most common pattern and based on repetition of tiles or templates without change.

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Charles Darwin, who conceived the survival of the fittest theory, detested ???

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cephalopod mollusk with a spiral shell and numerous short tentacles around its mouth. It showcases Fibonacci numbers and spiral.

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Examples of Patterns in Nature

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it is group of numbers that follow a pattern based on a specific rule. List of things (usually numbers) that are in order.

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Sequence may consist?

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list of terms in a specific order and it has a first term and a last term. The order of the terms of a finite has an end.

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list of terms in a specific order without a limit. It has to continue and represented by dots in the sequence. The order of the terms of an infinite sequence has no end.

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arrangement of things or numbers in relation to each other according to a particular sequence, pattern, or method.

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collection of objects having with distinct commonality. Or simply a group of things that belong together

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system of symbols used to represent special thing.

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prescribed guide or an accepted procedure to observe and to follow.

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rule or relationship that are used to solve a problem.

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list of numbers follows a certain sequence. Patterns establish the relationship between two numbers. It is also known as the sequences of series in numbers.

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Types of Number Patterns in Math

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formed by simply adding or subtracting by the same value each time. The value that is added or subtracted is known as the common difference.

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simply multiplying or dividing by the same value each time. The value is known to be as the common ratio.

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from a pattern of dots that form a triangle. By adding another row of dots and counting all the dots, we can find the next number of the sequence. T = n(n+1)/2

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by squaring the number itself in their position in the sequence. Ex. 1, 4, 9, 16, 25, …

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terms are the cubes of their position in the sequence. Ex. 1, 8, 27, 64, 125…

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by adding the two previous terms or simply adding the two numbers before it. Named before Leonardo Fibonacci, born in 1170 in Pisa, Italy.

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a book published in 1202 that introduced Hindu-Arabic numerals to Europeans

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a pattern made by repeating regular polygon. The pattern is identical at each vertex.

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made of two or more regular polygons. The pattern at each vertex must be the same.

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creates balance, and balance in design creates harmony, and order. A proportionate similarity which is found in two halves of an object, that is, one-half is the mirror image of the other half

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Types of Symmetry

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

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what Leonardo da Vinci showed in the proportions and symmetry of the human body

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The line of symmetry can be based on its orientation as?

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symmetrical and covered in stripes almost everywhere except the underbelly and inner thighs.

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found in everything from the petals of a flower to the topside view of a jellyfish. In art and design, rotational symmetry can be used to portray motion or speed. Even on a static medium, rotational symmetry can convey action.

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The point around which you rotate is called the ??? and the smallest angle you need to turn is called ????

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describing rotational symmetry is by order 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

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when an object is relocated to another position while maintaining its general or exact orientation.

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combination of both and reflection transformations.

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designates the nth term of the sequence, as an expression of n (where n = the term's location). It defines the sequence as a formula in terms of n. It may be written in either subscript notation an, or in functional notation, f (n).

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it designates the starting term, a1, and the nth term of the sequence, an, as an expression containing the previous term (the term before it), a_n-1

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the long part divided by the short part is also equal to the whole length divided by the long part. It is also known as the golden section, golden mean, or divine proportion.

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we often say that history repeats itself.

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Through the use of mathematics, man is also able to exert control over himself and the effects of nature.

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characterized by: abstraction, symbols and rules, non-linearity and complexity of language, arrangement, coding, and decoding information.

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tells the number of elements of a set. (tells how many)

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tells the order of elements (tells the position)

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use number in giving a name or description (tells a name)

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tells the proportion or percentage (tells and compares values)

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simply collection of well-defined distinct objects

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can be referred to as patterns, characters or images used instead of words and are used to perform various operations. - symbols make it easier to refer the Math Quantities.

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the way how to write down the logic expressions to display a solution.

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mathematical expression that relates two variables and is written in the form of an equation.

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is an expression or equation that expresses the relationship between certain quantities.

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is a declarative sentence that is either true or false, but not both.

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who discovered that Uteruses looks normal and healthy based on its relative dimensions?

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euler's constant

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Who established that the golden ratio can also be found in the human body

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3 other words for golden ratio

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a relationship between sets of values. Or, it is a subset of the Cartesian product

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Given elements a and b, the symbol (a, b) denotes the ordered pair, consisting of a and b together with the specification that a is the first element of the pair and b is the second element.

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simply refers to a group or collection of well-defined distinct objects. It is also collection or aggregate of objects of any kind. This is usually represented by the uppercase letters, A, B, C.

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objects that belong in a set, they are called members of the set.  

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method of listing the elements inside a pair of braces. Commas are used to separate the elements. 

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integer greater than 0 and begin at 1 and increment to infinity. It also called "counting numbers" because they are used for counting and represented by symbol “N”.  N = {1,2,3,4,5,..}

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numbers without fractions and collection of positive integers and zero and represented by symbol “W”.  W = {0,1,2,3,4,5,…}

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number that can be in the form p/q where p and q are integers and q is not equal to zero and represented by symbol “Q”.

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whole number which can be negative, positive and zero

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number that cannot be written as a ratio of two integers and represented by symbol “P or Q”. 

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numbers on the Number Line and include all the Rational and Irrational Numbers and represented by symbol “R”. 

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number is squared it gives a negative result and represented by symbol “i”. 

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combination of a Real number and an Imaginary number and represented by symbol “C”. 

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defines the number of elements a set is having. It describes also the size of a set or simply the number of distinct elements in the set. Also, only unique elements within a set contribute to the cardinality.

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well defined if it is possible to determine whether any given item is an element of the set.  

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way the elements in the sets are being specified or depicted 

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well-defined description of the elements of the set is given and the same are enclosed in braces. 

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Listing the elements of a set inside a pair of braces { } and are separated by commas. 

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rule, or formula or a statement which is written within the pair of braces so that the set is well defined. In the set builder form, all the elements of the set, must possess a single property to become the member of that set 

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useful when describing infinite sets. It uses the format:  and read as, a set of x such that x is…

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set that contains no elements. The symbol or { } is used to represent the empty set and represented by this symbol ∅. 

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unique set which have no element in it. Its size is zero. 

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set of all sets, or the totality of sets. The symbol use to represent Universal set is U.  

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cardinal number of a finite set A is denoted by the notation n(A) or /A/.

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if the number of elements in the set is can be enumerated and counted for from start to finish. If in the process of counting of elements comes to an end. 

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if the numbers of elements cannot be listed or simply the members of the set is unlimited or uncountable. If in the process of counting of elements can never end and usually denoted by three dots. 

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said to be equal if they have exactly the same members or elements, order of elements in a set is not observe and it uses a symbol of “=”. 

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if they have exactly the same number of members or elements, order of elements in a set is not observe and it uses a symbol of “~ or ≡”. Or sets are said to be equivalent if their cardinality is same. 

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denoted by A’ or Ā or A^C is the set of all elements of the universal set U but are not elements of A. 

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Set A is a subset of set B, denoted by A ⊆ B , if and only if every element of A is also an element of B. it is denoted by as symbol “⊆” 

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The formula to find the number of subsets for A is given by 2ⁿ. Also, a  set with n elements has 2ⁿ subsets or /P(A)/ = 2ⁿ, where n is the number of  elements.

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The to find the number of proper subsets is given by 2ⁿ-1 

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the union of sets A and B, denoted by A ∪ B is the set that contains all the elements that belong to A, B or both.  

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denoted by A ∩ B is the set of elements common to both A and B. 

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denoted by A - B, is the set of elements that belongs to A but not in B. 

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set that contains the elements of A and the elements of B, but not the elements of their intersection, denoted by symbols ⊕ , ⊝ or Δ. 

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known as “Euler-Venn diagram” is a simple representation of sets by diagrams. The usual depiction makes use of a rectangle as the universal set and circles for the sets under consideration.

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rule that relates values from a first set of values.

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to a second set of values.

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Given elements a and b, the symbol (a, b) denotes the ordered pair, consisting of a and b together with the specification that a is the first element of the pair and b is the second element. 

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pair of elements that occur in particular order and are enclosed in brackets.

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Given sets A and B, the Cartesian product of A and B, denoted by AxB and read as “A cross B”, is the set of all ordered pairs (a, b), where a is in set A and b is in set B. Symbolically: (set builder notation) 

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who invented the Cartesian product. It derives the name from the same person.

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Arrow Diagrams and Ordered Pairs 

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used to represent a relation. The members of each set are listed inside an enclosed shape and arrows are drawn to connect related members 

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preserves the directional property of the relation. It is consistent with the order of points plotted on a Cartesian Plane represented by (x,y). 

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into a function

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may possibly come of a function

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what actually comes out of a function 

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if no two elements of A have the same image in B. Or simply every object only map to one image likewise, every image has only one object.

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if an element of A is related to two or more elements of B. Or simply one object is map to more than one image.

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if two or more elements of A are related to B. Or simply more than one object is map to one image.

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if two or more elements of A are related to two or more elements of B. Or simply one object is map to more than one image, and one image is map to more than one object.

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from a set A to a set B is a set of ordered pairs (a, b) where a is an element of A and b is an element of B. 

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8 properties of relation

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also known as Void Relation. If R = Ø, means the relation has no element in it.

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also known as Full Relation. if element is related to every other element of A.  Example: R = A x A 

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if every element of set A is related to itself only.  Thus, I = {(a, a), a∈ A} 

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If R is a relation from set A to set B, then by interchanging the first and second coordinates of ordered pairs of R, then a new relation is formed B into and this relation is said to be inverse relation denoted by R^-1.

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if (x, x) Є R for every x Є X. or reflexive if xRx ∀ x∈X. note: ∀ read as “for all”. It is the one in which every element maps to itself. 

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if x is not related to x. Symbolically, ∀ x∈A, (x, x) ∉ R 

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if for all (x, y) Є X, if (x,y) Є R,  then (y, x) Є R. or symmetric if aRb ⇒ bRa for all (a, b)∈A. note: ⇒ read  as “implies that” 

(a)  

if, ∀ (a, b) ∈A where (a, b) ∈R and (b, a) ∉ R where a ≠ b. 

(a)  

if it satisfies the following property: If (x, y) is in R, then (y, x) is not in R. In other words, it can't go both ways 

(a)  

Let R be a transitive relation defined on the set A. Then, R = { (a, b), (b, c), (a, c)}. In simple terms, aRb, bRc ⟹ aRc. A relation R on a set A is said to be transitive if (a, b)∈R and (b, c)∈R, then (a, c)∈R 

(a)  

if R is reflexive, symmetric and transitive relation.

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relation R⊆S×T in S to T such that every element of S relates to every element in T: relation which equals the product of the sets on which it is defined. An empty relation and a universal relation are also a trivial relation.

(a)  

method that is used to determine whether a given relation is a function or not. Graph represents a function if and only if each vertical line intersects the graph at most once 

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