Geometry in Nature

1
Geometry in Nature

• by
• Helen Browne
• Debi Geosits
• Jim Pilla
• PRIME Workshop 2005

2
How Geometry is Found in NatureThe Golden Ratio

• All types of crystals, natural cultured
• The hexagonal geometry of snowflakes
• Creatures with logarithmic spiral patterns, such
  as snails shell fish
• The bodies wings of birds flying insects
• The way in which lightning forms branches
• The way in which rivers branch
• Molecular atomic patterns of all solid metals
• And

3
DNA

• This special ratio can be found in
  Deoxyribonucleic Acid (DNA), which is the
  foundation and guiding mechanism of all living
  biological organisms.

4
What is the Golden Ratio?

• The Golden Ratio, also known as the Golden Mean,
  is an irrational number just like Pi. It has an
  endless number of digits after its decimal point
  and has no repetition of the digits sequences.
• The Golden Ratio
• is approximately 1 1.618

5
Why is it important?

• The Golden Ratio is remarkable and unique in its
  characteristics because it is found in ALL living
  creatures on Earth. This is reflected in nature
  in the form of geometry. Geometry is the basis
  of our reality, and hence the golden ratio
  governs the proportion of our world.

6
Geometric shapes containing the Golden Ratio
7
Geometry in Crystals

• Crystals come in many geometric shapes, such as
  cubic, tetragonal, orthorhombic, monoclinic,
  triclinic hexagonal.
• Each shape has a certain arrangement
• of 3 or 4 axes.
• Crystals behave like jewels, refracting and
  reflecting sunlight between their faces.

8
Geometry in Snowflakes

• All snowflakes are in the form of a six-sided or
  cubic crystal. This crystal forms when the water
  freezes in such a way that a six-fold rotational
  symmetry or design is generated.

9
other snowflake examples
10
Geometry in Plants Animals

• The Golden Ratio presents the internal geometry
  of the shapes and patterns of both plants and
  animals. The same processes and laws, which
  occur in snowflakes, occur in flowers, birds,
  insects and sea life.

11
Examples of this phenomenon
12
Have you entered into the treasures of geometry
in the natural world?

• These links with nature have been the major
  driving forces for the development of the Golden
  Ratio.
• Remember geometry
• is all around us!