Nature of Mathematics Flashcards
Mathematics In The Modern World Prelims Exam
______ of mathematics, _________ of its practical, _______ and aesthetic _______ and ______ of mathematical tools in daily life.
Nature
Appreciation
Intellectual
Dimension
Application
Nature by Numbers
A short movie by __________, 2010
Cristὁbal Vila
Mathematic is a formal system of thought for _____, ______ and _________ patterns
Recognizing
Classifying
Exploiting
Mathematics; Science and _______
Technology
Mathematics; the origin of ________
Counting
Mathematics; _______ patterns
Geometric
Mathematics; Wave patters in ______ and on ______.
Water
Land
Mathematics; Patterns of ________
Movement
It has Fractals
Mathematics
To help us unravel the puzzles of nature, a useful way to think about nature
Mathematics
Organize patterns and regularities as well as irregularities
Mathematics
Mathematics; To able to ____
Predict
Mathematics; To help us control ________, _________
Weather
Epidemics
Mathematics; Provides tools for _________
Calculations
It provides new questions to think about
Mathematics
- With curiosity
- With a penchant for seeking patterns and generalities
Mathematics
- With a desire to know the truth
- With trial and error
Mathematics
- Without fear of facing more questions and problems to solve
- With tenacity (willingness to keep working)
Mathematics
Importance of Mathematics
- It gives order
- It helps us become better persons
- It helps the world a better place to live in
The Fibonacci numbers are the numbers in the following integer sequence, called the _____________.
Fibonacci Sequence
the ____________ are the numbers in the following integer sequence, called the Fibonacci sequence
Fibonacci Numbers
it characterized by the fact that every number after the first two is the sum ofthe two preceding ones.
Fibonacci Numbers
The sequence Fn of Fibonacci Numbers Formula
Fn = Fn-1 + Fn-2
____________ appear to have first arisen in perhaps ____ BC in workby ____________ a on enumerating possible patterns of poetry formed from syllables of two lengths.
Fibonacci Numbers
200 BC
Pingala
The Fibonacci sequence is named after Italian mathematician
_________________ which means Leonardo of Pisa, known as Fibonacci.
Leonardo Pisano
Leonardo Pisano which means _____________, known as Fibonacci.
Leonardo of Pisa
Leonardo Pisano (Fibonacci) Year?
1170-1250
__________ is better known by his nickname Fibonacci.
Leonardo Pisano
Leonardo Pisano was born in __________ but was educated in ________ where his father held a __________ post.
Italy
North America
Diplomatic
Fibonacci was taught mathematics in _______ and travelled widely with his______, recognizing the enormous advantages of the ____________ used in the countries they visited.
Bugia
Father
Mathematical systems
- He was considered to be the most talented mathematician in the middle ages
- “the most talented western mathematician” of the Middle Ages.
Leonardo Pisano
In _________, Fibonacci wrote a very famous book “________” to describemathematics he learned.
1202
Liber abaci
Fibonacci Sequence ThingsExamples:
- Flower petals
- Leaves
- Spiral
- Tree Branches
Golden Ratio symbol in greek
“phi”
The golden ratio is a special number approximately equal to _______.
1.618
It appears many times in geometry, art, architecture and other areas.
The golden ratio
The golden ratio, also known as the ____________
Divine Proportion
The Golden Ratio is also sometimes called the _______, _____, ______, ______ ______, _________ and ________.
golden section
golden mean
golden number
divine proportion
divine section
golden rectangle
golden proportion.
__________ is a mathematical ratio. It is commonly found in nature, and when used in design, it fosters organic and natural looking compositions that are aesthetically pleasing to the eye.
The Golden Ratio
Golden Ratio in Art Examples:
- Pyramids in Giza
- the Parthenon in Athens
- Michelangelo’s The Creation of Adam on the ceiling of the Sistine Chapel
- Da Vinci’s Mona Lisa
- Apple
- Toyota
- Pepsi Logo
a/b = a+b/a =
1.618
the Golden Ratio boils down to _________— creating and appreciating a sense of beauty through ________ and ________.
Aesthetic
Harmony
Proportion
When applied to design, the Golden Ratio provides a sense of _____; an X-factor; a certain ____________
artistry
je ne sais quoi
je ne sais quoi means
a quality that cannot be described or named easily.
Golden Ratio in things Examples:
- Sunflower
- Spiral Aloe
- Nautulis Shell
- Human Face
FORMS OF PATTERNS IN THE NATURE
FRUITS: A banana has ______ sections
3 Sections
FORMS OF PATTERNS IN THE NATURE
FRUITS: An apple has _____ sections
5 Sections
