 1994 to sellFCC airwave spectrum, in a financial application ofgame theory ? - ...properties of
Pascal's triangle have application in many fields ofmathematics includingcombinatorics ,algebra ,calculus andgeometry ? - ...work in
artificial intelligence makes use ofSwarm intelligence , which has foundations in the behavorial examples found in nature of ants, birds, bees, and fish among others? - ...that statistical properties dictated by
Benford's Law are used in auditing of financial accounts as one means of detecting fraud? - ...that
Modular arithmetic has application in at least ten different fields of study, including the arts, computer science, and chemistry in addition to mathematics?

The ** Mathematics WikiProject** is the center for mathematics-related editing on Wikipedia. Join the discussion on the project's

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General | Foundations | Number theory | Discrete mathematics |
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