Math

100問 • 2年前

Dasay Montes

通報

問題一覧

WHAT IS PATTERN?

regular and repeated

example of pattern

shoe lace

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

symmetry

example of symmetry

Butterfly, Leonardo the Vinci's Vitruvian Man, Starfish

types of symmetry, The butterfly is symmetric about the axis indicated by the line. Note that the left and right portions are exactly the same

bilateral symmetry

There are other types of symmetry depending on the number of sides or faces that are symmetrical, Note that if you rotate the starfish you can still achieve the same appearance as the original position. This is known as

rotational symmetry

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

angle of rotation

A more common way of describing rotational symmetry is by

order of rotation

A figure has a rotational symmetry of order n (n- fold rotational symmetry) if 1𝑛 of a complete turn leaves the figure unchanged.

order rotation

formula of order rotation

angle of rotation= 360°/n

It involves finding the optimum method of filling up a given space such as a cubic or spherical container.

packing problem

formula of packing problem

area of circle / area of square x 100

area of the circle

π ²

area of square

a ²

He introduced the Arabic number system in Europe.

Leonardo of pisa- fibonacci

He is the greatest European mathematician of the middle ages

leonardo of pisa- fibonacci

Fibonacci was born on

1170

Fibonacci died on

1240

Fibonacci Sequence was discovered after an investigation on the reproduction of

rabbits

φ (Phi)

golden ratio

φ (Phi) is approximately equal to

1.618

THE GOLDEN RATIO IN NATURE example

mona lisa, Notre Dame Cathedral, parthenon

is a systematic way of communication with other people use of sounds or conventions symbols.

language

IMPORTANCE OF LANGUAGE

invented to communicate ideas to other

The language of mathematics was designed

numbers, sets, functions, perform operation

0, 1, 2, …9

ten digits

+, - , x, ÷

operations

∩, ∪, ⊂, ⊃

sets

a, b, c, x and y

variables

=, <, >, ≤, ≥, 𝜋

special symbols

~ , ^, v, →, ↔

logic symbols

N, W, Z, Q, R, C

notations

N = {1, 2, 3, …}

natural numbers

W = {0, 1, 2, 3,…}

whole numbers

Z = {…-3, -2, -1, 0, 1, 2, 3,…}

integers

rational numbers

Q’

irrational numbers or Q' prime

used to separate elements in a set

comma

real numbers

C stand for

complex number

CHARACTERISTICS OF THE MATHEMATICS LANGUAGE

precise, concise, powerful

could mean equality, inequality, or member in a set.

Different use of a number

cardinal nominal ordinal ratio

It is represented by a letter, like x or y.

variables

A symbol for a value we don’t know yet

variables

says that a certain property is true for all elements in a set. “For all”

universal statement

says if one thing is true then some other thing also has true be true. “If- then”

conditional statement

says that there is at least one thing for which the property is true.

existential statement

For all animals a, if a is a dog, then a is a mammal.

universal conditional statement

A statement that is _____ because its first part says that a certain property is true for all objects of a given type, and it is _______ because its second part asserts the existence of something.

universal existential statement

is a well-defined collection of distinct objects.

set

the number of elements is countable.

finite

the numbers of elements cannot be counted.

infinite

set with exactly, the same elements and cardinality.

equal sets

set with the same number of elements or cardinality.

equivalent sets

are set with common elements(intersection) Example: A = {c, a, r, e} B = {b, e, a, r, s}

joint sets

set with no common elements. Example: The set A = {a, b, c} and B = {e, f, g}

disjoint sets

Quantity being talked about which is represented by symbols. • Collection of algebraic terms separated by different operations. • Has an incomplete thought.

mathematical expressions

Expressions written differently but their values are the same when simplified.

synonymes

Consists of mathematical expressions related using equality ( = ) and inequality symbols ( >, ≥, <, ≤ ). • Has complete thought

mathematical sentences

Accepted rules and practice of spelling, writing, and punctuations. • Symbols used in writing mathematical expressions and sentences, including their meanings and rules in writing.

conventions

numbers

babylonian number system

numbers

egyptian number system

numbers

roman number system

numbers

hindu-arabic number system

geek alphabet A

alpha

geek alphabet B

beta

geek alphabet Y

gamma

geek alphabet ∆

delta

geek alphabet E

epsilon

geek alphabet Z

zeta

geek alphabet H

eta

Number of elements contained in a set

cardinality

Contains all the possible elements of any set used in the present situation being studied. • Always represented by U

universal set

Empty set. • A set with no elements. • Denoted by an empty pair of braces { } or Ø

null set

A set with exactly one elements.

unity set

Set with definite and countable number of elements.

finite set

Indefinite or non-countable number of elements. • Uses ellipses at the start or end of the braces

infinite set

OPERATION ON SETS: Venn Diagram • Contains the elements found in set A or in set B, or in both. • In symbols; A Ս B = { x | x is in A OR in B}

union

OPERATION ON SETS: Contains the elements found in both set A and B. • In symbols: A ∩ B = { x | x is in A AND in B}

intersection

set B from set A contains the elements in set A but not in set B. • In symbols: A – B = {x | x is in A but not in B}

Difference

“two quantities” • Any operation that combines two values to create a new one

binary operation

is a statement requiring a solution, usually by means of mathematical operation/geometric.

problem

means the ways or techniques used to get answer which will, usually involve one or more problem solving strategies.

method

is a process – an ongoing activity in which we take what we know to discover what we don’t know.

problem solving

PROBLEM – SOLVING INVOLVES THREE BASIC FUNCTIONS:

seeking information, generating new knowledge, making decisions

refers to the ability of a person to analyze problem situations and construct logical arguments to justify the process or hypothesis, to create both conceptual foundations and connections, in order for him to be able to process the information.

mathematical reasoning

The process of reaching a general conclusion by examining specific examples.

inductive reasoning

"or" is represented by

union

"and" is represented by

intersection

process result in an vefined spiral structure

equiangular spiral

If every element of a set A is related with one and only one element of another set then this kind of relation qualifies as a

function

function can represent a function in three ways name by:

algebraic form, tabular form, graphical form

is the set of all first elements of R.

domain

is the set of all second elements of R.

range

types of function, both range and domain of the function is the same

identify function

types of function, the range of the function is constant.

constant function

types of function, ______for every value of x.

polynomial function

these are y=f(x)=g(x)/h(x) type of function where both g(x) and h(x) are polynomials and h(x) ≠0.

Rational function

100

types of function, the range of the function is positive plus the set of 0.

modulus function

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問題一覧

WHAT IS PATTERN?

regular and repeated

example of pattern

shoe lace

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

symmetry

example of symmetry

Butterfly, Leonardo the Vinci's Vitruvian Man, Starfish

types of symmetry, The butterfly is symmetric about the axis indicated by the line. Note that the left and right portions are exactly the same

bilateral symmetry

rotational symmetry

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

angle of rotation

A more common way of describing rotational symmetry is by

order of rotation

A figure has a rotational symmetry of order n (n- fold rotational symmetry) if 1𝑛 of a complete turn leaves the figure unchanged.

order rotation

formula of order rotation

angle of rotation= 360°/n

It involves finding the optimum method of filling up a given space such as a cubic or spherical container.

packing problem

formula of packing problem

area of circle / area of square x 100

area of the circle

π ²

area of square

a ²

He introduced the Arabic number system in Europe.

Leonardo of pisa- fibonacci

He is the greatest European mathematician of the middle ages

leonardo of pisa- fibonacci

Fibonacci was born on

1170

Fibonacci died on

1240

Fibonacci Sequence was discovered after an investigation on the reproduction of

rabbits

φ (Phi)

golden ratio

φ (Phi) is approximately equal to

1.618

THE GOLDEN RATIO IN NATURE example

mona lisa, Notre Dame Cathedral, parthenon

is a systematic way of communication with other people use of sounds or conventions symbols.

language

IMPORTANCE OF LANGUAGE

invented to communicate ideas to other

The language of mathematics was designed

numbers, sets, functions, perform operation

0, 1, 2, …9

ten digits

+, - , x, ÷

operations

∩, ∪, ⊂, ⊃

sets

a, b, c, x and y

variables

=, <, >, ≤, ≥, 𝜋

special symbols

~ , ^, v, →, ↔

logic symbols

N, W, Z, Q, R, C

notations

N = {1, 2, 3, …}

natural numbers

W = {0, 1, 2, 3,…}

whole numbers

Z = {…-3, -2, -1, 0, 1, 2, 3,…}

integers

rational numbers

Q’

irrational numbers or Q' prime

used to separate elements in a set

comma

real numbers

C stand for

complex number

CHARACTERISTICS OF THE MATHEMATICS LANGUAGE

precise, concise, powerful

could mean equality, inequality, or member in a set.

Different use of a number

cardinal nominal ordinal ratio

It is represented by a letter, like x or y.

variables

A symbol for a value we don’t know yet

variables

says that a certain property is true for all elements in a set. “For all”

universal statement

says if one thing is true then some other thing also has true be true. “If- then”

conditional statement

says that there is at least one thing for which the property is true.

existential statement

For all animals a, if a is a dog, then a is a mammal.

universal conditional statement

A statement that is _____ because its first part says that a certain property is true for all objects of a given type, and it is _______ because its second part asserts the existence of something.

universal existential statement

is a well-defined collection of distinct objects.

set

the number of elements is countable.

finite

the numbers of elements cannot be counted.

infinite

set with exactly, the same elements and cardinality.

equal sets

set with the same number of elements or cardinality.

equivalent sets

are set with common elements(intersection) Example: A = {c, a, r, e} B = {b, e, a, r, s}

joint sets

set with no common elements. Example: The set A = {a, b, c} and B = {e, f, g}

disjoint sets

Quantity being talked about which is represented by symbols. • Collection of algebraic terms separated by different operations. • Has an incomplete thought.

mathematical expressions

Expressions written differently but their values are the same when simplified.

synonymes

Consists of mathematical expressions related using equality ( = ) and inequality symbols ( >, ≥, <, ≤ ). • Has complete thought

mathematical sentences

Accepted rules and practice of spelling, writing, and punctuations. • Symbols used in writing mathematical expressions and sentences, including their meanings and rules in writing.

conventions

numbers

babylonian number system

numbers

egyptian number system

numbers

roman number system

numbers

hindu-arabic number system

geek alphabet A

alpha

geek alphabet B

beta

geek alphabet Y

gamma

geek alphabet ∆

delta

geek alphabet E

epsilon

geek alphabet Z

zeta

geek alphabet H

eta

Number of elements contained in a set

cardinality

Contains all the possible elements of any set used in the present situation being studied. • Always represented by U

universal set

Empty set. • A set with no elements. • Denoted by an empty pair of braces { } or Ø

null set

A set with exactly one elements.

unity set

Set with definite and countable number of elements.

finite set

Indefinite or non-countable number of elements. • Uses ellipses at the start or end of the braces

infinite set

OPERATION ON SETS: Venn Diagram • Contains the elements found in set A or in set B, or in both. • In symbols; A Ս B = { x | x is in A OR in B}

union

OPERATION ON SETS: Contains the elements found in both set A and B. • In symbols: A ∩ B = { x | x is in A AND in B}

intersection

set B from set A contains the elements in set A but not in set B. • In symbols: A – B = {x | x is in A but not in B}

Difference

“two quantities” • Any operation that combines two values to create a new one

binary operation

is a statement requiring a solution, usually by means of mathematical operation/geometric.

problem

means the ways or techniques used to get answer which will, usually involve one or more problem solving strategies.

method

is a process – an ongoing activity in which we take what we know to discover what we don’t know.

problem solving

PROBLEM – SOLVING INVOLVES THREE BASIC FUNCTIONS:

seeking information, generating new knowledge, making decisions

mathematical reasoning

The process of reaching a general conclusion by examining specific examples.

inductive reasoning

"or" is represented by

union

"and" is represented by

intersection

process result in an vefined spiral structure

equiangular spiral

If every element of a set A is related with one and only one element of another set then this kind of relation qualifies as a

function

function can represent a function in three ways name by:

algebraic form, tabular form, graphical form

is the set of all first elements of R.

domain

is the set of all second elements of R.

range

types of function, both range and domain of the function is the same

identify function

types of function, the range of the function is constant.

constant function

types of function, ______for every value of x.

polynomial function

these are y=f(x)=g(x)/h(x) type of function where both g(x) and h(x) are polynomials and h(x) ≠0.

Rational function

100

types of function, the range of the function is positive plus the set of 0.

modulus function