Mandelbrot B., The Fractal Geometry of Nature (0716711869, 1982)
Geometry in Nature PROJECT 1
-
Upload
remya-r-kumar -
Category
Documents
-
view
27 -
download
0
description
Transcript of Geometry in Nature PROJECT 1
Geometry in Nature
Symmetry
• Definition-The preservation of form and configuration across a point, line or a plane.
• Transformations
• Types of Symmetry
Symmetry in Nature
Symmetry Can Be Found All Around Us.
Reflective Symmetry
• Also known as line symmetry, means that 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.
Reflective Symmetry
• Another example of this particular symmetry in nature, is a reflection on the water.
Reflective Symmetry
• As we look at this photograph, the ground acts as the bisecting line between the two images.
Rotational Symmetry
• Radial symmetry is one kind of rotational symmetry.
Rotational Symmetry
• The planets, with slight variation due to chance, exhibit radial symmetry.
Rotational Symmetry
• Snowflakes also provide an example of radial symmetry.
• They have hexagonal symmetry around an axis.
Rotational Symmetry
• All snowflakes have this sort of symmetry due to the way water molecules arrange themselves when ice forms.
Polygons
• Polygons are closed plane figures made up by 3 or more connecting line segments.
• Simple/Non-Simple
• Convex/Non-Complex
Polygons in NaturePolygons 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 inanimate things that we see in nature that are
geometrically arranged?
Polygons found in FruitPolygons 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.
Look closely at a pineapple and you will see that all pineapples have the same skin, they are tessellations of trapezoids.
This is also true for an apple, except it is a slightly different version of a pentagon, it becomes a star.
Polygons found in Polygons found in PlantsPlantsThis is an example of a polygon found within a plant. Each leaf is a triangle, a three-sided polygon.
There are many types of flowers that form polygons. This tulip, has three triangles on top of three other triangles.
This poppy makes the shape of a regular pentagon.
On your own time:On your own time:Next time you step outside, take a look around you and see what polygons you can find within nature itself. You might be surprised as to what you actually do find!
Spheres in Nature
• Geometry– Geo-Earth– Metry-measurement
• Angles
• Great Circle
The Earth
• Sphere• Lines of latitude and
longitude• Equator
Other Examples of Spheres
• Sun• Moon• Planets• Oranges