MMW chapter 1

identify the flower and the number of its petals

Lilies 3 petals

identify the flower and the number of its petals

Buttercups 5 petals

identify the flower and the number of its petals

Delphinium 8 petals

identify the flower and the number of its petals

Cineraria 13 petals

identify the flower and the number of its petals

Aster 21 petals

Fibonacci Sequence

The number 3,5,8,13 and 21 are all part of the

Golden ratio

a special number which is approximately equal to 1.618034 and it is used to calculate fibonacci number.

Golden ratio

It is usually denoted using the Greek letter “phi”

Vitruvian Man by Leonardo da Vinci

15th century drawing known as “the proportions of the human body”

Mathematics

-study of numbers and arithmetic operations

-an art which studies patterns

-a specialized language that deals with form and size

Galileo Galilei

Natural patterns include

symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks, stripes and pattern formation

Symmetry

Is pervasive in living things
• Animals mainly have bilateral or mirror symmetry or strip pattern
• Leaves of plants and some flowers such as Orchids
• Plants often have radial or rotational symmetry

Radial

it is a rotational symmetry around a fixed point known as the
center.

Radial symmetry

can be classified as either cyclic or
dihedral.

Dihedral and Cyclic symmetry

Each rotation angle will be
equal to 360/n degrees and the angle between each mirror will
be 180/n degrees

Strip Pattern

can be classified in seven
distinct patterns. Each pattern contains all or some
of the following types of symmetry: Translation
symmetry, Horizontal mirror symmetry, Vertical
mirror symmetry, Rotational symmetry, or Glide
reflection symmetry.

Wallpaper patterns

are patterns of symmetry that
tessellate the plane from a given fundamental region

Perfect shape

allow bees to store the largest possible amount of wax

Bilateral symmetry

s symmetry across a line of
reflection, which means that they can be split into
two matching halves, if they are evenly divided
down a center line

Fractals

is a never-ending pattern.

iinfinitely
complex patterns that are self-similar across different scales.
They are created by repeating a simple process over and
over in an ongoing feedback loop.

SPIRALS

• Such arrangements in molluscs, sunflower seed heads or
structure of a pineapple fruit

Some of these
spirals can be generated mathematically from Fibonacci ratio

CHCHAOS, FLOW, MEANDERSAOS, FLOW, MEANDERS
•

is a facet of the complex world
of pattern; speaking to the tricky patterning found in

Chaos

unpredictable behavior which
appears random and is often the result of disorder and confusion

Flow

Meander

is one of a series of regular sinuous curves, bends,
loops, turns, or windings in the channel of a river, stream