Explain Rotational Symmetry

Introduction:

           The rotational symmetry is objects that look the same after a certain amount of rotation. A object may have more than 1 rotational symmetry for instance, if reflections or turning it over are not counted, the trickling appearing on the Isle of Man's flag (see opposite) has three rotational symmetries (or "a threefold rotational symmetry").

Key Factors of Rotational Symmetry:-

• The rotational symmetry is proportion with value to some or all rotations in m-dimensional Euclidean space.

• Rotations are through isometrics, i.e, isometrics preserve orientation.

• herefore a proportion group of revolving symmetry is a subgroup of E+ (m)

• Rotational symmetry by way of admiration to all rotations about all points implies translational regularity with respect to all translations, so space is all the same, and the rotational symmetry group is the whole E (m).

• The rotational symmetry through deference to any angle is, in two extents, circular symmetry. The basic domain is a half-line.

• That is, no dependence on the angle use cylindrical coordinate and no dependence on either angle using spherical coordinates.

• The basic sphere of influence is a half-plane from side to side the axis, and a radial half-line, correspondingly.

• Ax symmetric or ax regular are adjectives which refer to an object have cylindrical symmetry, or ax rotational symmetry.

• In mains, continue or separate rotational regularity about a plane correspond to correspond mains rotational symmetry in every perpendicular plane, about the point of intersection.

  Hope you liked the above explanation. Please leave your comments, if you have any doubts.

Common Data Representation

Introduction to Common Data Representation:

Representing a Numerical Data:
             A numerical data is a set of mathematical values which is used for measuring and counting and it can be represented by graphs(Pie-chart, bar graph). A numerical value is generally used for scaling purposes i.e. to find out the range, value ,mean and count of a particular object. We can even represent the data on number line based on the values. Depending on values we can represent data in statistical tables and can give ranks to the data, we can even find frequency distribution.
We can represent the Data by:
Pie Chart:

     Pie chart is a representation on a circle. Therefore its also known as "circle graph". The circle is divided into different partition depending on Category. It is one of the most common graphs for describing a set of measurements. It is the best graphical display for displaying data arranged in categories. Each category is represented by a wedge of the pie and the size of each wedge is in proportion to the percentage of each category.

Bar Graph:

     A bar graph consist two axes and a series of horizontal bars or vertical bars which are placed in the x ,y plane,depending on the value. It is another way of displaying qualitative data.The frequencies along the vertical axis (ordinate) of the chart and the categories on the horizontal axis of the chart(abscissa). Bar chart is used to display frequency and percentages.
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How to multiply decimals

Introduction to Multiplying decimals:

         A number that contains the decimal point is called as decimal. The decimal numbers are always has ten as its base value. In Hindu-Arabic numeric system, decimal notation refers the positional notation of the number. It can also used to refer the non-positional system in Roman and Chinese numerals. Decimals are always can be represented as another form of fractions.

Place Value:

       To know the decimals, we need to understand the place value. The value of a digit can be determined by its position in a number is called as place value. Each place in a decimal number has a different place value.

For Example, 25.64

Here 2-tens

         5-ones

         6-tenths

         4-Hundredths      

Multiplying Decimals:

Rules for multiplying Decimals:

• Multiply the numbers normally, ignoring the decimal points.

•  After multiplying normally, put the decimal point in the answer – The answer will have as many decimal places as the two given numbers combined.

 Consider the following Example,

              13.7* 12.5

Step1: Multiply normally by ignoring the decimal points

              137*

              125

             685

           274

         137 

        17125

How to find the Mean and Median of a data set

INTRODUCTION:

           A group of variables or a set of information is referred as Data. In general, sets are the collections of numbers and set can contains any kind of data. Data set is nothing but a collection of data. Data set can be represented as tables and graphs. Data collection is the method of collecting or preparing the data. For a given data set, we can find the mean, median, mode and range which is explained below.

Mean of data set:
         For finding the mean of all the values in a given data set, we have to find the sum of all numbers given in data set and we have to divide the total sum by the total number of elements.
Example:
Find the mean of data set: {8, 18, 23, 35, 51}
Solution:
         Mean      =    Total sum of data set  / Total number of elements in data set
                         =    (8 + 18 + 23 +  35 + 51) / 5
                         = 135 / 5   = 27
Median of a data set:
        In general, median is referred as the middle value of the given data set.
Example 1 :
Find the median for the given values: {5, 6, 9, 25, 34}
Solution:
      Here, the middle value is 9. Hence median = 9. 

How to translate word problems into algebraic expression

Introduction:

             Translating words into algebraic expression is the process of translating the word problems into an algebraic expression which can be used to solve the word problem and produce the solution for the given words problem. It is the simple way to solve words problem. Let us discuss about translating the words into algebraic expression.

Example problems to translating words into algebraic expression:

Problem 1:
Flowers shop has thirty Roses and forty Lilly. How many pieces of flowers does flowers shop have? 
Solution:
            Let a = Total number of Flowers in the flowers shop.
            The sum of thirty Roses and forty Lilly is equal to the total number of flowers in the flowers shop. It translates the words problem into an algebraic expression.
            a = 30 + 40
Solve this expression.
            Let a = Total number Pieces of Flowers in the flowers shop
                  a = 70.
There are 70 Pieces of Flowers in the flowers shop.

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Example on how to solve polynomial

Introduction:

          In math, variables and constants with the operations of addition, subtraction, multiplication, and non-negative, whole-number exponents of finite length is known as a polynomial or in-determinates. For example, x² − 4x + 7 is a polynomial, but x² − 4/x + 7x^3/2 is not, because its second term involves division by the variable x and because its third term contains an exponent that is not a whole number.

Example:

X²+4X-5=0,

                   X²-X+5X-5=0,

                   X(X-1) +5(X-1) =0,

                   (X-1)(X+5) =0.                         Therefore the roots are X =1, -5...

                       (OR)

USING THE FOMULAE:

                   X = ` (-B + sqrt (B^2 - 4AC))/(2A)`

                   X²+4X-5=0 -------------------> (2)

                    AX²+BX+C=0----------------> (3)

Comparing (2) and (3),

A = 1, B =4, C =-5 Substitute these values in one.

        x = `(-4 +- sqrt (4^2 - 4(1)(-5)))/(2(1))`

          x = `(-4 +- sqrt (16 +20))/(2)`

          x = `(-4 +- sqrt (36))/(2)`

         x = `(-4 +- 6)/(2)`

        x = `(-10)/(2)``(2)/(2)`

       x = -5, 1

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Numeric sequence and Types

Introduction:

The numeric sequence is called linear sequence. The numeric sequence are communicable to the constant rates of change and form the straight lines which is graphed.

        The numeric sequence are  15, 17, 19, 21, 23, 25… is a linear sequence that are represented in the table. The numeric sequence is used to draw graph, they provide straight line.

Example:

15, 17,19,21,23 this example numeric sequence the constant value  is 2.

Numeric Sequence Explanation and Types:

The numeric sequences contain any one number series. Some of then numeric sequences are given below.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ….etc the constant numeric sequences value is one

15, 17, 19, 21, 23, 25, 27, 29…..etc. the constant numeric sequences value is one

The above are simple explanation of the numeric sequence.

Different types of numeric sequences are :

• Arithmetic sequence
• Geometric sequence  
• Fibonacci Sequence