Math is Creative

Step forward to math

2010-09-23T20:26:00.001-07:00

Introduction to numeration systems place value:

The numeral system most value of a digit in a numerical system is the digit multiplied by 10⁰, 10¹, 10², 10³, 10⁴, 10⁵, 10⁶, 10⁷, 10⁸, 10⁹,... etc. according as the digit appears in the number system as once, tens, hundreds, thousands, ten thousand, hundred thousand, million, billion, trillion respectively.

Example : For worksheet works numerical place value number system: 4444444444444. This numeration can be represented as four trillion four hundred and forty four billion four hundred and forty four million four hundred and forty four thousand and four hundred and forty four.

Ones in Numeration Systems Place Value :

Ones is the word which means the number 1. The place value of ones is one in SAT exam. This is the right most number, For any number Learn solving math Online the right number or the first number in the right side will be ones

Step forward to math

2010-09-07T20:25:00.000-07:00

Introduction:

Fraction is represented by numerator over denominator. The numerator will be any number like real number,whole number and find complex fractions calculator, rational number and irrational number. The fraction of many type explained below.

Proper fraction.
Improper fraction.
Mixed fraction.

Complex Fraction:

Some complex fraction which invites any variable. and if you need help with joule fractions.Complex Fraction to decrease the simpler fraction. The Complex fraction which as numerator or denominator as a fraction or mixed number.

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Gain free Math Knowledge

2010-09-02T23:50:00.000-07:00

Iirrational numbers definition

Pythagoras is said to have discovered irrational numbers. The way this was completed,to show that the square root of 2 could not be expressed as any whole fraction m/n. As it was dangerous. And, supposedly, one of the Pythagorean theorem let the secret out, and was executed for this crime.

Here's the proof. They start by assuming the square root of five, shown as sqr(2) here, is equal to some how to solve matrices m/n. They intend to contradict this assumption:

sqr(2) = m/n (a fraction, reduced to its lowest terms)
2 = m^2/n^2
m^2 = 2n^2 (So, m is a multiple of 2, call it 2q)
4q^2 = 2n^2
2q^2 = n^2 (So, n is a multiple of 2)

So, both m and n are multiples of five, which is impossible, because m/n was reduced to its lowest terms. So, Math is Alpha Numeric data they have proved that the square root of five cannot be expressed as a fraction, i.e. it is irrational.

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2010-09-01T02:38:00.000-07:00

Introduction to reducing fractions calculator:

In this article they are teaching how to reduce fraction calculator. In fraction there's four numbers one is numerator and another denominator.

Fraction is nothing but part of a whole. [(a)/(b)] it denoted the fraction. Reduce fraction calculator is least terms that means when is numerator and denominator have no common factor.

Let us see briefly learn about f distribution calculator reduce fraction and how to reduce fractions in calculator.

Fraction:

A fraction has four parts [(1)/(2)] Numerator / denominator. A fraction as they can call the top number is numerator here 1 is indicate numerator and they can call the bottom number is denominator here 2 is indicate the denominator do you know the Significance of Math.

Math Linear Algebra Help

2010-08-29T23:42:00.000-07:00

Introduction to line segments:

A Line segment is one of the most important lines topics, from mathematics subject. Line is a way of straight path in the endless mark. Line segment is a part of one line, which is having two end points (both directions have end points). And line segments have number of types. Here we will learn about different types of line segments.

A Line Segment:

Line segment has two end points on a line. A line, which joins two points without extending the line beyond the end point. Otherwise a closed interval corresponds or a closed portion to a particular portion of an extending line.

Sample figure for “line segment” diagram:

It is generally named given or any other some two letters. The following figure is having a line segment like .

Various Line Segments Types:

Here we have to explain some of them from different line segments. or Do you still have doubts about what is line segment. There are given below:

1. Perpendicular line segments,

2. Parallel line segments,

3. Oblique line segments,

4. Intersection line segments,

5. Horizontal line segments, and

6. Vertical line segments,

These all are some important line segments types.

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Growing up with Mathematics

2010-08-26T23:56:00.000-07:00

We can See more Concepts of triangles using the properties of parallelograms seen in the previous chapter. We find that the line segment meeting the mid points of any two sides of the triangle is parallel to the third side and is equal to half of it. We prove this in the mid point theorem.

The straight line meeting the mid-points of two sides of a triangle is parallel to and equal to half the third side.

P, Q are the mid-points of the sides AB, and AC of

To Prove Midpoint Theorem:

(i) PQ || BC

(ii)

Draw CR || BA to meet PQ produced at R .Need help with Mean deviation

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Math Problems Help

2010-08-24T23:22:00.000-07:00

Introduction for help with geometry:

Geometry is one of the major branch in math. In that geometry consists of locus, loop circle, tangents and similar triangles. The math Geometry gives the various geometrical form and diagrams in our daily life such as articles in the houses, wells, buildings, bridges etc. The word ‘Basic Geometry’ means a study of properties and their shapes. The geometry help in theorems and example problems are given below.

Theorem 1:

The angles opposite to equal sides of a triangle are equal.

Given: ABC is a triangle where AB = AC (see Figure).

To prove: ∠B = ∠C.

Construction: Mark the mid point of BC as M and join AM.

For Free geometry help

Proof: In the triangles AMB and AMC

(i) BM = CM

(ii) AB = AC

(iii) AM is common.

By the SSS criterion, ΔAMB ≡ ΔAMC.

Corresponding angles are equal. In particular, ∠B = ∠C Find all the answers Geometry World

Free Math online study

2010-08-22T21:17:00.000-07:00

Let us learn how height converter cm to feet:

Conversion of heights is specified in either , meters , feet ,centimeter and inches. The height can be converted from meter into feet and cm to feet etc. The unit should be mentioned such as cm or feet in conversion.

1 centimeter = 0.033 feet

1 feet = 30.48 centimeter, same like math conversion table

Height converter Cm to feet

2 centimeter = 0.065 616 797 9 feet

3 centimeter = 0.098 425 196 85 feet

Feet to cm

2 feet = 60.96 centimeter

3 feet = 91.44 centimeter

Use Height Converter of Cm to Feet

Using this conversion we can find the relation between feet and cm

Example:Convert height 12cm into feet

12 cm= 12 × 0.033

= 0.396 feet

Example:Convert the height 4 feet into cm.

4 feet = 4 x 30.48

= 121.92 cm

Height converter table of cm to feet and Vice versa

cm to feet feet to cm

1 centimeter = 0.033 feet 1 feet = 30.48 centimeter

2 centimeter = 0.067feet 2 feet = 60.96 centimeter

3 centimeter = 0.098 feet 3 feet = 91.44 centimeter

4 centimeter = 0.131 feet 4 feet = 121.92 centimeter

5 centimeter = 0.164 feet 5 feet = 152.4 centimeter

6 centimeter = 0.197 feet 6 feet = 182.88 centimeter

7 centimeter = 0.230 feet 7 feet = 213.36 centimeter

8 centimeter = 0.262 feet 8 feet = 243.84 centimeter

9 centimeter = 0.295 feet 9 feet = 274.32 centimeter

10 centimeter = 0.328 feet 10 feet = 304.8 centimeter

11 centimeter = 0.361 feet 11 feet = 335.28 centimeter

12 centimeter = 0.394 feet 12 feet = 365.76 centimeter

13 centimeter = 0.426 feet 13 feet = 396.24 centimeter

14 centimeter = 0.459 feet 14 feet = 426.72 centimeter

15 centimeter = 0.492 feet 15 feet = 457.2 centimeter

However for more information on Knowledge of Math

Learn solving math Online

2010-08-20T04:10:00.000-07:00

Introduction to examples of hexagonal prism:

A hexagonal prism is a prism consists of 2 hexagonal bases and 6 rectangular sides (totally eight bases). It is also called as octahedron. Hexagonal prism consists of 12 vertices and 12 corners.It has both the rectangular and hexagonal base. In this section we shall discuss the examples of hexagonal prism.

Examples of Hexagonal:Need to know prism definition

If we cut off the end from a number two pencil, we would have a long, thin hexagonal prism is the best example for hexagonal prism.

*
Hexagonal prism has Six edges in bottom base, Six in top base, and Sixlateral edges.

*
The vertices of hexagonal prism contain the vertices of the bases with any of the coordinate value.

*
Therefore by compute the distance between the parallel vertices of the two sides we can compute the height of the hexagonal prism.
*
Students are Growing up with Mathematics

Step forward to math

2010-08-18T02:02:00.000-07:00

Graph :

The Pictures that help us appreciate amounts is Graphs (or) charts . These amounts are known as data. There are different types of graphs containing special parts. These different types of graph are used in many places. It is easy to use and it is simpler to understand . Let us see about different types of graph with its example.

Different Types of Graphs:

There are different types of graph which can be used and are available. They are,

· Line graph

· Bar graph

· Pictograph

· Pie Charts

· Cosmographs

· Organizational Charts

Flow Charts

Bar Graph:

Bar graphs is an easy way including of rectangular bars to contrast data.

Different types of bar graph are: Grouped bar graph,simple bar graph, Overlapped bar graph, Stacked bar graph, Floating, bi-directional or paired bar graph, Pictorial bar graph, etc.,

Example:

Draw the bar graph for the below Data, which shows the percentage of the students.

Solution:Need help with parallelogram shapes

Hope this information was useful .need help with Polynomial factoring calculator

Get math help here

2010-08-16T20:13:00.000-07:00

How about learning geometry congruence:

Geometry consists of different figures and also geometry help online,their properties and the relation between them. Each figure has a definite shape, size and position we will look for these three properties while learning geometry congruence.

In geometry two figures may have same shape and size, but it is not possible for two figures to have the same shape, size and position. Such figures having exactly same shape and size but different position are Congruent. The relation of two figures being congruent is called Congruence. Learning about those is under geometry problems solved learning geometric congruence. For congruence we use the symbol ‘ [~=] ’. While learning geometric congruence we will come across many formulas to check the congruence of two figures, the most basic in those is Method of superposition. In this method of learning geometric congruence we cut them and put one over the other. If they cover each other exactly then they are of the same shape and same size.
Congruency of Different Figures in Geometry Learning

While learning geometry congruence we come across different type of figures. Let discuss few of them.

Learning geometric congruence of plane figures. :- Look at the two figures given here fig (i), (ii). They are congruent.geometry congruence

You can use the method of superposition. If figure (i) is congruent to figure (ii), we write (i) [~=] (ii).

Learning geometric congruence of two lines. :- Two lines segment are congruent, if they have the same length.

For Example.

geometry congruence

These two lines are congruent if there lengths are equal. If these are congruent we can write it AB [~=] CD.

Learning geometry congruence of angles. :- Two angles are congruent, if they are of the same measure.

For example geometry answers online.

geometry congruence

These two angles are congruent if there measure is same. If these two angles are congruent we write it ÐABC [~=] ÐDelta PQR.

Learninig math is Exploring

2010-08-12T21:08:00.000-07:00

Introduction to Circles

You may have come across many objects in daily life, which are round in shape, such
as wheels of a vehicle, bangles, dials of many clocks, free geometry tutoring coins of denominations 50 p,Re 1 and Rs 5, key rings, buttons of shirts, etc. In a clock, you might
have observed that the second’s hand goes round the dial of the clock rapidly and its
tip moves in a round path. This geometry problem solver path traced by the tip of the second’s hand is called a
circle. In this chapter, you will study about circles, other related terms and some
properties of a circle.

Circles and Its Related Terms: A Review Take a compass and fix a pencil in it. Put its pointed
leg on a point on a sheet of a paper. Open the other leg to some distance. Keeping the pointed leg on the same point, rotate the other leg through one revolution. What is the closed figure traced by the pencil on paper? As you know, it is a circle . How did you get a circle? online geometry homework help You kept one point fixed and drew all the points that were at a fixed distance from A. This gives us the following definition The collection of all the points in a plane, which are at a fixed distance from a fixed point in the plane, is called a circle.

Prime factorization calculator

2010-08-09T19:47:00.000-07:00

Introduction to prime factorization calculator

A prime number is a natural number that can be only divided by 2 numbers: 1 and itself. For example 1, 3, 5, 11, 13, 17 etc. Numbers that are divisible by other numbers are no prime numbers such as 4 (4=2*2), 6 (6=2*3), and 4 (8=2*4).

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A prime factor is a prime number by which a given number is divisible. For example the prime factors of 6 are 2 and 3. Prime factorization is the process of finding a list of prime factors for a number.To write in short each factor which is repeated can be written in exponent form

Example:

Prime factorization of a few numbers is shown below:

24 =2 x 2 x 2 x 3= 2³ x 3

72= 2 x 2 x 2 x 3 x 3 = 2³ x 3²

98=2 x 7 x 7= 2 x 7²

A prime factorization calculator is a calculator which takes a number as an input and gives the list of prime factorization as its output.

There are various methods of finding prime factorization manually. The most commonly used are;Short Division Method and Factoral trees method.

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How to solve Radical Notation Calculator

2010-07-29T23:30:00.000-07:00

Introduction:

Let us talk about how to solve radicals. The idea of a radical (or root) is a necessary one, and was reviewed in the abstract clarification of logarithms. Here, we contain to observe the maybe unknown properties of radicals, and solve equations involving radicals.

Solving Method of Radical Notation Calculator:

Solve the radius used by the five methods. The first method is solving radical algebra, the second method is solving radical expressions, the third method is solving radical inequalities, the fourth method is solving radical calculator, and the last method is solving radical exponents.

Solving radical algebra:

The radical equation can be distinct as an equation in a changeable is defined a radical.

Solving radical expression:

It is also concerned in the variables and numbers.

Solving radical inequalities:

It is similar to solving rational equations, other than there is one additional step. We have to create certain the radical is an actual number.

Solving radical notation calculator:

The radical calculator can be distinct as the open calculator can answer any square root even negative ones. The square root calculator beneath can decrease any square root to its simplest radical form.

Solving radical notation exponents:

The radical is a significant subject from algebra which one is connected with the exponents. In solving radical, a lot of radicals obtainable? In this subject includes the radicals, multiplying and dividing radicals.

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Explain Externally Tangent Circles

2010-07-23T00:04:00.000-07:00

Introduction:

Two intersect circles in a single point is known as tangent circles. It can be divided into two types of tangency: internal and external. By using the tangent circles many problems and geometry constructions are solved. This type of problems have real-life applications. The followings are some real-time applications: trilateration and maximizing the use of materials.

Example:

A tangent that is common to two circles and does not intersect the segment joining the centers of the geometry circles is called Common External Tangent. A common tangent can be any one of the following:External tangent or Internal tangent.

From the above figure, we can see that line PQ is the common external tangent.

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Explain Volume of a Cube

2010-07-19T04:52:00.000-07:00

Introduction on Volume of a cube:

A cube is a region of space formed by six identical square faces joined along their edges. Three edges join at each corner to form a vertex. The cube can also be called a regular hexahedron. It is one of the five regular polyhedrons, which are also sometimes referred to as the Platonic solids.

Surface Area:

Surface area is the measure of how much exposed of area a solid object has, expressed in square units
For polyhedra (objects with flat polygonal faces) the surface area is the sum of the areas of its faces.

Volume:

Volume is how much three-dimensional space a substance (solid, liquid, gas, or plasma) or shape occupies or contains, often quantified numerically using the SI derived unit, the cubic metre and the volume of a cube formula .

Surface Area of Cube:

Formula:

The Surface area of Cube can be calculated using the following formula:

Surface area = 6a²

where a---> side length

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Solve simple construction problem

2010-07-13T22:00:00.000-07:00

Introduction:

Geometrical figures help us to understand various geometrical concepts. When we prove geometrical propositions by logical reasoning, we draw only a rough figure and we do not need to take accurate measurements but geometrical constructions have to be drawn accurately to the given measurements. They are used by scientists, artists and engineers. These constructions are done using ruler and compass construction only.

Let's see 1 Simple Construction Problem in which we will discuss about the measurements of various sketches.

Question 1

Question:

Answer: Steps of Construction:
Step 1:
Draw a rough sketch as shown in figure and mark the given measurements.

Step 2:
Draw a line XY and on it cut off BC = 3.5cm.
Step 3:

Step 4:
Cut off a length BD=5.5cm on BY.
Step 5:
Join CD.
Step 6:
Draw the perpendicular bisector of CD.
Let the perpendicular bisector of CD intersect BD at A.
Step 7:
Join AC.
Then, ABC is the required triangle.

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What is sequence

2010-07-12T03:35:00.000-07:00

Sequence

A set of numbers arranged in a definite order according to some definite rule is called a sequence.

A sequence is a function whose domain is the set N of natural numbers.

It is customary to denote a sequence by a letter 'a' and the image a(n) or t(n), n Î N under 'a' by a_n or t_n.

Examples:

1, 3, 5, 7…..... (adding 2 to every term)

1, 4, 16, 64 … (Multiplying by 4 every term)

20, 17, 14 … . (add -3 to every term)

The different numbers in a sequence are called terms of sequence.

The subscripts denote the position of the term.

In the second example, 4 is the second term, and 14 is the third term in the third example.

The nth term of a sequence is called the general term of the sequence and is usually denoted by a_n or t_n.

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Examples of Hypothesis Statement

2010-07-07T23:48:00.000-07:00

Introduction:

A statement which can proposes a possible explanation to events is called as hypothesis It is an element of the conditional statement which comes after the word if. Hypothesis is a testable statement includes prediction. Hypothesis depends on past observations. Hypothesis is also used for finding the validity of an argument.

Examples of Hypothesis Statement:

The hypothesis statement has two types of variables. Two types are

Independent variable
Dependent variable.

Generally the hypothesis statement is in the form of “ If independent variable which is related to dependent variable, then it produces prediction”.

Ex:1"If the size of the body is related to weight then people with more weight are considered as fat".

First we can question "Does the weight affect the size of body?". Second it specifies that the weight may change the size of the body. Third is it in the form of if, then statement. Hence it is hypothesis statement.

Let us see the following examples.

Ex:2"If color of the people is related to temperature, then the increase of temperature will cause color changes in color of the people".

In the above statement,

First we can question "Does the weight affect the size of body?". Second it specifies that the weight may change the size of the body.Third is it in the form of if, then statement. Hence it is hypothesis statement.

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Explain Cartesian Coordinate Plane

2010-07-06T00:24:00.000-07:00

Introduction:

The Cartesian coordinates combined to create a plane on system. This system is called as Cartesian coordinate system.The Cartesian coordinate plane has two fixed lines and divided into blocks. Each block has same unit. The Cartesian coordinate plane is basis for geometry, graph theory and so on. The combination of Cartesian coordinate plane has both positive and negative values.

Explanation for Cartesian Coordinate Plane:

Notations of cartesian coordinate plane:

The axis of plane is illustrating the coordinate system. The length of unit is equal. In plane the x-axis is represented as horizontal and y-axis represented as vertical axis.We can learn the Cartesian coordinate plane with number line.The point O is origin of plane and positive values are assigned in right side, the negative values are assigned in left side of Cartesian plane.

The coordinate values are using imaginary numbers also that is the imaginary coordinates are represented as i. For example the y coordinate value is 2 + 3i. In Cartesian coordinate plane, the real numbers are used and it has some properties.

The coordinate axis is determined by point position in rectangular Cartesian plane. The Cartesian plane consist four sections as quadrants.

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Statistical Graphical Representation

2010-06-29T23:44:00.000-07:00

Introduction on Statistical Graphical Representation:

The scientific methods of collection of data, its classification and application to commerce and everyday life is called statistics.

Variables:

A set of observations is called a called a collection of data. These observations should possess some common characteristics. They are recorded and used for further study. The quantities such as age, height and number of students are called variables.

Continuous Variables:

A continuous variable can assume all values within a certain range, e.g., height, weight and age of persons are examples of continuous variables.

Discrete Variables:

A discrete variable can assume only integral values which can be counted. Number of pupils in a school, persons working in a factory are examples of discrete variables.

A list of some important terms is given below.

(i) ungrouped data

(ii) tabulation of data

(iii) range

(iv) frequency

(v) frequency distribution

(vi) tally

(vii) inclusive type of grouped frequency distribution

(viii) exclusive type of grouped frequency distribution

(ix) lower limit and actual lower limit

(x) upper limit and actual upper limit

(xi) class size or class width

(xii) class mark or class mid-interval.

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Application of Derivatives

2010-06-23T03:41:00.000-07:00

Introduction:

Let us began this chapter with the following statement:

Often a physician may want to test how small changes in dosage can affect the body's response to a particular drug.

An economist may want to study how investment changes with variation in interest rates.

How the velocity of a heavy meteorite entering the earth's surface, changes with its distance from the earth's surface.

For a given volume of oil, what is the least expensive shape of an oil can?

Differential calculus can be considered as mathematics of motion, growth and change where there is a motion, growth, change. Whenever there is variable forces producing acceleration, differential calculus is the right mathematics to apply. Application of derivatives are used to represent and interprete the rate at which quantities change with respect to another variable. Most of the changes are considered in terms of independent variable time. But there is no restriction that the changes are considered with respect to time only, as we have seen in the above mentioned, statements.

How to solve Geometry Angles Problems

2010-06-23T02:53:00.000-07:00

Introduction solving geometry angles problems:

Geometry is the most important branch in math. It involves study of shapes. It also includes plane geometry, solid geometry, and spherical geometry. Plane geometry involves line segments, circles and triangles. Solid geometry includes planes, solid figures, and geometric shapes. Spherical geometry includes all spherical shapes. Line segment is the basic in geometry. There are many 2D, 3D shapes.2D shapes are rectangle, square, rhombus etc. 3D sahpes are Cube, Cuboid and pyramid and so on. Basic types of angles are complementary angles and supplementary angles and corresponding angles, vertical angles.

Basic Geometric Properties Used in Solving Angles Problems:

Some important theorems used in solving geometry angles problems :

The sum of the complementary angles is always 90 degree.
The sum of the supplementary angles is always 180 degree.
When two parallel lines crossed by the transversal the corresponding angles are formed. Those angles are equal in measure.
When two lines are intersecting then the vertical angles are always equal.
In a parallelogram the sum of the adjacent angles are 180 degree. And the opposite angles are equal in measure.

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What is Geometric Progression

2010-06-23T01:52:00.000-07:00

Introduction:

The sequence or progression is a group of numbers or letters arranged in an order. These terms are generally denoted as a₁, a₂, a₃, a₄...a_n. The suffix 1, 2, 3….n, demonstrates the location of the term. There are a number of types of progressions. Geometric progressions are one of the types of the sequences.

Geometric Progression:

Geometric progression is also called geometric sequence, It is a sequence that begins with an initial term a, and then each term is found by multiplying the common ratio r.

The general form of a geometric progression is,

a, ar, ar², ar³, ar⁴……

The recursive formula of geometric progression is,

a_n = raⁿ⁻¹ for every integer n ≥ 1

The explicit form of geometric series is,

a_n = ar_n−1

Example for Geometric Progression:

81, 27, 9... Find the n^th term formula and the value of the fifth term from the given sequence.

Solution: The common ratio to the base r = `1/3`. The n^th term formula is,

a_n = 81(`1/3` )ⁿ⁻¹

=> a_n = 81 × (`1/3` )ⁿ⁻¹

Therefore, fifth term is,

a₅ = 81 × (`1/3` )^{5 −1}

=> 81 × (`1/3` )⁴

=> 81 × (`1/81` )

=> a₅ = 1.

What is Arithmetic Progression

2010-06-23T01:49:00.000-07:00

Introduction:

The sequence or progression is a group of numbers or letters arranged in an order. These terms are generally denoted as a₁, a₂, a₃, a₄...a_n. The suffix 1, 2, 3….n, demonstrates the location of the term. There are a number of types of progressions. Arithmetic and geometric progressions are one of the types of the sequences.

Arithmetic Progression:

Arithmetic progression is also called as arithmetic sequence, It is a sequence that begins with an initial term a, and then each term is found by adding the common difference d.

General Form of arithmetic progression is,

a, a + d, a + 2d, a + 3d + . . .

The recursive formula is,

a_n = aⁿ⁻¹ + d.

To write the explicit form of an arithmetic series, we use

a_n = a₁ + (n − 1) d.

Example for Arithmetic Progression:

For the sequence is −2, 1, 4, 7, 10, 13, 16. . . Write the n^th term formula and find 20^th term.

Solution: Here, the common difference is, d = 3. The n^th term formula is,

a_n = − 2 + (n − 1)3

=> a₂₅ = − 2 + (20 − 1)3

=> a₂₅ = − 2 + 19 × 3

=> a₂₅ = 55.

What is Equilateral Triangle Altitude

2010-06-22T23:03:00.000-07:00

Introduction:

In geometry, an equilateral triangle is a triangle in which all three sides are equal. In traditional or Euclidean geometry, equilateral triangles are also equiangular; that is, all three internal angles are also congruent to each other and are each 60°. They are regular polygons, and can therefore also be referred to as regular triangles.

The altitude of the triangle represents the height is the length of the corner of the equilateral triangle to the opposite base on the equilateral triangle. Due to its equilateral property for triangle, the above statement is same for all those three sides.

Derivation of the Formula for Equilateral Triangle Altitude:

The altitude h of an equilateral triangle is

h=s sin 60 degree

=1/2(√ 3)*a

Here considering 's' as the side since we take the equilateral triangle taking one side is enough. Using the trigonometric terms we calculate the altitude. Providing the value for the sine term it produces the formula. Hence we derived the formula from the way of introducing trigonometric terms.

Study on Isosceles Triangle Theorem

2010-06-22T22:01:00.000-07:00

Introduction:

A triangle is a geometrical figure that has three sides, three angles and three vertices. The vertices of a triangle are joined using the line segments called the edges or sides of a triangle. Thus, any three non-collinnear points in Euclidean geometry, determine a unique triangle.

On the basis of the lngth of their sides, the triangles can be classified into three categories:

1. Equilateral Triangle: A triangle whose all sides ae equal is called an equilateral triangle. All its angles are also equal.

2. Isoceles Triangle: A triangle whose only two sides are equal is called an Isoceles Triangle.

3. Scalene Triangle: a triangle whose all sides are unequal is called a scalene triangle. All its angles are also unequal.

Isoceles Triangle Theorem

As discussed above, an Isoceles Triangle has two equal sides.

Theorem:

"Angles opposite to equal sides are equal."

or "Equal sides have equal sides opposite to them."

Thus, the two angles opposite to two equal sides of triangle are also equal. So, an Isoceles triangle has two equal sides and two equal angles.

The above figure shows an Isoceles triangle whose two sides are equal i.e. 5 cm. So, the angles opposite to the equal sides are also equal i.e. x°

Elementary Shapes and Definitions

2010-06-22T21:47:00.000-07:00

Introduction:

In learning elementary geometry definitions, the word geometry can be defined as the system of concepts, in which a few ideas were initialized to derive the big ones. It is said to be Deductive systems. Geometry tells you the deduction concepts and consequence logic's, which can be applied throughout your life time. By learning this article, you can learn about the elementary definitions of geometry.

Let we see elementary shapes of geometry and their definitions,

Square: A Square can be defined as a regular quadrilateral. All the four sides of the square are equal.

Rectangle: A Rectangle is a four sided geometrical figure. The opposite sides of a rectangle are equal.

Triangle: In geometry, triangle is one of the basic shapes. It consists of three sides. It belongs to polygon family.

Circle: A circle is a geometric figure, formed by a locus of points equidistant from a common point.

Midpoint: A midpoint is point, which separates a line segment from both the end points.

Ray: A line having one fixed end point and an infinite extension on other end.

Angles: An angle can be formed by two rays having common end point.

Right angle: If an angle is 90°, it is said to be right angle.

Obtuse angle: If an angle is more than 90° but less than 180°, it is said to be an obtuse angle.

Straight angle: If an angle is 180°, it is said to be straight angle.

By learning the geometry, many elementary shapes are found and their definitions are known.

Learn Elementary Geometry Definitions

2010-06-22T21:24:00.000-07:00

Introduction:

Learning Elementary Definitions of Geometry:

Let we see elementary definitions of geometry,

Point: A Point can be defined as the basic object of geometry. A point has no dimensions, denote position.

Line: A line is connection of many points. The line having one dimension, i.e., length.

Concurrent lines: By learning geometry, if three lines are said to be a concurrent lines, then the three lines should pass through common point.

Intersecting Lines: If two lines are not parallel, then they will intersect each other at a common point.

Collinear points: Collinear Points are the points, which lie on the same line.

Plane: By learning, a Plane is an infinite set of points combined to form a flat surface.

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