4. People associate mathematics with numbers,
numbers with computations, and
computations with complexities. This section
will set aside mathematics as a complex idea.
Nature is mathematics physical reflection.
One need not have mathematical training to
appreciate nature's beauty. Appreciation comes
in if one sees organized patterns in nature.
5. What is a pattern?
Pattern is a term used to describe repeating
objects or events. The patterns in nature do not
come from accident but from the connection
and interaction of organisms and other natural
objects. These patterns do not just give
aesthetic to one’s eyes but play an important
role.
6. What is a pattern?
In Ian Stewart’s book “Nature’s Numbers”,
he stated “by using mathematics to organize
and systematize our ideas about patterns, we
have discovered a great secret: nature’s
patterns are not just there to be admired,
they are vital clues to the rules that govern
natural processes”.
7. Here are some examples of nature's pattern.
Zebras and Tigers stripes
Image by treehugger.com Image by greenpeace.org.uk
8. These patterns are called "self-organized
patterns" which means patterns formed without
external intervention.
Leopards' dotted skin Sand dunes
Image by krugerpark.co.za
Image by daiichitravel.com
9. Image by ratemds.com
Image by beeculture.com
Bees hive Spider webs
These patterns are called "invoked
organized patterns" which means patterns
formed with external intervention.
11. Fibonacci sequence is a sequence of numbers in
which terms are obtained by adding the two
previous terms in the sequence.
“Fibonacci sequence” was named after an
Italian mathematician Leonardo Pisano Bigollo
commonly known as “Leonardo Fibonacci”
who discovered the said sequence.
What is Fibonacci sequence?
12. Consider the sequence
1 1 2 3 5 8 13…..
This process was observed during Leonardo
Pisano’s experiment on a pair of rabbits (one
male and one female) that lead to the discovery
of “Fibonacci sequence” or “Fibonacci
numbers”.
Patterns are related to numbers. The discovery
of Fibonacci numbers opened many other
discoveries from different fields in science.
13. Here are some examples of Fibonacci sequence
found in nature:
Flower petals (Lilies have 3, buttercups have 5,
delphiniums have 8, marigolds have 13, asters
have 21)
Image by homeguides.sfgate.com
14. Here are some examples of Fibonacci sequence
found in nature:
Spiral pattern of seeds in Sunflower
Broccoli
Image by mathisfun.com Image by artlink.com.au
16. Mathematics helps Organize Patterns
and Regularities in the World
• The numbers present not just in plants but
in any other natural objects display
mathematical regularities. These
regularities give deeper understanding on
nature’s phenomenon. Mathematics helps
organize these patterns which are clues to
uncover the underlying rules and
regularities in the world.
17. Mathematics helps Predict the Behavior of
Nature and Phenomena in the World
• Math does help predict the behavior of nature
and phenomena in the world. It is often
desirable to describe the behavior of some real-
life system or phenomenon, whether physical,
sociological, or even economic, in
mathematical terms. The mathematical
description of a system of phenomenon is
called a mathematical model and is
constructed with certain goals in mind.
18. • Researchers observe nature and phenomena
and try to make a mathematical model that
works for their observation. Basically, they
try to generalize, or find a rule, for what they
observe. After that, these models can be used
for simulations which help predict what will
happen.
19. Here are some known mathematical models:
Newton's Laws of Motion
Electromagnetic Equations
Theory of Relativity
Pythagorean Theorem
Exponential Growth Model
20. Models range from simple to complex, from
deterministic to stochastic or probabilistic, from
time-dependent to not. There are also usually
different models for the same phenomena,
depending on what aspect of the phenomena the
researchers focus on. As stated, models can be
probabilistic, so Math cannot always actually
determine phenomena. But, it can give probabilities,
or benchmarks. Although we could not predict
when earthquakes would happen, we can at least
give probability when will be its next occurrence
and can also identify which places to watch out for.
21. Mathematics helps Control Nature and
Occurrences in the World for our Own Ends
No one has the power to control natural
occurrences in the world. However, experts
developed models that will predict natural
phenomenon. As discussed in subsection
1.3.2, these models will somehow control
the occurrences or if not, it will give us
information to prepare ourselves from
future disaster.
22. Here are some examples:
Weather forecasting (helps us plan our
everyday activities)
Medical trials (helps us discover new
treatments, detect, diagnose and reduce the
risk of disease)
Population growth (helps us prepare the
possible effects in economics, environment
and health)
23. Mathematics has Numerous Applications in
Making it Indispensable
Mathematics is everywhere. We are living
in a world where mathematics is behind
every activity. We need not to understand
the intricacy of mathematics to live our
lives. All we have to do is to enjoy what it
offers.
24. Applications of Math in everyone‘s everyday life
1.Calculating money and finance
2.Counting number of students in a class
3.Time taken for your travel
4.Building construction
5.Measuring Quantity of liquid, food etc.
6.Distance covered when you walk from point A
to point B.
25. Some Scientific Applications:
• Finding time and position of objects
• Finding paths or trajectories
• Explaining theories in Physics and Chemistry
• Oscillating of currents, string, vibrations, LCR circuits
• Finding area, perimeter and volumes
• Calculating work, potential, torque, momentum
• Population growth of a city or a country
• Decay of nuclei, chemical reactions
• Calculating minimum and maximum values of function
• Solving and analyzing real-life situations
