PATTERNS AND
REGULARITIES
Mathematics is all around us. As we
discover more about our environment,
we can mathematically describe nature.
The beauty of a flower, the majestic
tree, even the rock formation exhibits
nature’s sense of symmetry. There are
also examples of microscopic level of
nature such as snowflakes. There are
different types of pattern such as
symmetry, fractals and spirals.
A. SYMMETRY
Symmetry is a sense of harmonious and
beautiful proportion of balance or
an object is invariant to any of
various transformations (reflection,
rotation or scaling). There are two
main types of symmetry, bilateral and
radical.
Bilateral symmetry is a symmetry in
which the left and right sides of the
organism
can
be
divided
into
approximately mirror image of each
other along the midline. Symmetry exists
in living things such as in insects,
animals, plants, flowers, and others.
Animals mainly have bilateral or
vertical symmetry, even leaves of
plants and some flowers such as orchids.
Radical symmetry (or rotational symmetry) is a
type of symmetry around a fixed point known
as the center and it can be classified as either
cyclic or dihedral. Plants often have radial or
rotational symmetry, as to flowers and some
groups of animals.
A five – fold symmetry is found in the
echinoderms, the group which includes starfish
(dihedral – D5 symmetry), sea urchins, and sea
lilies (dihedral – D5 symmetry). Radial
symmetry suits organisms like anemones whose
adults do not move and jellyfish (dihedral – D4
symmetry). Radial symmetry is also evident in
different kinds of flowers.
Among non – living things, snowflakes have six –
fold symmetry; each flake’s structure forms a
varying conditions during its crystallization,
with nearly the same pattern of growth on
each of its six arms. Generally, crystals have a
variety of symmetries and crystal habits; some
are cubic or octahedral
B. FRACTALS
Fractal is a curve or geometric figure, each part of
which has the same statistical character as the
whole. Fractal is one the newest and most exciting
branches of mathematics. It is a class of roughly
irregular shapes that are related to continents,
coastlines, and snowflakes. It is useful in modeling
structures in which similar patterns recur at
progressively smaller scales, and in describing
partly random or chaotic phenomena such as
crystal growth and fluid turbulence. Fractals can
be seen in some plants, trees, leaves and others.
C. SPIRALS
A logarithmic spiral (or growth
spiral) is a self – similar spiral curve
which often appears in nature. It was
first described by Rene Descartes and
was later investigated by Jacob
Bernoulli. Spirals are more evident in
plants. We also see spirals in typhoon,
whirlpool, galaxy, tail of chameleon,
and shell among others.
A logarithmic spiral (or growth
spiral) is a self – similar spiral curve
which often appears in nature. It was
first described by Rene Descartes and
was later investigated by Jacob
Bernoulli. Spirals are more evident in
plants. We also see spirals in typhoon,
whirlpool, galaxy, tail of chameleon,
and shell among others.
BEHAVIOR
OF NATURE
Behavior of nature can be observed in our daily life.
Such natural regularities of nature include
symmetry, fractals, spirals, trees, meanders, waves,
foams, tessellations, cracks, stripes, and spots.
Nature also shows the relationship in the existence
of the Golden ratio. Recall that the Golden ratio is
considered as the most pleasing to the human visual
sensation and creates a feeling of satisfaction and
harmony within an image. Golden ratio can be found
in the beauty of nature, the growth patterns of
many plants, insects, and the universe.
Honeycombs of the bee shows specific regular
repeating hexagons. The design is highly efficient, it
uses the least amount of wax to store the honey
giving a strong structure with no gaps. In a zebra’s
coat, the alternating patterns of blacks and white
are due to mathematical rules that govern the
pigmentation chemicals of its skin. Spider webs
illustrate a beautiful pattern. The spider creates a
structure by performing innate steps. The nautilus
shell has natural pattern which contains a spiral
shape called logarithmic spiral.
Age of the trees can be determined by applying
dendrochronology which is a scientific method of
dating based on the amount of rings found in the
core of a tree. Turtles have growth rings called
“scutes” which are hexagonal in shape. The age of
the turtle can be estimated based on its scutes. The
smallest scute is in the center and is the oldest one,
while the largest ones on the outside are the newer
ones. The hexagonal honeycombs formed by bees and
the spirals formed by spiders are among the
wonders of nature.
Lightning during storms creates fractals.
Foam bubbles formed by trapping pockets of
gas in a liquid or solid. In most foam, the
volume of gas is large, with thin films of
liquid or solid separating the region of gas.
Cracks create linear openings that form in
materials to relieve stress in the land.
The pattern of cracks indicated whether the
material of elastic or not. Cracks can also be
found on the barks of trees which show some
sort of weakness in the bark. The meander is one
of a series of regular sinuous curves, bends,
loops, turns, or windings in the channel of the
body of water (e.g., river, stream, or
watercourse). Meander is produced by a body of
water as it erodes the sediments comprising an
outer, concave bank and deposits this and other
sediments downstream on an inner convex bank.
Hurricane rotates, the enormous cloud
bands form golden spiral. Galaxies
form the same way as the golden
spiral. The waves of the sea also move
in golden spiral and even the fluid
dynamics create golden spiral.
THANK
YOU!