Define Convex Polygon

Author: mathqa22

In polygon comprise no reflex angle, followed in it is made-up to be a convex polygon. Polygon is a plane, that type to be restricted in a closed path, composed of a restricted series of directly line element by a closed polygonal series. Now we study about define convex polygon.

Using online polygon is a plane type to be restricted in a closed path, composed of a restricted series of directly line element by a closed polygonal series.

Define convex polygon:

A polygon is absolutely convex if every interior position is definitely less than 180 quantities. Commonly, a polygon is definitely convex if each line division by two noncontiguous vertices of the polygon is exactingly internal to the polygon however on its endpoints. Each non part triangle is definitely convex.

A polygon is a 2-dimensional instance of the more general polytope in several quantities of proportions. The internal of the polygon is recognized its group. These fraction are known its edges, with the points where two edges obtain together are the polygon's curve.

Commonly, a polygon is definitely convex if each line division by two noncontiguous vertices of the polygon is exactingly internal to the polygon however on its endpoints

Properties of convex polygon:

A convex polygon is an easy that's within is a convex set. The properties of an easy polygon are all equal to convexity:

Each one interior angle is less than 180 degree.

Each one line segment among two vertices remains inside or on the maximum of the polygon.

Examples for define convex polygon:

Example 1 for define convex polygon:

How to solve area of the polygon learning the sides are (6,3) (9,3)(7,5)

area of the polygon learning the sides are (6,3) (9,3)(7,5)

Solution:

Step 1: the given sides are (6,3) (9,3)(7,5)

Step 2: A =     1/2((x_1y_2-x_2y_1)+(x_2y_3-x_3y_2)+.......(x_ny_1-x_1y_n))

Step 3: x1=6, y1=3, x2=9, y2=3, x3=7, y3=5,

Step 4:     A =1/2(18+45+35)-(27+21+30)

Step 5:         so area is A =10

Example 2 for define convex polygon:

How to solve area of the polygon learning the sides are (7,2) (7,4) (6,5)

area of the polygon learning the sides are (7,2) (7,4) (6,5)

Solution:

Step 1: the given sides are (7,2) (7,4) (6,5)

Step 2: A =     1/2((x_1y_2-x_2y_1)+(x_2y_3-x_3y_2)+.......(x_ny_1-x_1y_n))

Step 3: x1=7, y1=2, x2=7, y2=4, x3=6, y3=5,

Step 4:      A =1/2(28+35+12)-(14+24+35)

Step 5: so area is A =1

Check this icse syllabus 2013 awesome i recently used to see.

Example 3 for define convex polygon:

How to solve area of the polygon and  prepare the sides are (7,6)(6,4)(6,2)

area of the polygon and prepare the sides are (7,6)(6,4)(6,2)

Solution:

Step 1: the given sides are (7,6)(6,4)(6,2)

Step 2: A = 1/2((x_1y_2-x_2y_1)+(x_2y_3-x_3y_2)+.......(x_ny_1-x_1y_n))

Step 3: x1=7, y1=6, x2=6, y2= 4, x3=6, y3=2,

Step 4:    A =1/2(28+12+36)-(36+24+14)

Step 5:         so area is A = 1

Normally in geometry polygon mean a plane figure which is closed by a line. Here we are going to learn about name of all polygons. We will name the polygons based on their number of sides. We will see the name of the polygons.  Totally we are having three types of polygons that are regular, irregular and equilateral polygons.

Name of all polygons:

Here we are going to name all the polygons based on their number of sides.

If any polygons having 3 sides we can say it is Triangle.

If a polygons with 4 sides we will say it is a Quadrilateral.

If a polygon is having 5 sides it is known as Pentagon.

If a polygon is having 6 sides it is known as Hexagon.

If a polygon is having the number of sides 7 then we can say it is Heptagon.

If any polygon is having the number of sides 8 then we can say it is Octagon.

If a polygon is having the number of sides 9 it is known as Enneagon or Nonagon.

If any polygon is having the number of sides 10 it is known as Decagon.

Name of all polygons: Sides above 10

If the number of sides is 11 then it is known as Hendecagon.

If the number of sides is 12 then it is known as Dodecagon.

If the number of sides is 13 then it is Tridecagon.

If the number of sides is 14 then it is known as Tetdradecagon.

If the number of sides is 15 is known as pentadecagon.

If the number of sides is 16 then it is known as Hexadecagon.

The number of sides of the polygon is 17 it is known as Heptadecagon.

The number of sides is 18 then we can say it is a Octadecagon.

The number of sides is 19 then we can say it is a Enneadecagon.

The number of sides is 20 then we can say it is a Icosagon.

Number of sidesName of the polygon

20Icosagon

30Triacontagon

40Tetracontagon

50Pentacontagon

60Hexacontagon

70Heptaconatagon

80Octacontagon

90Enneacontagon

100Hectagon

1000Chiliagon

10000Myriagon

1000000Hecatommyriagon

Article Source: http://www.articlesbase.com/k-12-education-articles/define-convex-polygon-6615656.html

About the Author

Learn more on about Online Volume Conversion and its Examples. Between, if you have problem on these topics Testing Bias, Please share your comments.

Polygon definition

Author: Matthew David

Introduction
Polygon

A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others. In geometry a polygon it can be traditionally a plane figure that is bounded by a closed path or circuit, composed of a finite sequence of straight line segments (i.e., by a closed polygonal chain). These segments are called its edges or sides, and the points where two edges meet are the polygon's vertices or corners.

In geometry a polygon  is usually a plane shape  that is bounded by a closed  circuit, composed of a finite sequence of straight line segments (i.e., by a closed polygonal chain). These segments are called edges or sides, and the points where two edges meet are the polygon's vertex or corners. A polygon is a 2-dimensional.Polygons is primarily classified by the number of sides.

Characteristics of Polygon

Convexity

Polygons may be characterized by their degree of convexity:

Convex: any line and it can be drawn through the polygon (and not tangent to an edge or corner) meets its boundary exactly twice.
Non-convex: a line may be found which meets its boundary more than twice.
Simple: the boundary of the polygon does not cross itself. All convex polygons are simple.
Concave: Non-convex and simple.
Star-shaped: the whole interior is the visible from and that is a single point, without crossing any edge. The polygon must be simple, and may be convex or concave.
Self-intersecting: the boundary of that  polygon crosses itself. Branko Grünbaum calls these Coptic, though this term does not seem to be widely used. The term complex is sometimes that can be used in contrast to simple, but this risks confusion with the idea of a complex polygon as one which exists in the complex Hilbert plane consisting of two complex dimensions.
Star polygon: it is a polygon which can be self-intersects in a regular way.

A digon is a closed polygon having two sides and two corners. On the sphere, we can mark two opposing points (like the North and South poles) and join them by half a great circle. Add another arc and it can be a different great circle and you have a digon. Regular Polygon Usually two edges meeting at a corner are required to form an angle that is not straight (180°); otherwise, the line segments will be considered parts of a single edge. A regular polygon is a polygon whose sides are all the same length, and whose angles are all the same. The sum of the angles of a polygon with n sides, where n is 3 or more, is 180° × (n - 2) degrees.

Special Nmaesof Polygons

Some polygons have special names and that are depending on the number of sides they have.



Number of sides              Name of polygon

3                            Triangle

4                            Quadrilateral

5                            Pentagon

6                            Hexagon

7                            Heptagon

8                            Octagon

9                            Nonagon

10                           Decagon

Classifying Polygons:

There are two categories of polygon. They are convex and concave. Polygons are also classified by the number of sides they have. The following list shows that the polygon name and number of sides they have.  

Triangle - three-sided polygon.

 Quadrilateral - four-sided polygon.

 Pentagon - five-sided polygon.

 Hexagon - six-sided polygon.

 septagon -seven-sided polygon.

 Octagon - eight-sided polygon.

 Nonagon - nine-sided polygon.

 Decagon - ten-sided polygon

Regular polygon:

A regular polygon is a polygon which has equal angles  and equilateral . Regular polygons may be convex or star.
Regular convex polygons:
1. Introduction to Square:

A square is one of the regular quadrilateral.  it has four equal sides and four equal angles .All angles are 90 degree .The total internal angles of square is 360 degree.

Square
2.Introduction to Equilateral triangle:

An equilateral triangle is one type of polygon.it has three sides.They are equal in length and the total internal angle of triangle is 180 degree.All the three angles are equal.(each 60 degree).

Equilateral triangle

3. Introduction to Pentagon:

The five sided polygon is known as pentagon. The sum of internal angle of a pentagon adds up to 540 degree. The all internal angles are equal( each 108 degree)

Pentagon
4.Introduction to Hexagon:

The six sided polygon is known as hexagon with equal length (regular hexagon).the sum of internal angle of a hexagon adds up to 720 degree. The all internal angles are equal (each 120 degree).

Hexagon

Article Source: http://www.articlesbase.com/k-12-education-articles/polygon-definition-6491446.html

About the Author

Between, if you have problem on these topics what are linear equations, please browse expert math related websites for more help on Area of a Triangle and different math topic.

Polygon Law Of Vectors

Author: johnharmer

Introduction to polygon law of vectors:

A vector is characterised by an absolute value(magnitude) and a direction. The vector, as a mathematical object, is defined as a directed line segment. Displacement, velocity acceleration, force momentum, angular momentum are a few examples of vector quantities.      A vector is geometrically represented by an arrow. Length of the arrow is proportional to the magnitude of the vector; head of the arrow gives the sense of direction. A displacement vector is represented as an arrow.In print a vector is represented by a single bold type letter such as d . The bold type letter signifies the properties, viz magnitude and the direction of the vector. In hand writing, an arrow is placed above the letter symbol like `veca` . If only magnitude of the vector is to be specified one has to write either  | `veca` |  or a; in print it is indicated as a.

Polygon law of vectors

If a number of vectors are represented as the sides of a polygon taken in order, the resultant is represented by the closing side of the polygon taken in the reverse order. In the case where number of forces act simultaneously at a point and keep it in equilibrium, this law states that, these forces can be represented as a sides of a polygon taken in order.

Polygon Law of Vectors

Vectors a,b,c,d,e,f are taken as the adjacent sides of the polygon; the vector shown with dashed line is taken in the reverse order to  represent the direction of the resultant ; its length is the magnitude of the resultant.

Other laws of vectors:

Triangle law :  If two vectors are represented by the sides of a triangle taken in order, the resultant (sum) of the vectors is given by closing side of the triangle taken in the reverse order.

Parallelogram law of vectors :  It two vectors are drawn from a point so as to represent the adjacent sides of a parallelogram both in magnitude and direction, the diagonal of the parallelogram drawn from the same point represents the resultant of the two vectors both in magnitude and direction.


Introduction to Orion Constellation

Orion is one of the most famous constellations in the night sky. As it is located on the celestial equator, it can be seen from anywhere in the world. The ancient Greeks imagined the constellation Orion as a hunter. The constellation formed its present configuration around 1.5 million years ago. However, as constellations are not physical groupings, but just apparent positions of stars as seen from earth, the constellation may change its shape over time.

The Orion Nebula and Horseshoe Nebula

The Orion Nebula:

The Orion Nebula is a beautiful deep sea object. It can be observed through a pair of binoculars, and it is made of heavy clouds which contain nascent stars, dust, and luminous gases.

The Horsehead Nebula:

The Orion constellation also has another famous deep sky object – the Horsehead Nebula. It has a dark dust cloud which is in the form of a horse's head.

The Orion Constellation : Features

The image shows the position of Orion in the night sky.

Orion constellation

The most striking feature is the 'Belt of Orion' which has the three bright stars Mintaka, Alnilam, and Alnitak in a row, Around the belt, there are four other bright stars, which are

Betelguese: This star serves as the "right shoulder" of Orion. It is a massive red supergiant star which is close to ending its life in a supernova explosion. This star is the second brightest in the constellation.
Rigel: This star serves as the "left foot" of Orion, and is a blue supergiant. This star is also close to ending the fusion stage of its life. It is the brightest star in Orion, and the sixth brightest star in the whole sky.
Bellatrix: Bellatrix is the 'left shoulder" of Orion. It is known as the "Amazon Star"
Salph: This is the "right foot" of Orion. The star emits radiation in the ultraviolet range and is quite faint when compared to the other stars From the belt of Orion, you can also see three smaller stars forming a line. This is known as the sword of Orion. The middle star in this line is not a star, but the Orion Nebula.

Article Source: http://www.articlesbase.com/k-12-education-articles/polygon-law-of-vectors-6618051.html

About the Author

Learn more on aboutLongitudinal Waves and its Examples. Between, if you have problem on these topics Magnetic Moment, please browse expert math related websites for more help.Please share your comment