Math Flashcards
is a structure, form, or design that is regular, consistent, or recurring.
can be found in nature, in human-made designs, or in abstract ideas
Pattern
6 types of pattern
geometric pattern
pattern of texture
patterns of visual
patterns of movement
patterns of rhythm
patterns of flow
are often unpredictable, never quite
repeatable, and often contain fractals. These patterns are can be seen from the
seeds and pinecones to the branches and leaves. They are also visible in self-similar
replication of trees, ferns, and plants throughout nature.
patterns of visual
are usually found in the water, stone, and even in the
growth of trees. There is also a flow pattern present in meandering rivers with the
repetition of undulating lines.
pattern of flow
.This prevalence of
pattern in locomotion extends to the scuttling of insects, the flights of birds, the
pulsations of jellyfish, and also the wave-like movements of fish, worms, and
snakes
pattern of movement
m is conceivably the most basic pattern in nature. Our
hearts and lungs follow a regular repeated pattern of sounds or movement whose
timing is adapted to our body’s needs. Many of nature’s rhythms are most likely
similar to a heartbeat, while others are like breathing. The beating of the heart, as
well as breathing, have a default pattern.
pattern of rhythm
is a quality of a certain object that we sense through
touch. It exists as a literal surface that we can feel, see, and imagine. Textures are
of many kinds. It can be bristly, and rough, but it can also be smooth, cold, and
hard.
pattern of texture
is a kind of pattern which consists of a
series of shapes that are typically repeated. These are regularities in the natural
world that are repeated in a predictable manner. cacti succulents
geometric patterns
3 types of symmetries
reflection symmetry, rotations, translations
4 types of pattern found in nature
symmetry, waves and dunes, spots and stripes, spirals
sometimes called line symmetry or mirror symmetry,
captures symmetries when the left half of a pattern is the same as the right half.
reflection symmetry
captures symmetries when it still
looks the same after some rotation (of less than one full turn). The degree of
rotational symmetry of an object is recognized by the number of distinct
orientations in which it looks the same for each rotation
rotation
Translational symmetry exists in
patterns that we see in nature and in man-made objects. Translations acquire
symmetries when units are repeated and turn out having identical figures, like the
bees’ honeycomb with hexagonal tiles.
translation
symmetries in nature
human body, animal movement, snowflakes, sunflowers, bee hives, starfish
refers to an ordered list of numbers called terms, that may have
repeated values. The arrangement of these terms is set by a definite rule.
refers to an ordered list of numbers called terms, that may have
repeated values. The arrangement of these terms is set by a definite rule.
sequence
4 types of sequence
arithmetic sequence, harmonic sequence, geometric sequence, fibonacci sequence
. It is a sequence of numbers that follows a definite
pattern. To determine if the series of numbers follow an arithmetic sequence,
check the difference between two consecutive terms.
arithmetic sequence
we need to look for the
common ratio.
geometric sequence
the reciprocal of the terms behaved
in a manner like arithmetic sequence.
harmonic sequence
italian mathematician named after the fibonacci sequence
Leonardo Pisano Bigollo 1170-1250
is a series
of numbers governed by some unusual arithmetic rule. The sequence is
organized in a way a number can be obtained by adding the two previous
numbers.
Fibonacci sequence
is made up of squares
whose sizes, surprisingly is also behaving similar to the Fibonacci sequence.
golden rectangle
3 chaRACTERistics of a mathematical language
precise concise powerful
is a collection of well-defined objects.
set
introduced the word set in 1879
georg cantor
is a set that contains only one element.
unit set
s a set that the elements in a given set is countable.
finite set
a set that elements in a given set has no end or not
infinite set
e numbers that used to measure the number of
elements in a given set. It is just similar in counting the total number of element in a set.
Illustration:
A = { 2, 4, 6, 8 } n = 4
B = { a, c, e } n = 3
cardinal set
if and only if they have
equal number of cardinality and the element/s are identical.
A = { 1, 2, 3, 4, 5} B = { 3, 5, 2, 4, 1}
equal set
U is the set of all elements under discussion
universal set
sets if and only if they
have common element/s.
A = { 1, 2, 3}B = { 2, 4, 6 }
Here, sets A and B are joint set since they have common element
such as 2.
joint sets
mutually exclusive or if they don’t have common element/s.
disjoin sets
2 ways of describing a set
roster or tabular, set-builder or rule
(a, b) = (c, d) means that a = c and b = d
ordered pair
5 operation on sets
union of sets, intersection of sets, difference of sets, compliment of sets, cartesian product
Expression
n is the mathematical analogue of an English noun; it is a correct arrangement
of mathematical symbols used to represent a mathematical object of interest.
equivalent set
Two sets, say A and B, are said to be equivalent if and only if they
have the exact number of element. There is a 1 – 1 correspondence.
Illustration:
A = { 1, 2, 3, 4, 5 } B = { a, b, c, d, e }
cardinal set
Two sets, say A and B, are said to be equal if and only if they have
equal number of cardinality and the element/s are identical. There is a 1 -1
correspondence.
Illustration:
A = { 1, 2, 3, 4, 5} B = { 3, 5, 2, 4, 1}
joint set
if and only if they
have common element/s.
A = { 1, 2, 3}B = { 2, 4, 6 }
disjoint set
if and
only if they are mutually exclusive or if they don’t have common element/s.
Venn diagram
are used to
depict set intersections (denoted by an upside-down letter U). This type of diagram is used in
scientific and engineering presentations, in theoretical mathematics, in computer applications,
and in statistics.
George Polya
is one of the foremost recent mathematicians to make a study
of problem solving. He was born in Hungary and moved to the United States in
1940. He is also known as “The Father of Problem Solving”.
george polya
He made fundamental contributions to combinatorics, number theory,
numerical analysis and probability theory. He is also noted for his work in heuristics
and mathematics education
Heuristic
a Greek word means that “find” or “discover”
refers to experience-based techniques for problem solving, learning, and discovery
that gives a solution which is not guaranteed to be optimal.
