Week 2 – Nature of Mathematics

Bachelor of Science in Medical Technology (1st Year): MATHEMATICS IN MODERN WORLD

• is the study of pattern and structure.

• is fundamental to the physical and biological sciences, engineering and information technology, to economics and increasingly to the social sciences.

• is a tool to quantify, organize and control our world, predict phenomena and make life easier for us.

Mathematics

• in nature are visible regularities of form found in the natural world and can also be seen in the universe.

Patterns

• which are not just to be admired, they are vital clues to the rules that govern natural processes.

Nature patterns

PATTERN defined as:

• Regular

• Repeated

• Recurring forms or designs

• Identify relationships.

• Find logical connections to form generalizations.

• A repeating pattern using regular polygons.

• No gaps or overlaps

• Each vertex is the same.

• Examples are honeybees.

Tessellation

Other Geometric transformation

➢ Translation

➢ Rotation

➢ Reflection

➢ Dilation

• is a never-ending pattern, 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.

Fractal

• His real name was ___________, and he lived between 1170 and 1250 in Italy.

• As well as being famous for the Fibonacci Sequence, he helped spread Hindu-Arabic Numerals(like our present numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9) through Europe in place of Roman Numerals (I, II, III, IV, V, etc). That has saved us all a lot of trouble!

Leonardo Pisano Bogollo

Meaning of "Fibonacci"

Son of Bonacci

• is an integer in the infinite sequence 1, 1, 2, 3, 5, 8, 13, ... of which the first two terms are 1 and 1 and each succeeding...

Fibonacci number

• Fibonacci Sequence was discovered after an investigation of ______

Rabbits

• is also sometimes called the golden section, golden mean, golden number, divine proportion, divine section and golden proportion.

The Golden Ratio

Symbol of The Golden Ratio

φ

Golden Ratio

1.618034...

Simple Rule of The Fibonacci Sequence

Add the last two terms to get the next.

Term number

Xₙ

Previous term

Xₙ-1

The term before that

Xₙ-2

Write the Rule

Xₙ = Xₙ-1 + Xₙ-2