Nature of Mathematics

Where is Mathematics?

• Many patterns and occurrences exist in nature, in our world, in our life.

• Mathematics helps make sense of these patterns and occurrences.

What Role does Mathematics play in our world?

• Mathematics helps organize patterns and regularities in our world.

• Mathematics helps predict the behavior of nature and phenomena in the world.

• Mathematics helps control nature and occurrences in the world for our own ends.

• Mathematics has numerous applications in the world making it indispensable.

Symmetry

refers to a correspondence of body parts, in size, shape, and relative position, on opposite sides of a dividing line or distributed around a central point or axis.

Trees

is fractal as the branches remain approximately self-similar, repeating as they progressively decrease in size culminating in twigs. As for all fractals, tree branches repeat at different scales, having a fine and detailed structure that reiterates.

Spiral

would be described as a circular pattern beginning at a center point and circling around the center point as the pattern moves outward. beginning at a center point and circling around the center point as the pattern moves outward.

Meanders

are patterns seen in nature where curved lines are the dominant design. River curves, a slithering snake, or the curling tendrils of a climbing vine are examples of a meandering pattern in nature.

Waves

can be seen in bodies of water, cloud formations, or sand where the material has been disturbed by a force such as wind.

Foam

• are patterns in nature that are formed from repeating spheres.

• are a volume of bubbles of many sizes, where the spaces between each larger bubble contain smaller bubbles.

• in some ways, foams can be fractal.

Tesselation

is simply a tiling that has a repeated pattern of one or more shapes. For a pattern to truly be a tessellation, the shapes can’t overlap and can have no spaces between them. The pattern can be created by rotating, translating (sliding), and/or reflecting (mirroring) the shapes.

Cracks

often seen in dried landscapes, mud cracks, and tree barks, these patterns arise due to tension and drying.

Stripes

• a pattern of bands or strips, often of the same width and color along the length.

• are a brilliant way of providing camouflage. They break up the edges of an organism, making it harder to see against the background.