This document summarizes Ian Stewart's book "Nature's Numbers" which discusses how mathematics is found throughout nature. It provides examples of numerical and geometric patterns in nature like snowflake symmetry, flower petal patterns, wave patterns, animal stripes and spots, and fractals. It explains that recognizing these patterns allows us to deduce natural rules and regularities. Figures like Johannes Kepler and Benoit Mandelbrot are mentioned for their work in finding mathematical order in nature. The document ends by stating nature provides clues that reveal its secrets through new mathematical theories and that understanding these patterns gives insight into the universe.

1. CHAPTER 1
THE NATURAL
ORDER
NATURE’S NUMBERS BY IAN
STEWART
Group Members:
DENISE C.
CAMPILLANOS
BENJARDLYN B. PAALA
JAYVE DIOSO OCAMPO

2. We live in a universe of
patterns.
Six fold symmetry
Spherical drops
Mathemati
cs
Patterns of
stripes
Patterns of
spots
Colored arcs of
light
Bright circular
halo
formal
system of
thoughts
Recognizing,
Classifying, and
Exploiting patterns
Human mind
and Culture

3. Snowflakes
must be
made by
packing tiny
identical
units
together.
He performed
no experiments,
he just thought
very hard and
trust his own
knowledge.
German
Astronomer who
wrote a book “The
Six-Cornered
Snowflakes”.
He formulated
also an accurate
mathematical
description of
planetary orbits.
Johannes Kepler
Evidences: Six fold
symmetry of
snowflakes, which is
a natural
consequence of
regular packing.
Example: Coins- pack
them as closely you can
get a honeycomb
arrangement/perfect
hexagon.
Natures Clues
Nightly Motion= Earth
Rotates
Waves and Dunes=
Govern the flow of water
Tiger’s Stripes and
Hyena’s spots=
biological growth and
form
Rainbows= Scattering of
light
Raindrops= Spheres
Lunar Haloes=Ice
Different
kind of
beauty that
deduce the
rules and
regularities
in
Mathemati
cs
Sherlock
Holmes and
Evidenc
e
Mathematics
Different
Pattern and
Clues in
Nature

4. Clues to the rules
behind gravity and
motion
PLANETES = WANDERER =
PLANET
Against the circling
background of stars, a
small numbers of stars
move differently.

5. Patterns possess utility as well
as beauty. Once we have
learned to recognize a
background pattern,
exceptions suddenly stand out.
* Things that look simple from outside often look much more complicated
Fractals Chaos
Geometric
waves shapes
that repeat
their structure
on ever finer
scales.
Apparent
randomness
whose
origins are
entirely
deterministic
.
Cloud
s
Weather
The simplest mathematical objects are
numbers, and the simplest of nature’s
patterns are numerical.
A very curious pattern indeed occurs in the petals of flowers
Number of petals occur in strange sequence 3, 5, 8, 13 21,
34,55, 89.
There is a definite pattern to those
numbers: Each number is obtained by
adding the previous two numbers
together.

6. Easiest and
consequently
the most
dangerous
method for
finding patterns.
The
significant
observation
of
Numerology.
Verdict of
posterity, the
calculation of
squares and
cubes.
Numerical Pattern of
key to theory of gravity
by Newton. Explained
all sorts of puzzles.
* Geometric ones
are also Numerical
Patterns.
Title sounds
better w/o “and
shapes”
Mathematical shapes
can always be
reduced to numbers
which computers
handle graphics.
Better to think shape as shapes
to make use of our powerful
intuitive visual capabilities.
Main shapes appealed to
mathematicians were very simple
ones.
Triangles, squares, pentagons,
hexagons, circles, ellipses,
spirals, cubes, spheres, cones
and etc.
Flow of fluids provides an
inexhaustible supply of natures
patterns.
Wave patterns on
land
A general shape is a collection of
dots and can be represented as
list of pairs of numbers.

7. The shape and patterns of animals
and plants ( stripes, spots, dots, ets.)
is hunting ground for mathematically
minded.
Patterns of movement
Human
walk
Horse
Scuttling of
insects
Flight of birds Pulsation
of Jellyfish
Movements of
fish, worms, and
snakes.
Patterns of Human
Imagination
Patterns that exist where we
thought everything was random
and formless.
Benoit
Mandelbrot
All Fractals. A new
science of irregularity-
Fractal Geometry-has
sprung up within the last
15 years.
Development of new mathematical
theories, these more elusive of nature’s
patterns are beginning to reveal their
secrets.
- Ian Stewart
Formless is still a pattern
for a clue or evidence

8. Newfound
understanding
of natures
secret
Seeing practical
impact as well as an
intellectual one (
Clues, Patterns) .
Used to steer artificial
satellites to new
destinations with less
fuel.
To help avoid wear on
wheels of locomotives
and other rolling
stock.
To improve the
effectiveness of heart
peacemakers.
To manage forest and
fisheries.
But most important of
all, Giving us the deeper
vision of the universe in
which we live, and of
our own place in it.

9. Thank you!!!