Geometry in Nature

1
Geometry in Nature

• Denise Hyatt, Angela Long, Jocelyn Johnson, and
  Nakeesha Trammell.

2
Introduction

• Discovering the link between geometry and nature
  is not a difficult task.
• Geometry is everywhere in the natural environment
• Geometry in Nature is also known as Fractal
  Geometry developed by Benoit Mandelbrot.

3
Natures highest points in Geometry

• Fibonacci Numbers and Nature
• Solar System
• Reflectional symmetry
• Weather
• The Nazca Lines

4
Fibonacci and Nature

• Fibonacci numbers describes a series of numbers
  in which successive numbers is equal to the sum
  of the two proceeding numbers.
• Examples range from animals, vegetables, and
  flowers.

5
Fibonacci and Nature Cont

• The Echinacea purpura flower, also known as the
  cone flower.
• The orange petals follow Fibonaccis pattern by
  the spirals curving left and right.
• The numbers in each spiral follows the
  neighboring pattern of Fibonaccis sequence.

6
Solar Geometry

• The distance from each planet from the sun can be
  described by a unique geometric formula.
• The orbital distance between each planet from the
  sun is calculated by using various geometric
  shapes, which include square sides, radius of a
  circle, equilateral triangles, and isosceles
  triangles.
• Four examples are Mecury and Venus, Venus and
  Earth, Earth and Mars, and Mars and Jupiter.

7
Solar Geometry Cont

• reflection of light
• Even though the discovery of the geometrical
  basis for all natures designs were publised by
  Fuller more than 30 years ago, todays society
  still is not aware of this huge achievement.
• Energy cannot stand still , it is always in
  motion, so it is constantly moving in some
  direction.
• Since energy is traveling in a direction for a
  specific amount of time, it is called a vector.
• Anything with an inside and outside is called a
  system, and the minimum system in the universe
  has to be a tetrahedron.

8
Reflectional Symmetry

• Reflectional symmetry is shown in many areas of
  nature
• These include moths, the human body, and fruit.

9
Weather

• As snow crystals form, they become a hexagonal
  shape, it seems like an infinite number of
  variations for being six-sided.
• The temperature that the crystals forms, and to
  less extent the humidity of the air, determine
  the basic shape.
• Snow crystals form a hexagonal shape because of
  the way the two hydrogen atoms join with an
  oxygen atom to form a water molecule.

10
The Nazca Lines
11
The Nazca Line

• Discovered in 1930
• Scattered over 500 square km
• Contains over 50 geoglyphs
• Over 1,300 km straight lines
• 300 geometric shapes

12
Geoglyphs

• These geometrical forms include straight lines,
  triangles, spirals, circles,trapezoid and
  depiction of animals and plants

13
How Are They Formed?

• Pampas
• Desert with little wind covered with black
  wind-smoothed rock

• Lines were created by removing the black
  fragments and topsoil

14
The Nazca Lines

• The Nazca lines can be as narrow as 6 inches and
  as wide as hundreds of yards.

15
Thunderbird

• One of the most famous geoglyphs
• Lines are formed by one continuous line

16
Intersecting Lines

• These two Nazca Lines are intersecting because
  they share a common point.

17
Trapezoid

• Wedge-like
• This trapezoid has sides that are 2,500 ft long
• Its sides run parallel for about 5 miles

18
Theories of the nazca Lines

• Space craft landing
• Population control systems
• Running footraces
• Astronomical purposes

19
Fractal Geometry

• Developed by Benoit Mandelbrots study of
  complexity and chaos.

20
Modern Uses

• Landscaping
• Intricate models
• Images of natural scenes
• Mountain ranges and coast lines