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Patterns and Symmetries in Nature: Snowflakes, Honeycombs, and Animal Markings, Essays (high school) of Mathematics

Mathematics

The concept of patterns and symmetries in nature, focusing on snowflakes, honeycombs, and animal markings. It discusses the various types of symmetries, such as line symmetry, rotational symmetry, and the angle of rotation. The document also touches upon the mathematical principles behind these natural designs and how they optimize space and resources. Additionally, it mentions the role of chemicals and diffusion processes in determining animal growth patterns.

Typology: Essays (high school)

2019/2020

Uploaded on 11/29/2021

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1.1 PATTERNS AND NUMBERS

IN NATURE AND THE WORLD

PATTERNS are regular, repeated and

recurring forms of designs. Patterns

are commonly observed in natural

objects , such as the six-fold symmetry

of snowflakes, the hexagonal structure

and formation of honeycombs

Partial preview of the text

Download Patterns and Symmetries in Nature: Snowflakes, Honeycombs, and Animal Markings and more Essays (high school) Mathematics in PDF only on Docsity!

1.1 PATTERNS AND NUMBERS

IN NATURE AND THE WORLD

PATTERNS are regular, repeated and

recurring forms of designs. Patterns

are commonly observed in natural

objects , such as the six-fold symmetry

of snowflakes, the hexagonal structure

and formation of honeycombs



The tiger’s stripes and hyena’s spots, the

number of seeds in a sunflower, the spiral

of a snail’s shell, and the number of

petals of flowers.



Humans are hard wired to recognize

patterns and by studying them , we

discovered the underlying mathematical

principles behind nature’s design.

 Recall that symmetry indicates that you can draw an imaginary line across an object and the resulting parts are mirror images of each other.  The figure above is symmetric about axis indicated by the line.  Note that the left and right positions are exactly the same.  This type of symmetry , known as line or bilateral symmetry , is evident in most animals, including humans.  Look in a mirror and see how left and right sides of your face closely match.

SPIDERWORT WITH 3 –FOLD SYMMETRY



Note that if you rotate the spiderwort and

the starfish above by several degrees, you

can still achieve the same appearance as

the original position. This is known as the

rotational symmetry



The smallest angle that a figure can be

rotated while still preserving the original

formation is called the angle of rotation



For spiderwort is 120 for starfish its 72

degrees respectively.

Consider the image of a

snow flake



It can be observed that the

patterns on a snow flake repeat

six times, indicating that there is a

six-fold symmetry. To

determinethe angle of rotation ,

we simply divide 360^o by 6 to

get 60^o.

ANOTHER MARVELOF NATURE

DESIGN IS THE STRUCTURE AND

SHAPE OF A HONEYCOMB



People have long wondered how bees,

despite their small size, are able to

produce such arrangement while

humans would generally need the use

of a ruler or a compass to accomplish

the same feat. It is observed that such

formation enable the bee colony to

maximize their storage of honey using

the smallest amount of wax.

HYENAS SPOTS



Patterns are also exhibited in the external

appearances of animals. We are familiar with

how a tiger looks--- distinctive red-orange fur

and dark stripes.



Hyenas, another predator from Africa, are

also covered with patterns of spots. These

seemingly random designs are believe to be

governed by mathematical equations.



According to Alan Turing , chemical reactions

and diffusion processes in cells determine

these growth patterns.

THE SUNFLOWER



Patterns and Symmetries in Nature: Snowflakes, Honeycombs, and Animal Markings, Essays (high school) of Mathematics

Related documents

Partial preview of the text

Download Patterns and Symmetries in Nature: Snowflakes, Honeycombs, and Animal Markings and more Essays (high school) Mathematics in PDF only on Docsity!

1.1 PATTERNS AND NUMBERS

IN NATURE AND THE WORLD

PATTERNS are regular, repeated and

recurring forms of designs. Patterns

are commonly observed in natural

objects , such as the six-fold symmetry

of snowflakes, the hexagonal structure

and formation of honeycombs

The tiger’s stripes and hyena’s spots, the

number of seeds in a sunflower, the spiral

of a snail’s shell, and the number of

petals of flowers.

Humans are hard wired to recognize

patterns and by studying them , we

discovered the underlying mathematical

principles behind nature’s design.

SPIDERWORT WITH 3 –FOLD SYMMETRY

Note that if you rotate the spiderwort and

the starfish above by several degrees, you

can still achieve the same appearance as

the original position. This is known as the

rotational symmetry

The smallest angle that a figure can be

rotated while still preserving the original

formation is called the angle of rotation

For spiderwort is 120 for starfish its 72

degrees respectively.

Consider the image of a

snow flake

It can be observed that the

patterns on a snow flake repeat

six times, indicating that there is a

six-fold symmetry. To

determinethe angle of rotation ,

we simply divide 360^o by 6 to

get 60^o.

ANOTHER MARVELOF NATURE

DESIGN IS THE STRUCTURE AND

SHAPE OF A HONEYCOMB

People have long wondered how bees,

despite their small size, are able to

produce such arrangement while

humans would generally need the use

of a ruler or a compass to accomplish

the same feat. It is observed that such

formation enable the bee colony to

maximize their storage of honey using

the smallest amount of wax.

Patterns are also exhibited in the external

appearances of animals. We are familiar with

how a tiger looks--- distinctive red-orange fur

and dark stripes.

Hyenas, another predator from Africa, are

also covered with patterns of spots. These

seemingly random designs are believe to be

governed by mathematical equations.

According to Alan Turing , chemical reactions

and diffusion processes in cells determine

these growth patterns.

THE SUNFLOWER

Looking at a sunflower up close, you will

notice that there is a definite pattern of

clockwise and counter clockwise arcs or

spirals extending outward from the center

of the flower. This is another

demonstration of how nature works to

optimize the available space. This

arrangement allows the sunflower seeds

to occupy the flower head in a way that

maximizes their access light and

necessary nutrients.