Lesson 1: Mathematics in Nature Mathematics has numerous applications
in the world making it indispensable
Fibonacci and Nature
In the introduction, we see from the video that
mathematics is found everywhere. An ancient What is Mathematics about?
math contribution that is pretty obvious and
Numbers, symbols, notations
common to see around is the Fibonacci
Operations, equations and functions
sequence. A lot of things we see show quantities
Proof - a story rather than a sequence of
found in the Fibonacci sequence.
statements
The astronomer Galileo Galilei in his IL How is Mathematics done?
Saggiatore wrote that,
with curiosity
”[The universe] is written in the language of with a penchant for seeking patterns and
mathematics, and its characters are triangles, generalities
circles, and other geometric figures.” with desire to know the truth
with trial and error
Artists who strive and seek to study nature must
without fear of facing more questions and
first, in Galileo’s view, fully understand
problems to solve
mathematics.
Who uses Mathematics?
God used beautiful mathematics in creating the
mathematicians: pure and applied
world – Paul Dirac
scientists: natural and social
EVERYONE but, different people use
different mathematics at different times,
What is Mathematics? for different purposes, using different tools
” Human mind and culture have developed a Why is mathematics important to know?
formal system of thought for recognizing,
classifying, and exploiting patterns called it puts order in disorder
mathematics” (Stewart, p.1) it helps us to become a better person
it helps make the world a better place to
1. The origin of counting live
2. Geometric patterns
3. Patterns of movement
4. A tool to quantify, organize and control our
Fibonacci Sequence (Vila)
world, control phenomena, and make life
easier for us This is an infinite sequence of natural numbers
where the first value is 0, the next is 1 and, from
Where is Mathematics?
there, each amount is obtained by adding the
We see hints or clues of it in nature; In our daily previous two.
routine; In our work; In people and communities;
and In events
Written as a rule, the expression is
What is Mathematics for?
Xn = Xn – 1 + Xn - 2
helps unravel the puzzles of nature
helps organize patterns and regularities as The Fibonacci sequence was invented by the
well as irregularities in the world Italian Leonardo Pisano Bigollo (1180-1250), who
helps predict the behavior of nature and is known in mathematical history by several
phenomena in the world names: Leonardo of Pisa (Pisano means “from
provides tools for calculations Pisa”) and Fibonacci (which means “son of
helps control nature and occurrences in Bonacci”).
the world for our own ends such as
The Fibonacci sequence was the outcome of a
weather and epidemics
mathematical problem about rabbit breeding.
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(THE HABBIT RABBIT) From the book “BOOK of - Helps control nature and occurrences in
CALCULATION” – Liber Abacci the world for our own ends
Fibonacci Sequence in Nature – Flower petals
Fibonacci Spiral (Vila) or Nautilus Spiral (Vila) or Where can we apply mathematics?
Golden Spiral (Vila)
- At home
Golden Rectangle/Golden Ratio – 1: 1.61803 - Forensic, business, medical field, fluid
mechanics, information technology,
The Golden Ratio is the relationship
cryptography, archaeology, social
between numbers on the Fibonacci sequence
sciences, economics, political science,
where plotting the relationships on scales results
music and arts, and many more
in a spiral shape. In simple terms, golden ratio is
expressed as a equation, where a is larger than Patterns and Numbers in Nature and the World
b, (a+b) divided by a is equal to a divided by b,
which is equal to 1.618033987… and represented Types of Patterns:
a+b a - Symmetry
by φ (phi). φ= = =1.618033987
a b A sense of harmonious and
beautiful proportion of balance or
The ratios of sequential Fibonacci numbers
an object is invariant to any
approach the golden ratio. In fact, the higher the
various transformations (reflection,
Fibonacci numbers, the closer their relationship is
rotation or scaling.)
to 1.618.
a) Bilateral symmetry – a
The golden ratio is sometimes called the “divine symmetry in which the left and
proportion” because of its frequency in the natural right sides of the organism can
world. be divided into approximately
mirror image of each other
PARTHENON (ATHEN)
along the midline (e.g. butterfly,
TREE
leaves, tiger and firefly)
ANGELINA JOLIE
b) Radial symmetry – a symmetry
ROMANESCO BROCCOLI
around a fixed point known as
LEAVES
the center and it can be
classified as either cyclic or
dihedral (starfish, mushroom,
The Bayeux Tapestry (11th century) algae, flower)
- Work before the introduction of geometry - Fractals
(people are as tall as the castle) A fractal is a never-ending pattern
found in nature. The exact same
Leonardo da Vinci, “The Last Supper” (c. 1498) shape is replicated in a process
called “self-similarity” (e.g branch
- Geometry: painting on a canvass (2D)
of trees, lightning, circulatory
with a 3D effect
systems)
Non – Euclidean Geometry: evolution of the
designs of buildings
- Spirals
Patterns and designs as trademarks of tribes and A curved pattern that focuses on a
culture center point and a series of circular
shapes that revolve around it (e.g
galaxy, storm and worms)
What role does mathematics play in our world?
math around us
- Helps organize patterns and irregularities
in our world. The video Can one Mathematical Model Explain
- Helps predict the behavior of nature and All Patterns in Nature?
phenomena in the world
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Video Player is loading. another stack i.e. a disk can only be moved if it is
Play Video the uppermost disk on a stack.
will be an eye opener for us, that indeed math is 3) No disk may be placed on top of a smaller disk.
everywhere.
Click this link to play Tower of Hanoi.
All patterns in nature might be describable using
mathematical theory. How did Alan Turing
influence how we see the natural world?
In the article Alan Turing's Patterns in Nature, and
Beyond,
"once one starts to look, there seems to be no
end to Turing patterns: their forms can be seen in
weather systems, the distribution of vegetation
across landscapes and even the constellations of
galaxies."
Other Examples of the Fibonacci Sequence
appears in naturally.
People of all ages love to play games that are fun
and motivating. Games give students
opportunities to explore and develop familiarity
with fundamental number concepts, such as the
counting sequence, one-to-one correspondence,
computation strategies using different number
system (such as 2s, 10s, 100s and 1000s).
Furthermore, they afford opportunities for
students to deepen their mathematical
understanding and reasoning.
When games are repeatedly played, it supports
student's development of computational fluency.
The Tower of Hanoi is a familiar math game that
even appears in film as an intelligence test of
some creatures. It was was created by Lucas in
1883. It has three rods and n disks. The objective
of the puzzle is to move the entire stack to
another rod by following the simple rules:
1) Only one disk can be moved at a time.
2) Each move consists of taking the upper disk
from one of the stacks and placing it on top of
This study source was downloaded by 100000795253973 from CourseHero.com on 12-29-2023 11:53:11 GMT -06:00
https://www.coursehero.com/file/212371685/MIDTERM-NOTESdocx/
This study source was downloaded by 100000795253973 from CourseHero.com on 12-29-2023 11:53:11 GMT -06:00
https://www.coursehero.com/file/212371685/MIDTERM-NOTESdocx/
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