Formula Mathematics Equation Mathematical Symbol Geometry Information Concept
Mathematics and Art
Traditionally, people tend to see a divide between Maths and Art- it's thought that you can get involved in one or the other, but not both. This couldn't be further from the truth- the two have always enjoyed a symbiotic relationship, with mathematical concepts providing powerful techniques to all kinds of artists, and mathematicians seeing a fundamental beauty in the form of their work. Artistic flair and the scientific method drive each other through new innovations- maths forever invents new potential for a scenic view, while art lies at the heart of every 'Eureka!'-moment. Below are just a few examples of concepts in maths that link directly to art. For more, check out these websites: bugman123.com , mathforum.org/mathimages , rockini.name
Fractal geometry is the study of "roughness"- Fractals are shapes that remain infinitely frayed, no matter how far you zoom in (technically, they're shapes with higher Hausdorff dimension than topological dimension). This gives them a very intricate appearance, which not only means they're good at modelling nature, but also that they look breathtaking.
File:Mandel zoom 03 seehorse.jpg. Wolfgang Beyer.
Graphs of Parametric Equations
Mathematical Graphs in two and three dimensions can be extremely appealing to the eye, producing elegant curves and surfaces with potentially high complexity. Intricate shapes are most easily produced when co-ordinate variables are defined as functions of one or more parameters (like t, etc.). Here are a few examples of classes of parametric graphs, but it is impossible to even attempt to cover the whole field, and the concept can be generalised to higher dimensions.
By Dnttllthmmnm (Own work) [CC BY-SA 4.0 (http://creativecommons.org/licenses/by-sa/4.0)], via Wikimedia Commons
Dodeca-Spidroball - POV-Ray 3.6.1, 7/29/10
A Spidron® is a flat figure made of a number of triangles, where each triangle shares at least one side with another. They were first realised in 1979 by Dániel Erdély as homework in Ernő Rubik's design class. When cut out of paper, they can be deformed to make an intricate 3-D shape, which can in turn be attached to the face of a polyhedron to make a "spidronised" solid.
7 Arm Sphidron - POV-Ray 3.6.1, 7/21/10, Paul Nylander