MATHWORLD

Languages

Languages

·        Defined as a systematic means of communicating ideas or feelings by the use of conventionalized signs, sound, gestures, or marks having understood meanings;

Mathematics

is a system of communication about objects like numbers, variables, sets, operations, functions and equations.

Mathematics

The aforementioned components, as defined in the dictionary, are found in mathematics, thus mathematics qualifies as a language.

Importance of Language

Invented to communicate ideas with the others

Importance of Language

Language of mathematics was designed to interpret:

○ Numbers
○ Sets
○ Functions
○ Perform Operations

Language of Mathematics

●As universal Language in terms of numbers, letters and symbols.
●As mathematical expressions / sentences
●As mathematical equations
●As mathematical sentence

The Grammar of Mathematics

The mathemathical notation used for formulas has it’s own grammar, not dependent on a specific natural language, but shared internationally by mathe,athecians regardless of their mother tounges.

Characteristics of the Language of Mathematics

●Precise – able to make very fine distinctions
●Concise – able to say things briefly
●Powerful – able to express complex thoughts with relative ease

Order of Operations

●GEMDAS – is used to remember the order of operations in Math Problems
●G for grouping symbols such as parenthesis, brackets, and braces
●E for exponents

Proposition

•A ________ is a sentences that is either true or false but not both.

Proposition

•If the ________ is true, then the truth value is true denoted by T.

Proposition

•If the ________ if false, then the truth value is false denoted by F.

Properties

   Math __________ are rules in math. Properties are always true for every number.

Commute

To ________ means to travel from one place to another.

Commutative Property

• Just like you commute from home to school, a number may commute from one spot to another.
• A + B = B + A (The numbers change places.)
• This is called the commutative property of addition.

Commutative Property

The __________ may be used with addition as seen previously and also with multiplication.

Associate

• An ________ is a friend or someone you work with.
• For example, the head cheerleader is an associate of the school mascot.

Associative Property

The __________ ______ is when a number associates with a different number.

Identity

• Your ______ is who you are.
• Changing your clothes or getting a new haircut does not change your _______.
• Your _______ remains the same.

Identity Property of Addition

• A number also has an identity
• The identity of a number is the value of the number
• The ______ _____ is the number that when added to another number does not change the identity of the original number
• 3 + __ = 3 (What goes in the blank?)

Zero

• The additive identity is _____.
• We can add ____ to any number and the answer is the original number.

Identity Property of Multiplication

• We also have a ____________ identity
• 3 * __ = 3 (What goes in this blank?)
• We can multiply any number by one and the answer will be the original number.

Zero Property

• The ___________ sounds just like what it is, a property about zero.
• A * 0 = 0
The ______ tells us that any number multiplied by zero equals zero.

PATTERNS

Ø  are regular, repeated or recurring forms or designs.

PATTERNS

Ø  In studying ______, it helps us identify relationships and find local connections to form generalizations and make predictions.

SYMMETRY

• _______ indicates that you can draw an imaginary line across an object and the resulting parts are mirror images of each other.

ROTATIONAL SYMMETRY

• If you rotate the starfish in 72 degree , you can still achieve the same appearance as the original position. This is known as the _______________.

ANGLE OF ROTATION

• The smallest measure of angle that a figure can be rotated while still preserving the original position is called the angle of rotation.

ANGLE OF ROTATION

A figure has a rotational symmetry of order n ( n- fold rotational symmetry) if 1/n of a complete turn leaves the figure unchanged. To compute for the ___________, we use the formula

Origin of the Fibonacci

Fibonacci Sequence was discovered after an investigation on the reproduction of rabbits.

Leonardo of Pisa - Fibonacci

_______ is the greatest European mathematician of the middle ages.

Leonardo of Pisa - Fibonacci

Born in 1170 and died in 1240

Leonardo of Pisa - Fibonacci

He introduced the Arabic number system in Europe

Fibonacci The Man

His real name was Leonardo Pisano Bogollo, and he lived between 1170 and 1250 in Italy.

Son of Bonacci

"Fibonacci" was his nickname, which roughly means

Fibonacci The Man

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! Thank you Leonardo.

Fibonacci Day

November 23rd, as it has the digits "1, 1, 2, 3" which is part of the sequence. So next Nov 23 let everyone know!

Origin of the Fibonacci

Fibonacci Sequence was discovered after an investigation on the reproduction of rabbits.

GOLDEN RATIO

Φ = 1.618

GOLDEN RATIO

Geometrically, it can also be visualized as a rectangle perfectly formed by a square and another rectangle, which can be repeated infinitely inside each section.

MATHEMATICS & Physical Beauty

the proportions of the length of the nose, the position of the eyes and the length of the chin all conform to some aspect of the Golden Ratio.

aesthetically pleasing

Shapes and figures that bear the Golden Ratio are generally considered as

Golden Ratio

The _____ (symbol is the Greek letter "phi" shown at left) is a special number approximately equal to 1.618 It appears many times geometry, art, architecture and other areas.