MMW Midterms

Symmetry

When the figure has two sides that mirror each other

Bilateral

Symmetrical objects that mirror each other

Radial or Rotational

This is where there is a center point and numerous lines of symmetry could be drawn

Fivefold

Echinoderms (starfish, sea urchin)

Sixfold

Snowflakes

Crystal Habits

Cubic, Octahedral, Rhombic, Dodecahedral (Fluorite, Garnet). The ideal shape of crystal.

Spherical

Volvox

Fractals

Infinitely self similar, iterated mathematical constructs having dimension. (corals, honeycomb, leaf, broccoli, angelica flowerhead).

Chaos

Sensitive to initial conditions, which require topological mixing. (shell of gastropod mollusk, vortex street of clouds).

Meander

Sinuous bends in rivers or other channels. (Flowing water, crawling snake, brain coral)

Waves

Disturbances in that carry energy

Dunes

When wind blows the sand

Tesellation

Repeating patterns on a flat surface

Cracks

Linear openings due to stress or tension. (Tree bark, old pottery surface)

Spots and Stripes

Common to many species of animals (leopards, ladybirds)

Leonardo Pisano Bogollo

Fibonacci sequence

Fibonacci

Son of Bonacci

Golden Ratio

Ratio of any two successive fibonacci numbers

Mathematical Language

system used to communicate mathematical thought

Precise, Concise, Powerful, Non-temporal

Characteristics of mathematical language

Summation

∑

There exist

∃

and

∧

or

∨

for every

∀

Element of

∈

not an element of

∉

if then

→

if and only if

⟹

Real numbers

R

Natural Numbers

N

Integers

Z

Rational Numbers

Q

Therefore

∴

Infinity

∞