1) Mathematics exists everywhere and describes patterns found in nature. Many natural phenomena like the calendar, days of the week, and seasons exhibit regular repeating patterns. 2) Specific examples of patterns in nature discussed include symmetry, spirals, meanders, waves, foam, tessellations, cracks, and stripes. Fractals are also patterns in nature that are self-similar across scales. 3) The Fibonacci sequence and golden ratio are exhibited in seed heads, pine cones, tree branches, shells, spiral galaxies, and hurricanes. This demonstrates the mathematical patterns underlying forms in nature.

1. MATHEMATICS IN THE MODERN
WORLD
PREPARED BY: MIA A. RUIZ
Instructor

2. INTRODUCTION
Mathematics is a useful way to think about nature and our
world. Mathematics exists everywhere and it is applied in the
most useful phenomenon.
Mathematics is an integral part of daily life; formal and
informal. It is used in technology, business, medicine, natural
and data sciences, machine learning and construction.
Mathematics is not just about numbers, most of it
problem solving and reasoning- inductive and deductive, it
also discusses also intuition, proof and certainty.

3. CHAPTER1: MATHEMATICS IN OUR WORLD
Patterns in Nature and the Regularities in the World
Patterns and counting are correlative. Pattern in nature goes with
logic and logical set up.
Patterns can be sequential, spatial, temporal and even linguistic.
Most basic example of pattern is the sequence of the dates in the
calendar. (1 to 30 being used month after month); the seven (7) days in
the week; the twelve (12) months.
All these phenomena create a repetition of names or events called
regularity.

4. A regularity (Collins, 2018) is the fact that the same thing always
happens in the same circumstances.
A pattern is a discernible regularity in the world or in a man-made
design.
Patterns in nature are visible regularities of form found in the
natural world.
(Symmetries, trees, spirals, meanders, waves, foams tessellations, cracks
and stripes)

5. SOME EXAMPLE OF PATTERNS IN NATURE
SYMMETRY – means agreement in dimensions, due
proportion and arrangement. In mathematics, “symmetry”
means that an object is invariant to any of various
transformations including reflection, rotating or scaling.
SPIRAL – is a curve which emanates from a point, moving
moving farther way as it revolves around the point.
MEANDER- is one of a series of regular sinuous curves,
bends, loops, turns or winding in the channel of a river, stream
or other watercourse.

7. SOME EXAMPLE OF PATTERNS IN NATURE
WAVE- is a disturbance that transfers energy
through matter or space with little or no associated
mass transport.
FOAM- is a substance formed by trapping pockets
of gas in a liquid or solid.
TESSELLATION- of a flat surface is the tilling of a
plane using one or more geometric shapes, called tiles
with no overlaps and no gaps.

9. SOME EXAMPLE OF PATTERNS IN NATURE
CRACKS- is the separation of an object or materials
into two or more pieces under the action of stress.
STRIPES- are made by a series of bands or strips,
often of the same width and color along the length.

11. SOME EXAMPLE OF PATTERNS IN NATURE
A FRACTAL is a never-ending pattern. Fractals are
infinitely complex patterns that are self-similar across
different scales. They are created by repeating a simple
process over and over in an ongoing feedback loop.
AFFINE TRANSFORMATIONS These are the processes of
rotation, reflection and scaling. Many plant forms utilize
these processes to generate their structure.

13. ACTIVITY:
Identify whether the following are
symmetry, spiral, meander,
foam, tessellation, cracks,
fractal and affine

18. FIBONACCI SEQUENCE
Fibonacci numbers are the numbers in the
following integer sequence, called the Fibonacci
sequence is a sequence which each number is the
sum of the two preceding ones
0,1,1,2,3,5,8,13,21,34,55,89,144, ……….
The sequence 𝐹𝑛 of Fibonacci numbers is defined
by the recursive formula:
𝐹𝑛= 𝐹𝑛−2 + 𝐹𝑛−1 , where 𝐹1 =1, 𝐹2 =1 ………..

19. SOME EXAMPLE OF GOLDEN RATIO
1.Seed heads – also a subject to Fibonaccian processes.
Typically, seeds are produced at the center, and then
migrate towards the outside to fill all the space.
2.Pine cones – the seed pods on a pinecone are arranged in a
spiral pattern. Each consists of a pair of spirals, each one
spiraling upwards in opposing directions.
3.Tree branches – a main trunk will grow until it produces a
branch, which creates two growth points.

21. SOME EXAMPLE OF GOLDEN RATIO
4. Shells
5. Spiral Galaxies and Hurricane

22. IMPORTANCE OF MATHEMATICS IN
LIFE
1.Restaurant Tipping 2. Netflix film
viewing
2.Calculating Bills 3. Computing Test
Scores
3.Tracking Career 4. Doing Exercise
4.Handling Money 5. Making
Countdowns
5.Baking and Cooking 6. Surfing Internet

23. NATURE OF MATHEMATICS
1.PATTERNS AND RELATIONSHIP
2.MATHEMATICS, SCIENCE AND TECHNOLOGY
3.MATHEMATICAL INQUIRY
4.ABSTRACTION AND SYMBOLIC
REPRESENTATION
5.MANIPULATING MATHEMATICAL STATEMENTS
6.APPLICATION

24. THE ROLES OF MATHEMATICS IN SOME DISCIPLINE
1.Mathematics in Physical Science
2.Mathematics in Chemistry
3.Mathematics Biological Science
4.Mathematics in Engineering and Technology
5.Mathematics and Agriculture
6.Mathematics and Economics

25. THE ROLES OF MATHEMATICS IN SOME DISCIPLINE
7. Mathematics and Psychology
8. Mathematics and Actuarial Science,
Insurance and Finance
9. Mathematics in Archaeology
10. Mathematics and Logic
11. Mathematics in Music
12. Mathematics in Arts

26. THE ROLES OF MATHEMATICS IN SOME DISCIPLINE
13. Mathematics in Philosophy
14. Mathematics in Social Networks
15. Mathematics in Political Science
16. Mathematics in Linguistics
17. Mathematics in Management
18. Mathematics in Computers
19. Mathematics in Geography

27. MATHEMATICS AS A HUMAN ENDEAVOR
Accountants
Agriculturists
Architects
Biologists
Chemists
Computer Programmers
Engineers

28. MATHEMATICS AS A HUMAN ENDEAVOR
Lawyers
Managers
Medical Doctors
Meteorologists
Military Personnel

29. MATHEMATICS AS A HUMAN ENDEAVOR
Nurses
Politicians
Salespeople
Technicians
Tradesmen

30. “MATHEMATICS
REVEALS ITS
SECRET ONLY
TO THOSE WHO
APPROACH IT
WITH PURE
LOVE, FOR ITS
OWN BEAUTY”
- ARCHIMEDES

31. ASSIGNMENT:
Watch a video “Nature by Numbers”
https://www.youtube.com/watch?v=kkGeOWYOFoA, a short movie of
Cristobal Vilas produced by Eterea Studios.
After watching the video, answer the guide questions that follows. Write
your answer on 1 whole sheet of paper to be submitted next meeting.
Guide Question:
• What patterns were shown in the video?
• How does this specific pattern occur?
• What figures illustrates same pattern?