Glass Painting

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What is Glass Painting?

Glass painting is a contemporary art which has been derived from the age old art of stained glass painting which involves putting smaller coloured pieces of glass together. It was a common feature in high windows and doors etc in the olden times and can still be seen in churches and old buildings. These days glass painting is becoming a popular feature and catching up as a hobby due to its awesome results and easy availability of glass painting equipment. Many companies launch glass painting ideas for hobbies. They can have different levels like beginners, which is basically for experimental purpose for children. At home (as a hobby), glass paintings can be as wall hangings, wine glasses painting, on windows, acrylic sheets, cups, mugs, tiles, mirrors etc.
glass painting image, patterns,outline wikipedia
Glass Painting Craft

If you are interested in glass painting and want to try it, go ahead and experience the joy! All you need is a glass piece, sheet of paper of almost same size as that of the glass sheet, glass paints, an outliner, a design, silver foil (if required) and some amount of patience. Water based acrylic glass paints are readily available in market. They are ready to use, convenient and suitable for beginners. Do not be afraid of mistakes as they can be removed after the painting has dried. This can be done for the outliner and paint, both. They can be carefully scraped off with a paper knife etc. But this has to be done very carefully as it can also put scratches on the glass. Cotton can also be used to wipe off the wet paint or outliner in case of a mistake. The most common and easiest glass paintings designs are that of peacocks, floral, marine life etc. These days stencils are also available, so if you are not too confident about your drawing, you can take their help.

Glass paintings look most beautiful when illuminated by sunlight. The sun rays going through the transparent coloured glass gives it a glow that no other artificial light can give. It looks simply awesome!(however, too much exposure can sometimes result into fading of colours). Some glass paintings are framed with silver foil to reflect light to create a similar effect. This technique can be used when it is not possible to expose the painting to required amount of light.

marine life glass painting, fish glass painting
Marine Life Glass Painting

So what are you waiting for???? Go and get your glass painting kit today and start exploring the world of this art and gear up for a journey filled with joy.... Happy painting :)

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Next we will discuss :- 
Steps and techniques of glass painting and
Tips on glass painting

Read More :
Introduction to Origami, a paper folding art
Instructions to make a origami paper plane
Tips for making perfect origami product

FaceBook Poke & Poke War

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What is Poke in Facebook ? What does poking mean on facebook?

Facebook is one of the largest social networking sites at present on internet. As you login to facebook, you connect yourself to a network of over six hundred million registered users all over the world. 'Poke' is one of the common terms in facebook terminology.

A Poke is like a nudge, which a friend gives you, to grab your attention. Poke on Facebook is just a casual gesture which means "I am thinking of you" or a simple "Hello". Although the meaning of the facebook poke can be interpreted variedly, it can also be done to irritate your enemies too. Some people use it to flirt with people they don't know, but have some common friends. Facebook lets you know if someone has poked you by displaying the poke symbol on the right side of your Home page. There is an option to poke back that person too.

How to Poke someone on Facebook?

Trying to grab attention of your girlfriend or boyfriend, but have nothing to say? Don't know what to do now? Just Poke her/him. To poke someone you just need to go to their profile page and press the Poke button on the top right hand side. Don't worry, only the person whom you have poked will get to know about it. You can poke only a "friend" or "friend of a friend".

What is Poke War on Facebook?

When you get a poke from friend, you have two options: either remove the poke or poke back (though it is considered rude if you don't poke back). Now if you choose to poke back and the original person pokes you again, a Poke War starts. This back and forth poking on facebook is Poke war. I know it sounds lame but people do enjoy it. Now the question that arises here is, when does a Poke war end ? Well, it never ends, it continues until one of the parties decides to stop poking. The person who gives-up is said to have lost the Poke War. So probably the best question to ask your friend after first poke is "Are you going to poke me Again?" Read Grievances of A Software (Just 4 Fun)


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Read More:-
How to Prove that you are not a liar
Summer Solstice in Northern Hemisphere
List of Famous Advertising Slogans
Promises - meant to be broken or for the keeps?

Numbers and Their Types in Mathematics

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What are numbers in Math ?

A number is a mathematical tool which is used in counting individual quantities, calculating and quantifying. In general, decimal number system is used which consists of 10 digits, from 0 to 9.

What are various operations that can be performed on numbers?


Arithmetic operations used on numbers
•  Addition: It is the process of finding out single number or fraction equal to two or more quantities taken together.
•  Subtraction: It is the process of finding out the quantity left when a smaller quantity (number/ fraction) is reduced from a larger one.
•  Multiplication: It signifies repeated addition. If a number has to be repeatedly added then that number is multiplicand. The number of multiplicands considered for addition is multiplier. The sum of the repetition is the product.
•  Division: It is a reversal of multiplication. In this we find how often a given number called divisor is contained in another given number called dividend. The number expressing this is called the quotient and the excess of the dividend over the product of the divisor and quotient is called remainder.

Now lets discuss how Classification of Numbers is done.
classification of numbers, types of numbers, number system wikipedia
Types (classification) of  numbers

What are different types of numbers in mathematics?

Classification of numbers:
•  Real numbers: Numbers which can be quantified and represented by a unique point on the number line are called real numbers.
•  Complex numbers: Complex numbers are the numbers which have both real and imaginary part.
•  Rational numbers: Numbers of the form p/q, where p and q are integers and q≠0 are called rational numbers.
•  Irrational numbers: Numbers which are not rational but can be represented on the number line are called irrational numbers.
•  Integers: Rational numbers of the form p/q, where p and q are integers and q= ±1 are called integers.
•  Fractions : Fractions are a type of rational numbers, which are of the form p/q, where p and q are integers and q≠0 and whose numerator is less than the denominator and both are in the lowest terms.
•  Whole numbers: Whole numbers are the set of positive integers from 0. They do not have any decimal or fractional part.
•  Negative integers: Negative integers are the set of negative numbers before 0. They do not have any fractional or decimal part.
•  Natural numbers: Natural numbers are the set of positive integers, that is, integers from 1 to ∞, excluding fractional n decimal part. They are whole numbers excluding zero.
• Even numbers: Numbers divisible by 2 are called even numbers.
• Odd numbers: Numbers which are not divisible by 2 are called odd numbers. Odd numbers leave 1 as the remainder when divided by 2.
• Prime numbers: Any number other than 1 which does not have any factor apart from one and the number itself is called a prime number.
•  Co-prime/relatively prime numbers: Two numbers are said to be co-prime or relatively prime if they do not have any common factor other than one.
•  Composite numbers: a number that has more than two distinct factors is called a composite number.
•  Perfect numbers: A number is said to be a perfect number if the sum of all its factors, excluding itself (but including 1) is equal to the number itself.

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Client Server Network : Advantages and Disadvantages

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What are the advantages and disadvantages of client-server networking ?

Earlier we saw what is a client/server architecture? and its main difference from peer to peer network, i.e. in client server there was one powerful computer (known as server) which acts as a provider of information to other sub-ordinate workstations (called client). Now Let us discuss the benefits and drawbacks of Server-Client computing over P2P computing :-

Advantages of Client Server Networks over Peer to Peer Networks

1)  Centralization : Unlike P2P, where there is no central administration, here in this architecture there is a centralized control. Servers help in administering the whole set-up. Access rights and resource allocation is done by Servers.
2)  Proper Management : All the files are stored at the same place. In this way, management of files becomes easy. Also it becomes easier to find files.
3) Back-up and Recovery possible : As all the data is stored on server its easy to make a back-up of it. Also, in case of some break-down if data is lost, it can be recovered easily and efficiently. While in peer computing we have to take back-up at every workstation.
4) Upgradation and Scalability in Client-server set-up : Changes can be made easily by just upgrading the server. Also new resources and systems can be added by making necessary changes in server.
5)  Accessibility : From various platforms in the network, server can be accessed remotely.
6)  As new information is uploaded in database , each workstation need not have its own storage capacities increased (as may be the case in peer-to-peer systems). All the changes are made only in central computer on which server database exists.
7)  Security : Rules defining security and access rights can be defined at the time of set-up of server.
8)  Servers can play different roles for different clients.

Disadvantages of Client Server Architecture v/s P-2-P Technology

1)  Congestion in Network :Too many requests from the clients may lead to congestion, which rarely takes place in P2P network. Overload can lead to breaking-down of servers. In peer-to-peer, the total bandwidth of the network increases as the number of peers increase.
2)  Client-Server architecture is not as robust as a P2P and if the server fails, the whole network goes down. Also, if you are downloading a file from server and it gets abandoned due to some error, download stops altogether. However, if there would have been peers, they would have provided the broken parts of file.
3) Cost : It is very expensive to install and manage this type of computing.
4) You need professional IT people to maintain the servers and other technical details of network.

It can the summarized that client-server model is not used in small scale networks and networks where security is not a big issue.

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Also Read :-
What are Client-server Networks ?
What is Peer to Peer Architecture ?
Advantages and disadvantages of peer to peer network
Network Topology and Types of Network Topologies
What are Proxy Servers?

What Are Complex Numbers? Examples and Solving techniques

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Define: Complex numbers

Complex numbers are the numbers which have both real and imaginary parts. The imaginary part of the complex number can’t be represented on number line. They are of the form a+ bi where a and b are real numbers while i is an imaginary part (i = √-1), “a” represents the real part while "bi" represents the imaginary part.
Complex were introduced to find the solution of equation
X2 + 1 = 0
Here x=√-1, that is represented as i.

Two complex numbers x+iy and a+ib are said to be equal if their real parts are equal and their imaginary parts are also equal, i.e. x=a and y=b.

Representation of Complex Numbers


examples of complex numbers, graph complex number wikipedia
Complex numbers on Argand Plane

In the Argand plane, the vertical axis is called the imaginary axis while the horizontal axis is called the real axis. The real numbers are complex numbers with imaginary part equal to zero.
Complex Numbers are used in engineering and other scientific calculations.

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Read More:-
What Are Perfect numbers?
List of Prime Numbers
Relatively Prime Numbers
Integers and Their Properties

Client Server Network Architecture

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What is a Client Server Network?

The type of computing system in which one powerful workstation serves the requests of other systems, is an example of client server technology. A computer network is an interconnection of computers which share various resources.

What is computer server?
A computer server is the powerful computer, or the set of computers connected to each other, which provide services to other systems. They usually have database integrated in them, and are very powerful machines with very advanced configuration. They process the requests of client machines. Their role is to make management of network easy and uniform.

Features of Servers :-
1)  They have large storage capacity.
2)  They are able to provide information to many computers simultaneously, therefore have large RAM.
3)  Its processor speed is high, as it may have to execute multi-tasking too.

What are clients in client-server model?
Clients are the individual components which are connected in a network. They have a basic configuration. Client sends a request/query to server and server responds accordingly. Please note that the client doesn't share any of its resources. They are subordinates to servers, and their access rights are defined by servers only. They have localized databases.

Client Server Diagram

client server image, client server topology, network diagram wikipedia
Client Server Architecture


Components of Client Server Network

1)  Clients or Workstations.
2)  Servers.
3)  Network Devices :- They connect the clients and servers, and at the same time ensure proper collision free routing of information.
4)  Other components like scanner,printer, etc can also be connected to network architecture.

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Read More:-
Automated Testing V/s Manual Testing
Advantages And Disadvantages of Client Server Network
Network Topology and Types of Network Topologies
What is Peer-to-Peer Architecture?
Advantages and Disadvantages of P2P network.
What are Proxy Servers?

Client server Network technology

Real Numbers: What are Real Numbers ?

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Definition of Real Number :

Numbers which can be quantified and represented by a unique point on the number line are called real numbers. Every point on the number line represents one and only one real number. The set of Real Numbers are denoted by “R”. The decimal expansion of a real number is either terminating, repeating or non-terminating and non-repeating.

Types of Real numbers :

• Rational numbers: Numbers of the form p/q, where p and q are integers and q≠0. Decimal expansion is terminating or repeating.
• Irrational numbers: any real number which is not a rational number is an irrational number. Decimal expansion is non-recurring and non-terminating.

Subsets of Real Numbers


real numbers chart wikipedia wiki
Venn Diagram for Real Numbers

Operation on Real Numbers


Operations on rational and irrational numbers:
•   The sum of a rational and an irrational number is irrational. For example: 3 + √3 = 4.73205…., which is irrational since it does not follow any specific pattern and goes on endlessly after the decimal.
•   The difference of a rational and an irrational number is irrational. For example: 3 - √3 = 2.73205…., which is irrational since it does not follow any specific pattern and goes on endlessly after the decimal.
•   The product of a non-zero rational with an irrational number is irrational. For example: 3 × √3 = 5.19615…. which is irrational.
•   The quotient of a non-zero rational with an irrational number is irrational. For example: 3 ÷ √3 = 1.73205…. which is irrational.

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Read More:-
Types and Properties of Integers
Types of Fractions
Definition of Relatively Prime Numbers
List of Advertising Slogans
Venn Diagram for Real Numbers

Irrational Numbers in Mathematics

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What are Irrational Numbers?

Irrational numbers are a subset of real numbers which are not rational numbers but can be represented on the number line. Any non-terminating and non-recurring decimal is an irrational number. An irrational number, unlike rational number, cannot be written in the form of p/q, where p and q are integers and q≠0. Between any two integers there are infinite irrational numbers. They are also called surds.
A non-recurring and non-terminating decimal is one which has one or more digits after the decimal point which goes on endlessly without any specific pattern or series which proves it is irrational. Pi is one of the famous examples of irrational numbers, and please note value of pi is not equal to 22/7.

Examples of Irrational Numbers


list of irrational numbers, rational and irrational numbers, examples, value of pi, value of e, value of square root of 2
Irrational Numbers

Operations on irrational numbers:


If we add, subtract, multiply or divide two irrationals, the result may be rational or irrational. For example:
√3 + √3 = 3.4641…., which is an irrational number,
√3 - √3 = 0, which is a rational number,
√3 × √3 = 3, which is a rational number and
√3 ÷ √3 = 1, which is a rational number.


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Read More:-
List of Perfect Numbers
What is a composite number?
Definition of Prime numbers
Co-prime numbers

Network Topology and Types of Network Topologies

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What is Network Topology?

Computer network topology is the way various components of a network (like nodes, links, peripherals, etc) are arranged. Network topologies define the layout, virtual shape or structure of network, not only physically but also logically. The way in which different systems and nodes are connected and communicate with each other is determined by topology of the network. Topology can be physical or logical. Physical Topology is the physical layout of nodes, workstations and cables in the network; while logical topology is the way information flows between different components.

In general, physical topology relates to a core network whereas logical topology relates to basic network.

Types of Physical Network Topologies


1)  Bus Topology
2)  Star Topology
3)  Ring Topology
4)  Mesh Topology
5)  Tree Topology
6)  Hybrid Topology

Factors to be taken into consideration while choosing a Network topology

1)  Scale of your project (in terms of number of components to be connected).
2)  Amount of traffic expected on the network.
3)  Budget allotted for the network i.e. amount of money you are willing to invest.
4)  Required response time

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Further Read
Define: Bus Topology and its Advantages and weaknesses
Define: Star Topology and its Benefits and drawbacks
Define: Ring Topology and its Advantages and disadvantages
Define: Mesh Topology and its Advantages and disadvantages
Define : Tree Topology Merits and Demerits
Token Passing
Define: Network Topologies, different types of network topologies and comparison of network topologies along with their merits and demerits.

Rational numbers in Mathematics

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What are rational numbers?

         Numbers of the form p/q, where p and q are integers and q≠0 are called rational numbers. In other words, rational numbers are the set of all ratios made up of real numbers, which do not have zero as denominator. Rational numbers are a type of real numbers. The set of rational numbers is denoted by “Q”. Rational numbers include natural numbers, whole numbers, integers and fractions.
Between any two numbers there can be infinite rational numbers.

Rational numbers are subdivided into:
• Integers : Rational numbers of the form p/q where q= ±1 are called integers.
• Fractions : Rational numbers of the form p/q where q ≠ 0 and p<q are called fractions. They can also be expressed as decimals.
Terminating decimals and recurring decimals are rational numbers.

A recurring decimal is one which has one or more digits after the decimal point and they repeat endlessly in a specific pattern. Any recurring decimal can be expressed as a fraction. Hence it is a rational number. The pattern of rational numbers which is repeated is denoted by a line above the pattern called “bar” or “vinculum”. For example 1/3 = 0.3333…, -2/3 = -0.6666…, 1/9 = 0.1111… are fractions which can be converted to recurring decimals.
A terminating decimal is one in which has limited number of numbers after the decimal place. Any terminating decimal can be expressed as a fraction. Hence it is a rational number. For example 5/8 = 0.625, 3/2 = 1.5, 3/4 = 0.75 are fractions which can be converted to terminating decimals.

List of Some Rational Numbers :-
rational numbers, list of fractions to remember, freations to decimal list, reciprocals wikipedia
Rational numbers

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Read More:-
What Are Perfect Numbers?
List of Prime Numbers
Irrational Numbers
Definition of Real Number

Mesh Topology: Advantages and Disadvantages

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What is Mesh Topology?

In a mesh network topology, each of the network node, computer and other devices, are interconnected with one another. Every node not only sends its own signals but also relays data from other nodes. In fact a true mesh topology is the one where every node is connected to every other node in the network. This type of topology is very expensive as there are many redundant connections, thus it is not mostly used in computer networks. It is commonly used in wireless networks. Flooding or routing technique is used in mesh topology.
Types of Mesh Network topologies:-

1)Full Mesh Topology:-

mesh network topology diagram, picture of mesh topology, mesh topology wiki,partial mesh topology
Mesh Topology Diagram
In this, like a true mesh, each component is connected to every other component. Even after considering the redundancy factor and cost of this network, its main advantage is that the network traffic can be redirected to other nodes if one of the nodes goes down. Full mesh topology is used only for backbone networks.

2) Partial Mesh Topology:-

This is far more practical as compared to full mesh topology. Here, some of the systems are connected in similar fashion as in mesh topology while rests of the systems are only connected to 1 or 2 devices. It can be said that in partial mesh, the workstations are ‘indirectly’ connected to other devices. This one is less costly and also reduces redundancy.

Advantages of Mesh topology


1) Data can be transmitted from different devices simultaneously. This topology can withstand high traffic.
2) Even if one of the components fails there is always an alternative present. So data transfer doesn’t get affected.
3) Expansion and modification in topology can be done without disrupting other nodes.

Disadvantages of Mesh topology


1) There are high chances of redundancy in many of the network connections.
2) Overall cost of this network is way too high as compared to other network topologies.
3) Set-up and maintenance of this topology is very difficult. Even administration of the network is tough.

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Read More :-
Star Topology : Advantages and Disadvantages
Bus Topology : Advantages and Disadvantages
Ring Topology : Advantages and Disadvantages
Tree Topology : Advantages and Disadvantages
Client Server Network : Advantages and Disadvantages

What is a fraction and examples?

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What are fractions?

The word fraction means a part of something that is whole i.e. its value should be less than 1.
Fractions are a type of rational numbers (which are of the form  p/q, where p and q are integers and q≠0), and have numerator less than the denominator (p < q) and both p and q are in the lowest terms.
math fractions, mathematics, what are fractions, decimals wikipedia
Some common fractions
A fraction is in the lowest terms if the only common factor between the numerator and denominator is 1.
Eg. 5/10 is not in the lowest terms since the common factors are 1 and 5; whereas 3/7 is in its lowest form.

A fraction can be treated as a division problem.

Equivalent fractions:
Two fractions are said to be equivalent if the cross products are equal. Cross product is the product of the numerator of one fraction with the denominator of another.

What are Equivalent Fractions?, Equivalent fractions in maths,
What are equivalent fractions?

Unit fractions:
Those fractions in which the numerator is one.
Eg. 1/2, 1/3, 1/4 etc.

Like and unlike fractions:
•   Like fractions are those which have the same denominators.
Eg. 1/9, 2/9, 4/9.

•   Unlike fractions are those which have different denominators.
Eg. 2/5, 2/3, 2/9.

Proper, improper and mixed fractions:
•  Fractions in which the numerator is less than the denominator are known as proper fractions.
Eg. 3/4, 5/10, 3/9 etc.

•  Fractions in which the denominator is less than the numerator are known as improper fractions.
Eg. 5/4, 9/8, 11/2 etc.

•  Fractions which are a combination of a whole number and a fraction are called mixed fractions or mixed numbers.
Eg. 11/4, 31/9 etc.
Mixed fractions are an example of improper fractions.
Improper fractions can be converted into mixed fractions and vice versa.

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Read More :-
Even and Odd Numbers
Co-prime or Relatively Prime Numbers
What are Perfect Numbers?

Ring Topology : Advantages and Disadvantages

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What is Ring Topology?

In Ring Topology, all the nodes are connected to each-other in such a way that they make a closed loop. Each workstation is connected to two other components on either side, and it communicates with these two adjacent neighbors. Data travels around the network, in one direction. Sending and receiving of data takes place by the help of TOKEN.

Token Passing (in brief) : Token contains a piece of information which along with data is sent by the source computer. This token then passes to next node, which checks if the signal is intended to it. If yes, it receives it and passes the empty to into the network, otherwise passes token along with the data to next node. This process continues until the signal reaches its intended destination.
The nodes with token are the ones only allowed to send data. Other nodes have to wait for an empty token to reach them. This network is usually found in offices, schools and small buildings.

ring topology,ring topology network,token ring topology, dual ring topology wikipedia
Ring Topology & token

Advantages of Ring Topology


1)   This type of network topology is very organized. Each node gets to send the data when it receives an   empty token. This helps to reduces chances of collision. Also in ring topology all the traffic flows in only one  direction at very high speed.
2)   Even when the load on the network increases, its performance is better than that of Bus topology.
3)   There is no need for network server to control the connectivity between workstations.
4)   Additional components do not affect the performance of network.
5)   Each computer has equal access to resources.

Disadvantages of Ring Topology


1)   Each packet of data must pass through all the computers between source and destination. This makes it slower than Star topology.
2)   If one workstation or port goes down, the entire network gets affected.
3)   Network is highly dependent on the wire which connects different components.
4)   MAU’s and network cards are expensive as compared to Ethernet cards and hubs.

Read Pros and Cons of Outsourcing Testing Activity

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Read More :-
Star Topology : Advantages and Disadvantages
Bus Topology : Advantages and Disadvantages
Mesh Topology : Advantages and Disadvantages
Tree Topology Advantages and Disadvantages
Pros and cons of Peer to Peer Architecture
What are the advantages and disadvantages of client-server networking ?

Integers : Types and Properties

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What are Integers?
Integers are a type of rational numbers. Rational numbers of the form p/q where q= ±1 are called integers. They are denoted by “Z”.

Integers are of two types :
•   Negative integers
Negative integers are the set of negative numbers before 0. They do not have any fractional or decimal part. Eg. -1, -2, -3 and so on.

•   Positive integers / Whole numbers
Positive integers / whole numbers are the set of natural numbers including zero. They do not have any fractional or decimal part.

To distinguish between the positive and negative sides of 0, opposite signs are used, i.e. positive (+) and negative (-).

Number line,numberline, whole numbers and natural numbers on number line,Positive negative numbers, wikipedia
Integers on Number Line 

Additive inverse:

    The opposite of an integer is called its negative or additive inverse.
5 + (-5) = 0. So 5 is the additive inverse of -5 and vice versa.
Each integer on the number line, except 0, consists of its mirror image of the opposite sign. Eg. Mirror image of 8 will be -8,that of -2 will be 2 etc.

Zero is lesser than every positive integer and greater than every negative integer.
It is not possible to find the greatest positive or least negative number.

Absolute value of an integer:

   The absolute value of an integer is the numerical value without taking into account its sign. The modulus sign represents the absolute value of the integer. Eg.|-1|=1, |2|=2. Thus, the absolute value of an integer is either greater than or equal to the integer.

positive negative numbers diagram, positive and negative graph,quadrants of graph,+ve -ve numbers

Rules for operations on integers:
Addition:
•   Addition of 2 positive or 2 negative integers:
 Add their absolute values and prefix the sign of addends to the sum.
 -2 + (-3) = -5
•   Addition of 1 positive and 1 negative integer:Find the difference of their absolute values and prefix the sign of the integer whose absolute value is greater.
 2 + (-3) = -(3-2) = -1

Subtraction:
•   Subtracting 1 negative from another negative:
 When there are 2 negative(-ve) signs placed side by side with no numeral in between, the 2 like signs  become a plus sign.
 -2 – (-3) = -2 + 3 = 1
•   Subtraction of 1 negative from 1 positive:
Convert the like signs in case of negative signs and then add the integers.
3 - (-2) = 3 + 2 = 5
• Subtraction of 1 positive from 1 negative:
 Convert the signs and then add the absolute values of integers add prefix minus sign.
 -3 – (+2) = -3 -2 = -5

Multiplication:
•   Multiplication of 2 positive integers:
 Multiply the values and prefix plus sign to the product.
 2 x 3 = +6 or 6
•   Multiplication of a positive and a negative integer:
 Multiply their absolute values and prefix minus sign to the product.
 2 x (-3) = -6
•   Multiplication of 2 negative integers:
 Multiply the absolute values and prefix plus sign to the product.
 (-2) x (-3) = +6 or 6

Division:
•   Division of integers with like signs:
 Divide their absolute values and prefix plus sign.
 (-3) ÷ (-2) = +3/2 or 3/2
•  Division of integers with like signs:
 Divide their absolute values and prefix minus sign.
 (3) ÷ (-2) = -3/2

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Read More :
List of Prime numbers from 1 to 1000
Composite numbers
What are Perfect Numbers
Even and Odd Numbers

Star Topology: Advantages and Disadvantages

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What is Star topology?
      In Star topology, all the components of network are connected to the central device called “hub” which may be a hub, a router or a switch. Unlike Bus topology (discussed earlier), where nodes were connected to central cable, here all the workstations are connected to central device with a point-to-point connection. So it can be said that every computer is indirectly connected to every other node by the help of “hub”.

All the data on the star topology passes through the central device before reaching the intended destination. Hub acts as a junction to connect different nodes present in Star Network, and at the same time it manages and controls whole of the network. Depending on which central device is used, “hub” can act as repeater or signal booster. Central device can also communicate with other hubs of different network. Unshielded Twisted Pair (UTP) Ethernet cable is used to connect workstations to central node.

star topology, star topology network, star topology diagram, extended star topology,wiki
Star Topology Diagram

Advantages of Star Topology

1)  As compared to Bus topology it gives far much better performance, signals don’t necessarily get transmitted to all the workstations. A sent signal reaches the intended destination after passing through no more than 3-4 devices and 2-3 links. Performance of the network is dependent on the capacity of central hub.
2)  Easy to connect new nodes or devices. In star topology new nodes can be added easily without affecting rest of the network. Similarly components can also be removed easily.
3)  Centralized management. It helps in monitoring the network.
4)  Failure of one node or link doesn’t affect the rest of network. At the same time its easy to detect the failure and troubleshoot it.

Disadvantages of Star Topology

1)  Too much dependency on central device has its own drawbacks. If it fails whole network goes down.
2)  The use of hub, a router or a switch as central device increases the overall cost of the network.
3)   Performance and as well number of nodes which can be added in such topology is depended on capacity of central device.

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Earlier Article:
    Advantages and Disadvantages of Bus Topology.
   Advantages and Disadvantages of Ring Topology
   Advantages and Disadvantages of Full Mesh Topology
   Advantages and Disadvantages of Tree Topology
   Advantages of a Client Server Network.
   Different types of Network Topologies

Bus Topology : Advantages and Disadvantages

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What is Bus topology?

Bus Topology is the simplest of network topologies. In this type of topology, all the nodes (computers as well as servers) are connected to the single cable (called bus), by the help of interface connectors. This central cable is the backbone of the network and is known as Bus (thus the name). Every workstation communicates with the other device through this Bus.

A signal from the source is broadcasted and it travels to all workstations connected to bus cable. Although the message is broadcasted but only the intended recipient, whose MAC address or IP address matches, accepts it. If the MAC /IP address of machine doesn’t match with the intended address, machine discards the signal.

A terminator is added at ends of the central cable, to prevent bouncing of signals. A barrel connector can be used to extend it. Below I have given a basic diagram of a bus topology and then have discussed advantages and disadvantages of Bus Network Topology

bus topology diagram,physical bus topology, linear bus network topology, wiki wikipedia
Bus topology diagram

Advantages (benefits) of Linear Bus Topology


1)  It is easy to set-up and extend bus network.
2)  Cable length required for this topology is the least compared to other networks.
3)  Bus topology costs very less.
4) Linear Bus network is mostly used in small networks. Good for LAN.

Disadvantages (Drawbacks) of Linear Bus Topology


1)  There is a limit on central cable length and number of nodes that can be connected.
2)  Dependency on central cable in this topology has its disadvantages.If the main cable (i.e. bus ) encounters   some problem, whole network breaks down.
3)  Proper termination is required to dump signals. Use of terminators is must.
4)  It is difficult to detect and troubleshoot fault at individual station.
5)  Maintenance costs can get higher with time.
6)  Efficiency of Bus network reduces, as the number of devices connected to it increases.
7)  It is not suitable for networks with heavy traffic.
8)  Security is very low because all the computers receive the sent signal from the source.

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Read More :-
What is Peer to Peer architecture?
Benefits and Drawbacks of P2P network
Token Ring Topology Advantages And Disadvantages
Mesh Topology Advantages And Disadvantages
Star topology Advantages And Disadvantages
Waterfall Model SDLC
Tree Topology: Advantages and Disadvantages

Whole Numbers and Natural Numbers

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What are Whole Numbers ?

Whole numbers are the set of positive integers. They do not have any decimal or fractional part. Natural numbers along with zero(0) are whole numbers.
Closure Property Of Whole Numbers

•     Addition of whole numbers always gives a whole number. Thus whole numbers are closed under addition.
            Eg. 5+7 = 12
•     Subtraction of whole numbers does not always give a whole number. Thus whole numbers are not closed under subtraction.
           Eg. 5-7 = -2, which is a negative integer and not a whole number.
•     Multiplication of whole numbers always gives a whole number. Thus whole numbers are closed under multiplication.
           Eg. 5x7 = 35
•      Dividing a whole number by another does not always give a whole number. Thus whole numbers are not closed under division.
           Eg. 5÷7 = a fraction, thus it will not be a whole number.

what are natural numbers, what are whole numbers, difference between whole and natural numbers, wiki wikipedia
Natural and Whole numbers on number line

What are Natural Numbers?

Natural numbers are the set of positive integers, that is, integers from 1 to ∞ excluding fractional n decimal part. They are whole numbers excluding zero. Natural Numbers are also called counting numbers.

Natural Numbers can further be sub-divided into different types :-

1)  Even and odd Numbers
2)  Prime Numbers
3)  Relatively prime/ co-prime numbers
4)  Composite numbers
5)  Perfect numbers

What is Zero ?
Zero is the only whole number which is not a natural number. It is represented by 0. "Zero is the only difference between natural and whole numbers."
 Properties of ZERO - 0
•     Zero added to any number gives the number itself. Hence, 0 is the additive identity for all numbers.
•     Multiplication with zero- 0 multiplied with any number always gives 0.
•     Zero divided my any number(except 0) gives 0.
•      Any number divided by 0 is not defined.
•      Zero raised to any power(except 0) gives 0.
•      Zero to the power 0 (00) is not defined.

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What are Even and Odd Numbers

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Even numbers and odd numbers

Integer numbers divisible by two are called even numbers whereas integers which are not divisible by two are called odd numbers. Odd numbers leave 1 as the remainder when divided by 2.
properties of even and odd numbers, even and odd numbers product, wiki wikipedia
odd n even numbers
Even numbers always end with 0, 2, 4, 6 or 8. Odd numbers always end with 1, 3, 5, 7 or 9. So if a given number has 0, 2, 4, 6 or 8 in its unit’s place it is even otherwise its odd.

Properties of Even and Odd numbers:


• Sum (or difference) of any number of even numbers is always even.
         Even ± Even = Even
• Sum (or difference) of even number of odd numbers is always even.
         Odd ± Odd = Even
• Sum of odd number of odd numbers is always odd.
         Odd + Odd + Odd = Odd
• Sum of an even and an odd number is always odd.
         Even + Odd = Odd
• Difference between an even and an odd number is always odd.
         ± Even ∓ Odd = Odd
• Product of any numbers of even numbers is always even.
         Even x Even = Even
• Product of any number of odd numbers is always odd.
         Odd x Odd = Odd
• Product of any number of numbers where there is an even number is always even.
         Even x Any number = Even

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Read More :-
What are composite numbers ?
What are Perfect Numbers ?
What are prime numbers ?
What are relatively prime numbers / co-prime numbers?

Peer-to-Peer (P2P) : Advantages and Disadvantages

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What are the advantages and disadvantages of a peer-to-peer network?

Earlier we saw What is Peer-to-Peer ?, "A peer-to-peer (P2P) network is created when two or more PCs are connected and share resources without going through a separate server computer" Now let us now discuss the advantages and disadvantages of P2P network architecture.

Advantages of Peer-to-peer networking over Client –Server networking are :-

p2p advantages and disadvantages, torrents wiki wikipedia, benefits and drawbacks of p2p network/ architecture
P2P technology behind torrents
1)  It is easy to install and so is the configuration of computers on this network,
2)  All the resources and contents are shared by all the peers, unlike server-client architecture where Server shares all the contents and resources.
3)  P2P is more reliable as central dependency is eliminated. Failure of one peer doesn’t affect the functioning of other peers. In case of Client –Server network, if server goes down whole network gets affected.
4)  There is no need for full-time System Administrator. Every user is the administrator of his machine. User can control their shared resources.
5)  The over-all cost of building and maintaining this type of network is comparatively very less.

Disadvantages(drawbacks) of Peer to peer architecture over Client Server are:-

1) In this network, the whole system is decentralized thus it is difficult to administer. That is one person cannot determine the whole accessibility setting of whole network.
2) Security in this system is very less viruses, spywares,trojans, etc malwares can easily transmitted over this P-2-P architecture.
3) Data recovery or backup is very difficult. Each computer should have its own back-up system
4) Lot of movies, music and other copyrighted files are transferred using this type of file transfer. P2P is the technology used in torrents.

Peer to peer networks are good to connect small number (around 10) of computer and places where high level of security is not required. In case of business network where sensitive data can be present this type of architecture is not advisable or preferred.

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Also Read :- Client Server Architectures
Advantages and Disadvantages of Client and Server Network
Network Topology And Their Types
Characteristics of a Good Software
Advantages and Disadvantages of Waterfall Model

Co-prime Numbers : What are Co-Prime Numbers?

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What are relatively prime numbers / co-prime numbers?

A set of numbers which do not have any other common factor other than 1 are called co-prime or relatively prime numbers. This means those numbers whose HCF is 1.

For example, 8 and 9 have no other common factor other than 1 so they are co-prime numbers.
What is a coprime number
Properties Of Co-prime Numbers:

• All prime numbers are co-prime to each other.
• Any 2 consecutive integers are always co-prime.
• Sum of any two co-prime numbers is always co-prime with their product.
• 1 is co-prime with all numbers.
• a and b (natural numbers) are co-prime only if the numbers 2a-1 and 2b-1 are co-prime.

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Read Grievances of A Software (Just 4 Fun)
What are co-prime numbers ?

Prime Numbers : What are Prime Numbers in Mathematics?

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What are prime numbers ?

A natural number which has only 2 distinct factors, which are, 1 and the number itself is called a prime number. The property of being prime is called primality.

2 is the smallest and the only even prime number.
One is not a prime number. Earlier it was counted as a prime number but since it has only one factor that is 1, it is now excluded from prime numbers.

Twin prime numbers :


Successive prime numbers(except 2 and 3), which have difference two.
Eg. (3 & 5), (5 & 7), (11 & 13), (59 & 61) etc.

Mersenne’s prime numbers :


Prime numbers of the form 2n-1 where n is prime.Example Merssene’s prime numbers of 3 & 7 are prime numbers. 23-1=7, 27-1=127.
However, all numbers of the form 2n-1 where n is prime, may not be prime.
For eg, 11 is a prime number but 211-1 = 2047, that is not a prime number.

List of prime numbers from 1 to 1000:
prime numbers list, list of prime numbers from 1 to 1000, what are prime numbers, define prime numbers wiki wikipedia, chart 1-1000
Prime numbers list from 1 to 1000
What is a prime number

Test of primality(whether the given number is prime or not):

To check if a number is a prime number trial division can be done. the most common and easy way of trial method is to check whether the prime number is a multiple of a number which lies between 2 and √n, where n is the prime number to be checked.
If n is a multiple of any of these integers then it is a composite number, and so not prime; if it is not a multiple of any of these integers then it is prime. Since this method requires trial division till √n, it becomes very lengthy and is not suitable for large numbers.

Example To check if 3 is a prime number :
Step I- find numbers between 2 and √3(=1.732)
There are no integers between 2 and √3. Thus 3 is a prime number as it is not a multiple of the numbers between 2 and √3.

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Read More :-
Composite Numbers
Perfect Numbers
List of Advertising Slogans
Prime Numbers - Facts, Examples, & Table Of All Up To 1000

P2P - What is Peer-to-Peer network ?

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In Peer to Peer (or P2P) network each of the participation workstation (computer) has same (equivalent) privileges, capabilities and responsibilities. This type of network architecture is completely different from client/server architectures. In Client Server Architectures, some computers store information and have access to resources, which other computers in network can access through them. These computers or machines with extra privileges are called Servers and dedicatedly “serve” clients.

peer to peer network, peer to peer file sharing, file sharing,what is p2p wiki wikipedia
P2P network

In Peer-to-peer (P2P) networking the need for central servers is eliminated, and all computers interact and share resources as equals. Thus it can be said P2P architecture is the alternative to server-client network design. Each communication node has both server and client capabilities.
This peer-2-peer application structure was first popularized by file sharing systems like Napster. P2P is especially popular in homes where an expensive, dedicated server computer is neither necessary nor practical. Peer-to-peer networks are generally simpler, but their performance usually decreases when there is heavy load.
This type of file transfer system is decentralized and allows a user to search through all the linked computers for desired file. To use P2P, a user should download P2P software on his machine and configure it.Torrents use this technology effectively.

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Read More :-
Pros and Cons of Manual Testing
Advantages and Weaknesses of Peer to Peer Network Topology
What are Client Server Networks?
Client Server Architecture : Advantages and Disadvantages
P2P - What is Peer-to-Peer sharing ?

What is composite number give example?

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What are composite numbers ?

Any number other than 1, which is not a prime number is a composite number.

Thus a composite number is a number which has at least one factor other than 1 and itself.
Every composite number can be written as the product of 2 or more distinct prime numbers.
The number 1 is neither prime nor composite.

Classification based on number of distinct prime factors:


  •  4 = 2 x 2         6=2 x 3
Both, 4 and 6 have prime numbers as their factors (excluding 1 and the number itself). Such numbers which have 2 prime numbers as their factors are called semiprime. One of the factors can even be a square of a prime number.
12 = 2 x 2 x 3
12 is multiple of 2 distinct primes 2 and 3. Thus 12 is also a semi prime number.
  •   30 = 2 x 3 x 5
30 is a multiple of 3 distinct primes, 2, 3 and 5.
Those composite numbers which have 3 distinct prime factors is called a sphenic number.

Classification based on repetition of prime factors:

What are composite numbers?, composite and prime numbers,composite number wikipedia wiki
Composite number

  • 64 = 26
A number in which all prime factors are repeated is called a powerful number. Thus 64 is a powerful number.
  • 210 = 7 x 5 x 2 x 3

When none of the prime factors of a number are repeated, the number is called a squarefree number.

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Also See :- What are Perfect Numbers ?
What is a Co-prime or Relatively prime number ?
Definition of prime number
Properties of Integers
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