MATHEMATICS IN THE MODERN WORLD
CHAPTER 1
OBJECTIVES
⮚
Classify patterns in nature and regularities in the world;
⮚
Explain the importance of mathematics in one’s life; and
⮚
Appreciate mathematics as a human endeavor through
creating self-designed patterns.
WHAT IS MATHEMATICS?
 the study of the relationships among numbers, quantities, and shapes.
 Enhances our critical thinking skills, reasoning, spatial thinking, and creativity.
 Helps organize patterns and regularities in the world.
PATTERNS AND NUMBERS IN NATURE AND THE WORLD
 What does the word pattern mean to you?
Pattern – is considered as any kind of regularity that can be recognized by the mind. These could
be non mathematical patterns; number patterns; and patterns that would be valuable to you as you
gain mathematical maturity and become a problem solver.
 Patterns are everywhere
Nature
Science
Man-made
Art
Software
PATTERNS IN NATURE
These are visible regularities of form found in the natural world. These patterns recur
in different contexts and can sometimes be modeled mathematically.
Natural Patterns include:
Symmetries
Fractals
Spirals
Tessellations
SPATTERNS AND NUMBERS IN NATURE AND THE WORLD
1. SYMMETRY
 Symmetrical pattern
 It is a design or pattern that is identical in both halves when folded.
SPATTERNS AND NUMBERS IN NATURE AND THE WORLD
2. SPIRAL
 Curve pattern the fucoses on a certain point and a series of circular shapes that revolve
around it.
 This pattern is usually seen in our natural environment.
SPATTERNS AND NUMBERS IN NATURE AND THE WORLD
3. FRACTALS
 Build from similar repeated shapes that reduce in size when repeated
 This pattern is usually seen in our natural environment.
SPATTERNS AND NUMBERS IN NATURE AND THE WORLD
4. TESSELLATIONS
 Created with an identical shape that exactly fits together with no gaps.
THE FIBONACCI SEQUENCE
 Leonardo Pisano Bigollo/Leonardo Pisano/Leonardo of Pisa
 An Italian mathematician who discovered the sequence
 His nickname was “ Fibonacci” which roughly means “ Son of Bonacci”
 November 23 is the Fibonacci Day
THE FIBONACCI SEQUENCE
 The sequence goes
 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597,
…
 Each sequence number is the sum of the two numbers that precede
it.
 The magic of Fibonacci numbers:
https://www.youtube.com/watch?v=SjSHVDfXHQ4&list=PLet3ghBI7jhEvurbOP5hk2GBGXjbycLZL&index=2&t=0s
THE GOLDEN RATIO
 Denoted by phi (Φ) which approaches a value of 1.618034…
RELATIONSHIP BETWEEN FIBONACCI SEQUENCE AND GOLDEN RATIO
A
B
2
3
𝑨
=Φ
𝑩
1.5
3
5
1.6666666667
5
8
1.6
8
13
1.625
…
…
...
144
233
1.61805555556
233
377
1.6180257511
…
…
…
Note: A (smaller number) and B (larger number) are consecutive numbers from
the sequence.
Φ~𝟏. 𝟔𝟏𝟖𝟎𝟑𝟒 …
PATTERNS AND REGULARITIES IN THE WORLD AS ORGANIZED BY
MATHEMATICS
 Motion of a pendulum
Show the time it takes to swing back to its original position can be explained by mathematics
through regularities in motion
PATTERNS AND REGULARITIES IN THE WORLD AS ORGANIZED BY
MATHEMATICS
 Reflection in a plane mirror
Which shows the regularities inside and distance, we could see the size of the objects in the
mirror can be mathematically explained by the Law of reflection.
IMPORTANCE OF MATHEMATICS IN LIFE
 Mathematics has played a major role in bringing these innovations to reality. Many
mathematical theories and models of real-world problems have helped scientists and
engineers grapple with seemingly impossible tasks. Today, mathematical techniques
reach even further into our society. In addition to making technology more efficient and
effective, mathematical techniques help organizations deal with financial, manufacturing,
and even marketing issues.
1. Restaurant Tipping
2. Netflix Film Viewing
3. Calculating Bills
4. Computing Test Scores
5. Tracking Career
6. Doing Exercise
7. Handling Money
8. Making Countdowns
9. Baking and Cooking
10. Surfing Internet
Mathematics is the language with which God wrote the universe. - Galileo Galilei
QUESTION:
 What is the application of mathematics in your chosen
course?
PERFORMANCE TASK
 Collect pictures showing the applications of mathematics in different workstations in your
community and write a short description. At least 5 pictures. Place your output on a short
bond paper and pass it next meeting.
Rubric
Graphics -Clarity
5 points
Graphics - Originality
5 points
Graphics - Relevance
5 points
Knowledge Gained
5 points
Total
20 points