MATHEMATICS IN MW
Our body follows naturally internal process that regulates sleep, wake cycle, and repeats roughly every 24 hours. It is called ______________ RHYTHM
CIRCADIAN RHYTHM
This are things that are repetitive or arrangement, which can be found in nature as color, shape, action, or some other sequences that are almost everywhere.
Patterns
Does mathematics express patterns?
Yes
THis indicates that you can draw an imaginary line across an object and the resulting parts are mirror images of each other
Symmetry
What are the types of symmetry? (3)
BILATERAL/MIRROR SYMMETRY
ROTATIONAL/RADIAL SYMMETRY
ANGLE OF ROTATION
(TYPES OF SYMMETRY)
It is the property of being into symmetrical halves on either side of a unique plane.
Examples: Shapes like triangle and trapezoid, small things like butterfly
BILATERAL/MIRROR SYMMETRY
(TYPES OF SYMMETRY)
When it still looks the same after some rotation depending on the numbers of sides and faces that are symmetrical. It also depends on faces and number of sides. It also have certain measurement.
Examples: Satrfish, Rollercoaster, hexagon 60 degree,
ROTATIONAL/RADICAL SYMMETRY
(TYPES OF SYMMETRY)
Smallest measurement of the angle that can be rotated while still preserving the original position. Another common way of describing rational symmetry is __________________ .
ANGLE OF ROTATION, ORDER OF ROTATION
It is a figure that has rotational symmetry of order n (n-fold rotational symmetry) if 1/n of a complete turn leaves the figure unchanged.
examples: Snowflakes pattern repeats 8 times, indication that there is 8-fold symmetry. Using the given formula, the angle of rotation is 45 degrees.
ORDER OF ROTATION
This are infinitely del-similar, iterated mathematical constructs having fractal dimensions. Infinite iteration is not possible in nature so all _________ patterns in nature are only approximate. This can be thought as the never ending patterns
EXAMPLE: Corals, Ferbs and Ferns
Fractals
It can be considered a type of fractal. The braching out of a nerve fiber at the end of a neuron. It branches out repeatedly.
Dentric Tree
It is a three-dmensional curve that turns around an axis at a constant or continously varying distance while moving parallel to the axis: a helix.
Examples: Nutrino shell, Comama Shell, Spiral alb plant, cyclone
Spiral
It is a tiling pattern and no gaps, it is a shape that repeats to make a pattern.
Example: Shell of turtle, Skin of snake
Tesselation
This sequence is a big help to the mathematics world, as of today they are most often applied within computers as search algorithms.
Fibonacci sequence
This sequence also occur naturally, the stems of leaves, the branching trees, the flowering of a sunflower etc.
Fibonacci sequence
Aside form the ____________________, this sequence is very important to mathematicians scientists, and naturalists for centuries is derived from the fibonacci sequence.
Golden ration of 1.618
Numbers are such that each number is the sum of two preceding numbers starting from zero.
Fibonacci sequence is the series of numbers
Enumerate the sequence numbers next in the sequence: 0,1,1,2,3,5,8,__ ,__ ,__ ,__ ,__ ,__ ,__
0,1,1,2,3,5,8,13,21,34,55,89,144
What does the notational symbol Fn represent?
(nth) Fibonacci number
What is the formula of recursive?
Fn=Fn-1 + Fn-2, where n>1
What are the 3 characteristics of math?
1. Math language is non-temporal
2. Math language carries no emotional content
3. Math language is precise and concise
It represent constant value, variables used are small letters
Mathematical Symbols
It is a group of characters or symbols representing a quantity and/or an operation.
Mathematical expressions
it is a mathematical expression which contains numbers, variables represented by letters and operations that indicatae addition, subtraction, and multiplication or division
Algebraic Expression
It is a mathematical expression which is either true or false
Mathematical Sentence
It is a statemennt of equality between two algebraic expressions which contain one ortwo unknowns.
Mathematical equation or simply equation
It is any group or collection of objects.
Set
Set can be defined by using ________ , or we can define a set by listing (________ method).
Words and Listing or Roster method
Objects listed in a set are called _______ or __________ of a set
elements or member of a set
What is the symbol E means in a set?
The symbol E means an object is found in, or is an element of a set
It is a set with no elements is and empty set, the symbol represent it as {}
Empty set or Null set
A set is _______ if the number of elements in the set is a whole number. Otherwise, ________. It is denoted as n(A) (Cardinality)
Finite and Infinite set
It is denoted as A' and it is the set of all elements in the universal set that are not elements of A.
Set compliment
The data are the quantities (_________) or Qualities (___________) measured or observed that are to be collected and/or analyzed. A collection of data is called a _________ ____
Numbers, attributes , data set
What are the 2 categories of data
Categorical and continous data
Types of Categorical data
Nominal scale and ordinal scale
Types of continous data
Interval and ratio scales
what are the 3 forms of data presentation
textual, tabular, and graphical presentation
It consists of a finite set of possible values having no particular order.
Examples: Gender, mode of transportation, nationality, occupation, civil status
Nominal scale
It is a set of possible values having a specific order
example: Age, level, social status
Ordinal scale
These are measured on continuum and differences between any two numbers on the scale are known size.
Examples: Temp, Income, #of arrests, tons of garbage
interval scale
It describes the order and equal separation between two values. No negative values are involved, and the variables may be multiplied, divided, added and removed.
Examples: Height and weight
Ratio scale
Its uses statements with numerals in order to describe the data for the concrete information and expository form
Textual presentation
It uses statistical table to directly display the quantities or values collected as data.
Tabular presentation
It illustrates the data in a form of graphs. Types of graphs are bar graph, circle graph, line graph, and pictograph
Graphical presentation
ARRANGE THIS IN A RIGHT SEQUENCE
___ Set the lowest value as the first lower limit and get the upper limit which is equal to first lower limit + class size -1
___ Determine as to estimate number of classes k, k=1=3log n. Where n is the number of populations
___ Obtain the class size, c=r/k
___ Do the same process again until you reach the last class limit that includes the highest value from the data
___ Determine the range, r= highest values - lowest values
4, 1, 3, 5 , 2