Math

Nature of Mathematics

The word mathematics comes from the greek word “mathema” which means learning

Mathema

It means learning

Pattern

is an organized arrangement of objects in space or time.

Natural Patterns

include symmetry, stripe, spot, crack, spiral, tesselation, foam, wave, dunesand fractal.

Symmetry

when a shape looks identical to its origial shape after being flipped or turned.

Symmetry

Crack

Stripes

Tessellation

Spot

Spiral

Foam

Wave

Fractal

Natural Patterns include

Reflective Symmetry

Rotational Symmetry

2 types of symmetry

Reflective Symmetry

mirror-image Ex. Butterfly (same image different direction

Rotational Symmetry

the original image is still the same whether it is flipped/turned

Crack

are linear openings that form in materials to relieve stress

Tesselation or Tiling

forms a class of patterns found in nature.  

Fractal Pattern

is when an object exhibits self similar shape or form at any scale and repeat itself overtime.

Divide Proportion

all patterns especially spirals is 1.618 (the golden ratio)

1.618

The golden ratio

Sequence

is an ordered list of numbers. The numbers in this ordered list are called the elements or the terms of the sequence.

Arithmetic Sequence

is a list of numbers with a definite pattern.

Common Difference

The constant difference in all pairs of consecutive numbers in a sequence is called

Geometric Sequences

- is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed non zero number called the common ratio.

Fibonacci Sequence

the exact origination of the fibonacci sequence is unknown

Leonardo Pisano Bigollo

many sources claim it was first discovered or "invented" by

Fibonacci Spiral

also known as golden spiral has an association with the golden mean, it is based on the fibonacci sequence.

Golden Ratio

the world mathematics, the numeric value is called "phi", named for the greek sculptor Phidias.

Phi

the world mathematics, the numeric value is called

Golden Section

Golden Meat

Divine Proportion

3 types of Golden Ratio

Golden Ratio In Humans

it is claimed that just about every proportion of the perfect human face has a link to the golden ratio.  

GOLDEN RATIO N ARTCHITECTURE & ENGINEERING

- it is used when determining features such as how to properly determine a building layout, space out windows, and determine a buildings layout.

GOLDEN RATIO IN ARTS AND DESIGN

been used by artist to (determine) locate aesthetically pleasing areas to place our subjects and distribute weight on our paintings

GOLDEN RATIO IN NATURE

nature is filled with patterns - spirals, in particular, are especially noticeable in species of plants and animals.  

➢ MATHEMATICS FOR ORGANIZATION

has a vital and unique role in the human societies and represents a strategic key in the development of the whole mankind.

Human Beings

Are the ones who create society

Society

- human being are the ones who create society

TECHNOLOGICAL

application of science

Industrial

Product and Service

ECONOMICAL -

stock exchange

Military

Tactics, weapons

MURPHY'S LAW

"anything that go wrong, can eventually go wrong".

MATHEMATICS FOR CONTROL -

can help us control nature and occurences in the world for our own good through mathematical modelling.

Murphy’s Law

Predicting the size and location

3 main Characteristics of Mathematical Language

Precision

Concise

Powerful

Precision

the quality of being exact and accurate set of positive integers

- it is a positve and negative whole of numbers.

Concise

it involves the appropriate and minimal numbers of words. (direct to the point)

example: - a regular hexagon that has a polygon of 6 sides and angles.

Concise

a line has a minimum of two points.

Powerful

you are able to convey, complex that derive with relative each.

THE GRAMMAR OF MATHEMATICS -

refers to the structural rules.

C

set of composite numbers

R(R)

set of real numbers

i

Imaginary numbers

Z

Integers

-zhalen numbers

Q

set of rational numbers/fractions/decimals.

N

Natural numbers (Counting Numbers)

CONVENTIONS

 

the use of equal sign.

- solving multiple operations.

Sets

well-defined collection of distinct objects.

Sets

based on a certain characteristic

Groups

Diverse collection

➢ ELEMENTS

things, objects, numbers and more that comprises a set.

UNIVERSAL SET(U)

the setunder investigation that contains all elements.

EMPTY SET (Null Set) -

set that has no element.

Finite Set

That are countable

Infinite set

That has no end

Subsets

Sets within the sets

Proper Subsets

not identical to the original sets.

Improper subsets

identical to the original.

EQUAL SETS -

sets that has the equal cardinality and same elements

EQUIVALENT SETS

sets that have the same cardinality.

JOINT SETS

that has at least one common element.

Disjoint sets

No common element

ROSTER METHOD -

list all elements

RULE METHOD -

describe the set.

SET-BUILDER NOTATION -

describe the elements

- x such that x is

Roster Method

Rule Method

Set Builder Notation

3 ways of writing sets