2. WHAT DOES MATHEMATICS HAVE TO DO WITH
NATURE?
The natural world is full of beauty and amazing shapes
and patterns. In his book, Nature by Numbers, Ian
Stewart mentioned that we live in a universe of
patterns. If you observe our nature diligently, you can
prove that our nature bounds in mystical colors and
intricate shapes and patterns that can be described
mathematically.
3.
4. WHAT MATHEMATICS IS ABOUT AND WHAT IT IS
FOR?
- Numbers are the heart of mathematics;
- Mathematics makes our life orderly and systematic,
and it prevents chaos;
-It can be used to express, solve, and interpret the
puzzles observed in nature;
- It helps us to see patterns needed to generalize a
broader solution to a problem.
5. WHAT MATHEMATICS IS ABOUT AND WHAT IT IS
FOR?
- It expounds the power of reasoning, creativity, abstract
or spatial thinking, critical thinking, problem solving
ability, and even effective communication skills.
6.
7. Patterns
Patterns are repetitive, which can be found in
nature as color, shape, action, or some other
sequences that are almost everywhere. Mathematics
expresses patterns. These sequences that repeat,
follows a rule or rules. A rule is a way to calculate or
solve a problem.
8. Patterns
-Natural patterns include symmetries, fractals,
spirals, meanders, waves, foams, tessellations, cracks,
and stripes. Studying patterns allows one to watch,
guess, create, and discover.
9. 1. Symmetry
is an exact correspondence of form and
constituent configuration on opposite sides of a
dividing line or plane or about a center or an axis.
10. a. Reflection or Bilateral
- It is also called mirror symmetry or line symmetry.
It is made with a line going through an object which
divides it into two pieces which are mirror images of
each other.
11. b. Radial Symmetry
- Radial symmetry is rotational symmetry around a
fixed point known as the center.
13. c. Translational Symmetry
- This kind of symmetry is exhibited by objects
which do not change its size and shape even if it
moved to another location. Note that the movement
does not involve with reflection or rotation.
14. 2. Fractals
These are never-ending patterns that are self-similar
across different scales. The image just reappears
repeatedly no matter how many times the object is
magnified.
16. 4. Spots and stripes
Patterns are also exhibited in the external
appearances of animals.
17. 5. Flower Petals
Flowers are easily considered as things of beauty.
Their vibrant colors and fragrant odors make them
very appealing as gifts or decorations.
20. Fibonacci Sequence
The Fibonacci numbers are a series of number that
often occur in nature.
To formally, define the Fibonacci sequence, we start
by defining F1 = 1 and F2 = 1. For n > 2, we define,
𝐹𝑛 = 𝐹𝑛−1 + 𝐹𝑛−2
21. Example
If we take the ratio of Fn to Fn−1 for n ≥ 1,
n 𝐹𝑛 𝐹𝑛/𝐹𝑛−1 n 𝐹𝑛 𝐹𝑛/𝐹𝑛−1
1 1 8 21
2 1 9 34
3 2 10 55
4 3 11 89
5 5 12 144
6 8 13 233
7 13 14 377
22. Example
If we take the ratio of Fn to Fn−1 for n ≥ 1,
n 𝐹𝑛 𝐹𝑛/𝐹𝑛−1 n 𝐹𝑛 𝐹𝑛/𝐹𝑛−1
1 1 - 8 21 1.61538…
2 1 1 9 34 1.61904…
3 2 2 10 55 1.61764…
4 3 1.5 11 89 1.61818…
5 5 1.666… 12 144 1.61797…
6 8 1.6 13 233 1.61805…
7 13 1.625 14 377 1.618025…
23. Example
we see that as n gets larger and larger, the ratio gets
closer and closer to a value denoted by 𝜑. The
number 𝜑 is called as the golden ratio and can be
formally defined as
𝐺𝑜𝑙𝑑𝑒𝑛 𝑟𝑎𝑡𝑖𝑜 = 𝜑 = 1.618
25. Mathematics is everywhere; whether it is on land, sea
or air, online or on the front line, mathematics
underpins every nook and cranny of modern life. Far
from a quaint subject to be forgotten upon leaving
school, it is the glue that holds our world.
26. Roger Bacon (1214-1294), an English Franciscan friar,
philosopher, scientist and scholar of the 13th century,
once stated: “Neglect of mathematics works injury to
all knowledge, since he who is ignorant of it cannot
know the other sciences or the things of the world.”
28. Mathematics helps organize patterns
and regularities in the world;
According to Ian Stewart (1995), we live in a universe
of patterns. Human mind and culture have developed
a formal system of thought for recognizing, classifying
and understanding patterns.
29. Mathematics helps predict the behavior
of nature and many phenomena
Mathematics is used to explain why the Sun set,
where it went and why it returned because it was
easier to count these events in numbers than to put
them into words. Based on historical patterns, we can
make forecasts or predictions to help us prepare for
our daily activities.
30. Mathematics helps control nature and
occurrences in the world for our own good.
Mathematical modelling and control theory can be used. By
mathematical modeling we see the inputs to events and their
most likely outcomes.
31. Mathematics has applications in many
human endeavors making it indispensable
Mathematics existed since the beginning of time, written or
unwritten. Its unwritten history is carved in all things found in
cosmos , found in the patterns created in nature, appreciated
in the juxtaposition of the heavens and the earth, contrast
between darkness and light , made sense in the harmony
created not just by a well-known orchestra but even by the
rain drops falling on offshore wind-turbines.
32. WHAT IS IT?
PERIMETER
The perimeter of a shape is defined as the total
distance around the shape. It is the length of the
outline or boundary of any two-dimensional geometric
shape. The perimeter of different figures can be
equal in measure depending upon the dimensions.
Have you ever thought of the ff. questions?
What does mathematics have to do with nature?
What is mathematics about and what it is for?
What is a mathematical pattern?
-The majority of the learners find mathematics dry, dull, and boring, and most of all, difficult and irrelevant. They consider the application of mathematics distinct from the natural world because they fail to relate it to the difficulties that they have in learning the subject. Thus, they could not see the essence of mathematics.
Look at the pictures below. Are these familiar to you? Have you ever recognized these patterns in nature?
According to Ian Stewart in his book Nature by Numbers, when we hear the word “mathematics”, the first thing that springs to mind is numbers.
According to Ian Stewart in his book Nature by Numbers, when we hear the word “mathematics”, the first thing that springs to mind is numbers.
According to Ian Stewart in his book Nature by Numbers, when we hear the word “mathematics”, the first thing that springs to mind is numbers.
We learned patterns through the concept of functions and sequences like arithmetic and geometric sequences. Number patterns, logic patterns, geometric patterns and word patterns are examples of the various patterns we learned in school. However, patterns are not limited to these types. One can observe patterns in nature, art, architecture, human behavior, anywhere. On this section, we will discuss the different patterns in nature, arts and architecture.
Symmetry-similarity or exact correspondence between different things:
In other words, the objects have a left side and a right side that are mirror images of each other. If a shape can be folded in half so that one half fits exactly on top of the other, then we say that the shapes are symmetric.
The lines of symmetry may be in any direction.
Images with more than one lines of symmetry meeting at a common point exhibits a radial symmetry
Images with more than one lines of symmetry meeting at a common point exhibits a radial symmetry
tessellation or tiling is a repeating pattern of figures that covers a plane with no gaps or overlaps. It is just like a wallpaper group in which patterns are created by repeating a shape to fill the plane.
The flowers below have different number of petals. Flowers with 5 petals are said to be the most common. Notice that these numbers are all Fibonacci numbers.
The flowers below have different number of petals. Flowers with 5 petals are said to be the most common. Notice that these numbers are all Fibonacci numbers.
The flowers below have different number of petals. Flowers with 5 petals are said to be the most common. Notice that these numbers are all Fibonacci numbers.
The flowers below have different number of petals. Flowers with 5 petals are said to be the most common. Notice that these numbers are all Fibonacci numbers.
The Fibonacci numbers appear in nature in various places. Another example is Pinecones, Speed Heads, Vegetables and Fruits, human body geography, weather, galaxy, Archetecture (the great pyramid of Pisa) lastly is the arts of Leonardo Da vinci (Monalisa).
The Fibonacci numbers appear in nature in various places. Another example is Pinecones, Speed Heads, Vegetables and Fruits, human body geography, weather, galaxy, Archetecture (the great pyramid of Pisa) lastly is the arts of Leonardo Da vinci (Monalisa).
Math helps us understand or make sense of the world - and we use the world to understand math. It is therefore important that we learn math contents needed to solve complex problems in a complex world; learn the mathematical knowledge and skills we need to understand the world and make contributions to the global community.
Mathematics provides a systematic way to understand and organize patterns and regularities found in various aspects of our world, such as the repeating cycles in nature, geometric shapes, and numerical sequences.
Through mathematical models and equations, we can make predictions about how natural phenomena will behave. For example, in physics, mathematical equations describe the motion of objects, allowing us to predict where planets will be in the sky or how fast a car will travel.
Mathematics enables us to control and manipulate our environment for beneficial purposes. For instance, engineering relies on mathematical principles to design bridges, buildings, and technologies that improve our quality of life.
Mathematics is indispensable in various fields and human activities, from finance and economics (calculating budgets and analyzing markets) to medicine (diagnosing diseases using statistics) and even art (using geometric principles in design). It plays a vital role across a wide range of human endeavors.
