NATURE’S GEOMETRY: SYMMETRY AND

POLYGONS IN NATURE

Symmetry Can Be Found All Around Us.

GEOMETRY IN NATURE

ByRebecca Dow, Sara Howard, Julie

Russell, Jessie Buchheim, and Jordann Tomasek

Symmetry Definition-The preservation of form

and configuration across a point, line or a plane.

Reflective Symmetry

Also known as flips, one half of an image is the mirror image of the other half.

Reflective Symmetry Point

symmetry - any straight cut through the center point divides the organism into mirroring halves.The line of symmetry on each leaf is the stem.

Butterflies

Butterflies and moths have great reflective/point symmetry. They frequently sit with their wings up so the points touch.

Reflective Symmetry

Another example of this particular symmetry in nature, is a reflection on the water.

As we look at this photograph, the ground acts as the bisecting line of symmetry between the two images.

Rotational Symmetry

Rotational symmetry means that one part can be moved around a center and duplicated.

Starfish show rotational symmetry

Rotational Symmetry

The planets, with slight variation due to chance, exhibit rotational symmetry.

Rotational Symmetry

Snowflakes also provide an example of radial symmetry.

They have hexagonal symmetry around an axis.

Incredible pictures of real snowflakes can be found at: SnowCrystals.com.

Rotational Symmetry

All snowflakes have this sort of symmetry due to the way water molecules arrange themselves when ice forms.

Attraction to Symmetry

People are naturally attracted to symmetry.

A face is considered beautiful when the features are symmetrical (matching on either side).

Animals have symmetry

Animals also show symmetry between two halves of the body.

POLYGONS IN NATURE

Polygons are closed plane figures made up by 3 or more connecting line segments.

POLYGONS IN NATURE

There are polygons found in nature everywhere, you just have to take a closer look!

Have you ever stopped to consider how many things that we see in nature that are

geometrically arranged?

Polygons found in FruitIf you slice a kiwi in half, you will see that the core forms a six-sided shape, also known as a hexagon.

This is also true for an apple, except it is a slightly different version of a pentagon, it becomes a star.

Look closely at a pineapple and you will see that all pineapples have the same skin, they are tessellations (repeated) of a trapezoid.

Polygons Found In Plants

This is an example of a polygon found within a plant. Each leaf is a triangle, a three-sided polygon..

This poppy makes the shape of a regular pentagon.

There are many types of flowers that form polygons.

What shapes can you see in these tulips and lilies?

Animals and Polygons

Most polygons found on animals are repetitive, but slightly altered. On these two cheetahs, almost all of the polygons are present, except a solid triangle.

.

A giraffe’s body is completely covered in regular polygons

Patterns in rocks

Patterns in starfish

Look closely at a honeycomb or a wasp nest.

Each cell wall stands at a correct 120 angle with respect to one another to form a tessellation of regular hexagons.

Can you guess at a definition of tessellation? We’ll find out if you are right.

A Master Designer

There are so many repeated designs, symmetries,

and patterns in our natural world. As you look for them,

ask yourself: are these just here by chance, or did a very creative God put them there?