MATHEMATICS IN THE MODERN WORLD
LESSON 1 resemble mineral casts of Plateau foam
boundaries
PATTERNS AND NUMBERS IN NATURE AND THE WORLD
PATTERN SPIRAL
- is defined as the regular or repeated way in
- is just like a pinecone seeds, the cactus plant,
which something happens or is done
the formation of tree branches and their
What is Mathematics leaves, rivers maps, water drops and bubbles
- “We have developed a formal system of thought for
STRIPE
reorganizing, classifying, and exploring patterns called
mathematics”. (Stewart, p.1) - A stripe is a line or band that differs in color or
- Mathematics is the science that deals with the logic of tone from an adjacent area. Stripes are a
shape, quantity and arrangement. group of such lines
-Mathematics is an art of patterns and connections CRACK
embedded in nature and in our environment.
- Are linear openings that form in materials to
MATHEMATICS IS A/AN
relieve stress.
ART
Mathematics helps us unravel the puzzles of nature,
STUDY OF PATTERNS
organizes patterns and regularities as well as
LANGUAGE
irregularities, and enables us to make predictions.
PROCESS OF THINKING
SET OF PROBLEM-SOLVING TOOLS Mathematics also helps us control weather and
epidemics. It also provides tools for calculations, and
Different Collected Patterns and Regularities found in provides new questions to think about.
Nature Patterns in Nature
JOSEPH PLATEU- Belgian physicist-examined
Symmetries soap films(19th century)
- are when different sides of something are alike. D’ARCY THOMPSON- pioneered the study of
The symmetry may be broken on one thing but growth patterns in both plants and animals
part of it is still there and creates a pattern ALAN TURING (20th century) ( british
which makes nature more beautiful and mathematoician) – predicted mechanisms of
fascinating. morphogenesis which give rise to patterns of
spots and stripes
FRACTAL
ARISTID LINDENMAYER- hungurian bologist
- is a detailed pattern that looks similar at any BENOIT MANDELBROT- American
scale and repeats itself over time mathematician
- Is a rough or fragmented geometric shape that Pythagoras (c. 570-c. 495 BC) explained
can be subdivided in parts, each of which is (at patterns in nature like the harmonies of music
least approximately) a reduce/size copy of the as arising from number, which he took to be
whole the basic constituent of existence.
- Fractals are formed from these examples of Plato (c. 4two7-c. 347 BC) argued for the
chaotic equations in our universe. existence of natural universals
TESSELATION Centuries later, Leonardo da Vinci (145two-
1519) noted the spiral arrangement of leaf
- are pattern that are formed by repeated cubes patterns, that tree trunks gain successive rings
or tiles. Sunflower is a tessellations found in as they age, and proposed a rule purportedly
nature. Other example are: pineapple, turtle,
satisfied by the cross-sectional areas of tree-
honeycomb.
branches.
Foam Johannes Kepler (1571-1630) pointed out the
presence of the Fibonacci sequence in nature,
- At the scale of living cells, foam patterns are
using it to explain the pentagonal form of
common, radiolarians, sponge spicules,
some flowers.
silicoflagellate exoskeletons and the calcite
skeleton of a sea urchin, Cidaris rugosa, all
Charles Bonnet observed that the spiral
phyllotaxis of plants were frequently
MATHEMATICS IN THE MODERN WORLD
expressed in both clockwise and counter-
clockwise golden ratio series. LESSON 2
, German psychologist Adolf Zeising explored FIBONACCI SEQUENCE
the golden ratio expressed in the arrangement
of plant parts, the skeletons of animals and FIBONACCI SEQUENCE
the branching patterns of their veins and
nerves, as well as in crystals. Fibonacci discovered that the number of pairs
Leonardo Fibonacci introduced the Fibonacci of rabbits for any month after the first two
sequence to the western world with his book months
Liber Abaci. Fibonacci presented a thought is the series of numbers: 0, 1, 1, 2, 3, 5, 8, 13,
experiment on the growth of an idealized 21, 34, ... Wherein the next number is found
rabbit population. by adding up the two numbers before it
The Belgian physicist Joseph Plateau (1801- TYPES OF NUMBER PATTERNS IN MATH
1883) formulated the mathematical problem
formulating Plateau’s laws which describe the Arithmetic Sequence
structures formed by films in foams.
the difference between consecutive terms is
Ernst Haeckel (1834-1919) painted beautiful
always the same.
illustrations of marine organisms, in particular
subtract it by the previous one
Radiolaria, emphasising their symmetry to
support his faux-Darwinian theories of Geometric Sequence.
evolution.
A geometric sequence is a list of numbers that
The American photographer Wilson Bentley
are multiplied (or divided) by the same
took the first micrograph of a snowflake in
amount.
1885.
Triangular Numbers or triangle numbers
What is Mathematics About?
Counts objects arranged in an equilateral
Numbers, symbols, notations
triangle.
Operations, equations, and functions
Processes and “thingification” (The fact or Square Numbers or perfect square
process
is an integer that is the square of an integer;
How is Mathematics Done? in other words, it is the product of some
integer with itself.
► Mathematics is done with curiosity, with a
CubeNumbers
penchant for seeking patterns and
generalities, with the desire to know the is a number multiplied by itself 3 times. This
truth, with trial and error, without fear of can also be called a number cubed
facing more questions and problems to solve
FibonacciNumbers
is a series of numbers in which each number is
the sum of the two preceding numbers. The
simplest is the series 1, 1, 2, 3, 5, 8, etc.
Mathematics can help us control nature and
MATHEMATICS IN THE MODERN WORLD occurences in the world for our own good
through mathematical modelling
LESSON 3
FUNCTIONALITY OF MATHEMATICCS
Mathematics is for Organization
Mathematics is for Prediction
Mathematics is for Control
A. MATHEMATICS IS FOR ORGANIZATION
What is the role of Mathematics in the development
of the society?
Mathematics has a vital and unique role in the
human societies and represents a strategic key
in the development of the whole mankind.
Mathematics is the solution for all the
problems concerning about the pattern,
regularities, and numbers. All patterns were
organized since the beginning, and regularities
are involved when revealed in the world.
Thus, all living things around us had patterns
and regularities
B. Mathematics for Prediction
How can we say that Mathematics can help
predict the behavior of nature and
phenomena in the world?
Using mathematical tools we create models
which correspond to what we can measure
and observe in the world of reality
Weather forecasting is the application of
science and technology to predict the
conditions of the atmosphere for a given
location and time. Human beings have
attempted to predict the weather informally
for millennia and formally since the 19th
century.
Global Circulation Models (GCMs) describe
the interactions between oceans and
atmosphere to look at what the average
conditions could be in decades to come.
Mathematics for Control
How can mathematics help us control nature for our
own ends?
