Mathematics in our
World
mhsagujar@neu.edu.ph
Mathematics is …
The elephant and the blind men
Fibonacci Sequence
• Leonardo Fibonacci discovered the sequence.
• The sequence begins with zero. Each subsequent number
is the sum of the two preceding numbers.
• Thus the sequence begins as follows:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144….
The Fibonacci Spiral
• The Fibonacci numbers have geometric applications.
• The Fibonacci spiral is constructed by placing together
rectangles of relative side lengths equaling Fibonacci
numbers.
• Recall: 0, 1, 1, 2, 3, 5, 8, 13….
• A spiral can then be drawn starting from the corner of the
first rectangle of side length 1, all the way to the corner of
the rectangle of side length 13.
Activity
• Look at the rectangular shapes on the next slide.
• Chose the one figure on each group you feel has the most
appealing dimensions.
• Chosen figure will be tallied.
Activity
Activity
• The rectangles c and d were probably the rectangles chosen
as having the most pleasing shapes.
• Measure the lengths of the sides of these rectangles. Find
the ratio of the length of the longer side to the length of the
shorter side for each rectangles.
• This ratio approximates the famous Golden Ratio of the
ancient Greeks.
• These special rectangles are called Golden Rectangles
because the ratio of the length of the longer side to the
length of the shorter side is the Golden Ratio.
Golden Ratio
• In mathematics and the arts, two quantities are in the golden ratio if the
ratio between the sum of those quantities and the larger one is the same as
the ratio between the larger one and the smaller.
• In this case, we refer to a very important number that is known as the
golden ratio.
• The golden ratio is a mathematical constant approximately 1.6180339887.
• The golden ratio is also known as the most aesthetic ratio between the two
sides of a rectangle.
Golden ratio and Fibonacci numbers
Recall:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, ...
When we divide one of the Fibonacci numbers to the previous one, we
will get results that are so close to each other.
Moreover, after the 13th number in the sequence, the ratio will be fixed
at approximately 1.618, namely the golden number.
233 / 144, 377 / 233, 610 / 377, 987 / 610, 1597 / 987, 2584 / 1597,…
Golden Ratio in Arts and in Nature
Activity: Golden ratio in human body
Activity: Small group sharing
1. What is mathematics?
2. What mathematics is for?
3. What mathematics is all about?
4. Where is mathematics?
5. What role does mathematics play in your world?
Getting to know Mathematics
1. What is it?
2. Where is it?
3. What is it for?
4. What is it about?
5. How is it done?
6. Who uses mathematics?
7. Why is it important to learn or know?
What is Mathematics?
“Human mind and culture have developed a formal system of
thought for recognizing, classifying and exploiting patters.”
-- Stewart (p.1)
Where is Mathematics?
• in every people’s daily task or activity
• in nature, arts, music, medicine, and other disciplines
• in communities
• IT IS EVERYWHERE!
What is Mathematics for?
• useful in making conclusions and/or predictions of the
events of the world
• use to describe the natural order and occurrences of the
universe
• use to organize patterns and regularities as well as
irregularities
• help to control weather, epidemics
• provide tools for calculations
• provide new questions to think about
What is Mathematics all about?
Mathematics is about numbers, symbols, equations, operations,
functions, calculations, abstractions, and devising proofs.
How is mathematics done?
• with curiosity
• with a penchant for seeking patterns and generalities
• with the desire to know the truth
• with trial and error
• without fear of facing more questions and problems to solve
Who uses Mathematics?
• mathematicians (pure and applied)
• scientists (natural and social)
• everyone
Why is mathematics important to
know/learn?
• It puts order in disorder.
• It helps us become better persons.
• It helps make a world a better place to live in.
Suggested activities
• Look for Fibonacci numbers in fruits, vegetables, flowers, or
plants available in your locality. Write a report about your
obtained results.
• Group sharing, Chapters 4 - 9 Nature’s Numbers by Ian
Stewart
• Write a mathematical vignette (blog.kleinproject.org)
References:
• Calpa, MJ, Powerpoint Presentation: University of Eastern Philippines
(2017)
• Nature by Numbers,
https://www.youtube.com/watch?v=kkGeOWYOFoA
• Nocon R., Nocon E., Essential Mathematics for the Modern World
(2016)
• Stewart, I., Nature’s Numbers (1995)
• Vistro-Yu, C., Powerpoint Presentation: CHED ADMU GE Training (2016)
