mmw chapter 1: mathematics in our wold

Mathematics

It is the study of relationship between numbers, quantities, and shapes

Mathematics

Nurtures human characteristics like power of creativity, reasoning, critical thinking, spatial thinking and others

Mathematics

Helps organize patterns and regularities in the world

Mathematics

Predict the behavior of nature and phenomena in the world

1. Arithmetic

2. Algebra

3. Geometry

4. Tigonometry

5. Calculus

Branches of Mathematics:

Joseph Plateau

Belgian physicist

Joseph Plateau

Examined soap films, leading him to formulate the concept of minimal surface

Ernst Haeckel

German biologist and artist

Ernst Haeckel

Painted hundreds of marine organisms to emphasize their symmetry

D’arcy Thompson

Scottish biologist

D’arcy Thompson

Pionereed the study of growth patterns in both plants and animals, showing that simple equations could explain spiral growth

1. Joseph Plateau

2. Ernst Haeckel

3. D’arcy Thompson

19th Century

Alan Turing

British mathermatician

Alan Turing

Predicted mechanism of morphogenesis which give rise to patterns of spot and stripes

Aristid Lindenmayer and Benoit Maldenbrot/Mandelbrot

Hungarian biologist and French-American mathematician

Aristid Lindenmayer and Benoit Maldenbrot/Mandelbrot

Showed how the mathematics of fractals could create plant growth and patterns

W. Gary Smith

Adopts eight patterns in his landscape work

1. Scattered

2. Fractured

3. Naturalistic

4. Drift

5. Serpentine

6. Spiral

7. Radial

8. Dendritic

W. Gary Smith adopts eight patterns in his landscape work, namely:

1. Snowflake

2. Honeycomb

3. Tiger’s stripe

4. Sunflower

Patterns in Nature:

Sequence

An ordered list of numbers, called terms that may have repeated values. The arrangement of these terms is set by definite rule

Fibonacci Sequence

Each number in the sequence is the sum of the two numbers

Leonardo Pisano Bogollo

His nickname is Fibonacci which roughly means “Son of Bonacci"

1170 and 1250

Leonardo Pisano Bogollo lived in Italy between

November 23

Fibonacci Day

Golden Ratio

Mathematical ratio

phi and 1.618034

Golden ratio is referred and represented as _____ which is approximately equal to _____

Golden Spiral

Is a logarithmic ratio whose growth factor is phi, the golden ratio

3-petal lily and iris

8-petal delphiniums

Fibonacci Flowers:

Fractal Patterns

Patterns the build into a simple repetitive shapes that are reduced in size every time they are repeated

The Motion of Pendulum

Swing

Reflection in a Plane Mirror

An image formed by an object in a plane mirror

Motion of a Falling Object

Object that is falling under the sole influence of gravity

The Action-Reaction Paif of Forces

A pair of forces acting acting on the twi interacting objects