MODULE I
NATURE OF MATHEMATICS
Lesson 1 Patterns and Numbers in
Nature and the World
Lesson 2 The Fibonacci Sequence
Lesson 3 Mathematics for our World
, 2
MODULE I
NATURE OF MATHEMATICS
INTRODUCTION
A hike in the woods or a walk along the beach reveals an endless
variety of forms. Nature abounds in spectral colors and intricate shapes -
the rainbow mosaic of a butterfly's wing; the delicate curlicue of a grape
tendril; the undulating ripples of a desert dune. But these miraculous
creations not only delight the imagination, they also challenge our
understanding. How do these patterns develop? What sorts of rules and
guidelines, shape the patterns in the world around us?
Some patterns are molded with a strict regularity. At least
superficially, the origin of regular patterns often seems easy to explain.
Thousands of times over, the cells of a honeycomb repeat their hexagonal
symmetry. The nautilus is another meticulous craftsman, who designs its
shell in a shape called a logarithmic or equiangular spiral (explained ahead).
This precise curve develops naturally as the shell increases in size but does
not change its shape, ever growing but never changing its proportions. Think
of the striking regularity of alternating dark and light stripes on a zebra's
coat, or the reticulations on the surface of fruiting body of a morel (a
variety of mushroom) mushroom. Zooming in for a close-up of a slime mold,
you can observe the branching network patterns that emerge as the mold
grows. On a still smaller scale, magnified several hundred times, similar
patterns emerge on the surface of a pollen grain.
The living world is filled with striped and mottled patterns of
contrasting colors, with patterns of organization and behavior even among
individual organisms. Do you also notice patterns around you? What other
examples can you think of?
In this module, we will be looking at patterns and regularities in the
world, and how mathematics comes into play, both in nature and in human
endeavors.
Module 1 includes the discussion of the following:
Lesson 1 Patterns and Numbers in the Nature and the World
Lesson 2 The Fibonacci Sequence
Lesson 3 Mathematics for our World
Mathematics in the Modern World - Module I -
, 3
OBJECTIVES
After studying the module you should be able to:
1. Identify patterns in nature and regularities in the world.
2. Articulate the importance of mathematics in one’s life.
3. Argue about the nature of mathematics, what it is, how it is
expressed, represented, and used.
4. Express appreciation for mathematics as a human endeavor.
DIRECTIONS/ MODULE ORGANIZER
1. Module 1 consists of three (3) lessons. Take time to read all these
three (3) lessons, so you can have a better understanding and
appreciate about patterns, nature of mathematics, and how they are
represented and used.
2. Accomplish all the learning activities and submit them to your tutor
in the next face-to-face meeting.
3. For difficulties, try to contact the curriculum adviser or your
tutor/professor.
Mathematics in the Modern World - Module I -
NATURE OF MATHEMATICS
Lesson 1 Patterns and Numbers in
Nature and the World
Lesson 2 The Fibonacci Sequence
Lesson 3 Mathematics for our World
, 2
MODULE I
NATURE OF MATHEMATICS
INTRODUCTION
A hike in the woods or a walk along the beach reveals an endless
variety of forms. Nature abounds in spectral colors and intricate shapes -
the rainbow mosaic of a butterfly's wing; the delicate curlicue of a grape
tendril; the undulating ripples of a desert dune. But these miraculous
creations not only delight the imagination, they also challenge our
understanding. How do these patterns develop? What sorts of rules and
guidelines, shape the patterns in the world around us?
Some patterns are molded with a strict regularity. At least
superficially, the origin of regular patterns often seems easy to explain.
Thousands of times over, the cells of a honeycomb repeat their hexagonal
symmetry. The nautilus is another meticulous craftsman, who designs its
shell in a shape called a logarithmic or equiangular spiral (explained ahead).
This precise curve develops naturally as the shell increases in size but does
not change its shape, ever growing but never changing its proportions. Think
of the striking regularity of alternating dark and light stripes on a zebra's
coat, or the reticulations on the surface of fruiting body of a morel (a
variety of mushroom) mushroom. Zooming in for a close-up of a slime mold,
you can observe the branching network patterns that emerge as the mold
grows. On a still smaller scale, magnified several hundred times, similar
patterns emerge on the surface of a pollen grain.
The living world is filled with striped and mottled patterns of
contrasting colors, with patterns of organization and behavior even among
individual organisms. Do you also notice patterns around you? What other
examples can you think of?
In this module, we will be looking at patterns and regularities in the
world, and how mathematics comes into play, both in nature and in human
endeavors.
Module 1 includes the discussion of the following:
Lesson 1 Patterns and Numbers in the Nature and the World
Lesson 2 The Fibonacci Sequence
Lesson 3 Mathematics for our World
Mathematics in the Modern World - Module I -
, 3
OBJECTIVES
After studying the module you should be able to:
1. Identify patterns in nature and regularities in the world.
2. Articulate the importance of mathematics in one’s life.
3. Argue about the nature of mathematics, what it is, how it is
expressed, represented, and used.
4. Express appreciation for mathematics as a human endeavor.
DIRECTIONS/ MODULE ORGANIZER
1. Module 1 consists of three (3) lessons. Take time to read all these
three (3) lessons, so you can have a better understanding and
appreciate about patterns, nature of mathematics, and how they are
represented and used.
2. Accomplish all the learning activities and submit them to your tutor
in the next face-to-face meeting.
3. For difficulties, try to contact the curriculum adviser or your
tutor/professor.
Mathematics in the Modern World - Module I -
