Sameen Ahmed Khan

The writer teaches at Engineering Department, Salalah College of Technology (SCT), Salalah, Sultanate of Oman.


Our Multiplication Tables

30 Oct 2016 logo 0 comments


Arithmetic is the oldest and the most elementary branch of mathematics.  Its primary purpose is to study numbers and perform the four basic operations namely: addition, subtraction, multiplication and division. These operations are encountered in everyday life.  For example, one may collect fruits from a tree and put them together.  Addition helps us to keep the count of the fruits in the heap.  At the end of the day, one may give away the fruits from this heap, which will require the knowledge of subtraction to keep the account. Suppose we have many trees and many heaps.  Then keeping an account of the total fruits would involve big numbers. One can still manage with addition.

But the third arithmetic operation namely the multiplication takes care of the large numbers. Multiplication of whole numbers can be thought of as repeated addition. For illustration, let there be six heaps with eight fruits in each of them. Then there are  fruits. This can be seen either as counting ‘six heaps eight times’ or equivalently ‘eight sets six times’. Two approaches are possible because . Order does not matter in addition and multiplication.

These statements may appear to us as obvious but are of great mathematical value. This property of the order not mattering has a special name and we say that ‘addition is commutative’ and ‘multiplication is commutative’, respectively.  To visualise the division, let us consider a heap of 20 fruits, which has to be distributed among four persons. Symbolically, this task is stated as . Each person gets 5 fruits. After the distribution, one can get back the size of the original heap as . Hence, the division is sort of opposite of multiplication.  We note, that subtraction and division are not commutative.  This can be checked by considering the example with the numbers say, 2 and 5; as  and .  

Since, ancient times there have been attempts to obtain mastery of the four basic arithmetic operations. Addition and subtraction are relatively easy.  The multiplication is facilitated with the help of tables. Division is the most difficult and an expertise in multiplication is a must. The oldest known multiplication tables date back to four thousand years and were used by the Babylonians (in the modern day they include parts of Iraq, Kuwait, Syria, Turkey and Iran).  The Babylonian tables used base 60 (same as our clocks use for time, 1 hour = 60 minutes and each minute = 60 seconds). Such tables have been also found in other ancient civilizations from later periods.

In this article, we shall have a closer look at the modern day base 10 ‘multiplication table’ (also called the ‘times table’) and some of its many properties.  In our school books, we are introduced to a multiplication table. 


The figure has a  table.  We note some basic properties.  Multiplication with 1 does not change the number.  Multiplication with 10 only appends a zero in the end.  This is the advantage of using the base 10.  The diagonal distributes the table into two identical triangles having the same set of numbers, with the diagonal acting as a mirror.  The two triangles have the same set of numbers because the multiplication is commutative.  The diagonal has the perfect squares: 1, 4, 9, 16 and so on. This reduces the burden of memorising the multiplication table to a little more than the half.  One has to memorise either of the triangles and the diagonal only. 

Now, we note some advanced properties of the multiplication table. Numbers within the diagonal do not repeat. But numbers within each of the triangles repeat. For example, within each triangle, the numbers 6, 8, etc. repeat.  The numbers in the diagonal and the triangle also have an overlap. For example, 4, 9 etc. occur both in the diagonal and the triangles.

Because of these repetitions and overlaps, it becomes difficult to count the numbers in the multiplication table! The repetitions and the overlaps only increase with the size of the multiplication table, that too in an unpredictable manner.  Using these properties of the table, we note the sets of numbers in the multiplication tables of different sizes. The sets designated by  contain the numbers occurring in the multiplication table.  For completeness, we start with a table of size 1.  The first few sets are

Sets of larger size completely contain all the sets of lower size. The size or order of the sets denoted by  grows as 1, 3, 6, 9, 14, 18, 25, 30 and so on. More terms of this infinite sequence can be obtained from The On-Line Encyclopedia of Integer Sequences at  It may surprise the reader, but there is no simple formula for the size or order of the sets.  Even the legendry mathematician Paul Erdős could provide only a rough estimate.

Some very complicated formulae have been obtained involving logarithms and other advanced functions. For practical purposes, a good estimate is given by the simple inequality . In mathematics, there are many such surprises.  Even easy to understand problems such as the ‘size of the multiplication sets’ defy solutions. It is such problems, which keep some of the brightest mathematicians engaged!

[HAJIRA KHAN is a student of Indian School Salalah; and SAMEEN AHMED KHAN teaches at Department of Mathematics and Sciences, College of Arts and Applied Sciences, Dhofar University, Salalah, Sultanate of Oman.]

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Time for Summer Vacations and Madrasa

22 May 2016 logo 0 comments


The days after the exams are very relaxing. Kids plan a lot of things. Every kid has a plan. Like beach-parties, sleepovers, going to theatres and a lot of fun things. They are completely in freedom during this time as there is no homework, tuitions and studies. They can sleep late in the morning and generally be very lazy. Some schools organise Summer Programmes like crafts, games and some literary activities like learning languages. But there is no serious stuff whatsoever!  
Most schools have a heavy study and examination schedules round the year. This leaves little time and stamina to cover other aspects essential for a complete development of an individual.
Summer is a good time to learn new things, which are not covered in the regular school round the year. Summer vacations are about two months and an ideal time to catch up with the learning of Islamic studies. It is time to organise Summer Madrasa Programmes.  During the regular academic year Muslim children spend a good proportion of their time outside of Masajid and Madrasa.  During school term times, they do not get much opportunity to spend time in Islamic environment and further their Islamic learning. Therefore, school holidays, specially the summer holidays, present a great opportunity to enrol in Islamic classes, where they can learn more about Islam and put those teachings into practice.  
The Summer Madrasa Programme can cover the following:
1. Beliefs of Islam: Learn about the core beliefs of Islam.  
2. Qur’ān & Tajweed: Learn to read the Holy Qur’ān with Tajweed.  
3. Qur’ān Memorisation.  
4. Essentials of Islam: Learn the basics and essentials of Islamic way of life such as cleanliness, prayer and fasting.
5. The Blessed Life of Prophet Muhammad (peace and blessings of Allah be to him): Study the life and character of our beloved Prophet.
6. Translation of the Complete Salah (Prayer): Starting with the Azan (Prayer-call) to Salam (done at the end of each Salah).  
7. Qur’ānic Arabic: Basic Arabic in order to understand, when the Qur’ān is being recited.  
8. Islamic Etiquette.
This year, the Ramadan al-Mubarak is falling in the summer break. This is another impetus to run the summer Madrasa programmes. We ask Allah the Almighty to help us and all the Muslims to understand His religion and adhere to it, to bless us all by making us follow the Sunnah, and to protect us from shirk, taghut and bida’h, for He is the Most Kind and Generous.  May Allah bless our Prophet Muhammad, and his family and his companions.
[The writer is a student of Indian School Salalah, Salalah, Sultanate of Oman.]

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Never Give up

10 Apr 2016 logo 0 comments


There once lived a girl named Clarissa. She was good at studies and loved reading books. She had very good writing skills too. She was a very good student. But there was one thing she always wanted to do goo – sports. Every year there was sports day in her school. Students from fifth grade and higher were allowed to participate.
Clarissa was in sixth grade. When last year she was in fifth, she went to the sports day selection. She tried almost every event but unfortunately she was not selected. She was very disappointed. She thought she would never succeed in sports.

This year’s sports day was approaching. “I shall not go for the selection of sports day,” said Clarissa. “Why not?” asked her friend Margery. “Because I did not get selected last year.” “But you must try,” said Margery, “you never know what is going to happen”. “OK, fine. I will go,” said Clarissa.

It is five O’ Clock in the evening. There will be events like cricket-ball throw; skipping; long jump, etc. today. The running events will be tomorrow.

“Just hope for the best,” said Margery. When Clarissa reached home, she told her mother about the sports day selection and how she had denied going there first but then how she got new spirit. “Well, that is a strong decision you have made,” said her mother.

“And do not feel bad if you do not win any medal, participation is more important.” “Thanks Mom,” said Clarissa. When it was 5 O’ Clock, Clarissa’s mother dropped her at the school gate and wished her all the best. The first event was cricket-ball throw. She threw nicely but not far enough to get selected. She tried many other events but unfortunately she was not selected in any of them, and it was time to go home. “I knew it,” Clarissa said to Margery, I told you I will not get selected. But you can try out for tomorrow’s running events. “Yeah, yeah as if I will get selected in the running events, when I could not get selected in such easy events.” “Now, now I told you not to think like that. Just come for tomorrow’s running events or your name is not Clarissa Wilson”. “Fine,” said Clarissa smiling.

The next day Clarissa went to try out for the running events. The first race was 50 metres, 80 metres, and then there were 200 metres plus there were hurdles. “Looks like there are a lot of races I can try out for,” thought Clarissa to herself. She tried out for 50 metres and 80 metres but sadly she was not selected. She did not want to try out for hurdles because she did not have the practice for jumping heights. Next race was 200 metres. “I should get selected at least in this race,” she thought, “This is my last chance.”

The headmaster’s whistle blew and everyone started to run. This time she ran with all her might and before she knew it, her name was announced. She had been selected for 200 metres!! She had come third. She could not believe it. Now she had to run on the sports day!

“I told you to try and see,” said Margery. “Thanks a ton for your advice,” said Clarissa. Now Clarissa had to concentrate on her running practice. She started jogging every day at dawn and in the evening. At last the day for which she was waiting day and night came.

It was sports day, the day her race was. Her mother accompanied her to the school as the parents were also invited. Her race was at 4:30 PM and now it was 3:30. She still had an hour’s time. There were four houses in her school: red, blue, green and yellow. She was in yellow house and so was Margery. “So you made it after all,” said Margery thumping her on the back. “Yup, because of your words.” “Excuse me what are you talking about?” asked Margery confused.

“If you had not encouraged me for going to the sports day selection, I would not be standing here today in my house colour T-shirt waiting for my race,” said Clarissa.

“Hey, it was my duty to encourage you, you are my friend.”

“Thanks for that,” said Clarissa and chatted with Margery for a while waiting for her race to be announced. And then the time came; it was 4:30. The headmaster announced the race. She was supposed to run in lane number three. All the athletes sat on their knees on the wet grass. Clarissa’s heart was thumping fast as the headmaster said ON YOUR MARK, SET and he gave a loud clap. All the athletes started to run. Clarissa ran with all her might, she had to win this race somehow.

The finish line was approaching instant by instant and before she knew it she crossed the finish line. She could not believe it. She had come first. Everyone was clapping for her. This was the best moment of her life. She received gold medal by the chief guest standing on the pedestal.

“I knew you could do it,” said Margery hugging her friend, and saying, “Always try your best and never give up.”
[HAJIRA KHAN studies at Indian School Salalah, Salalah, Sultanate of Oman]

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Sameen Ahmed Khan

The writer teaches at Engineering Department, Salalah College of Technology (SCT), Salalah, Sultanate of Oman.


Better Health with Honey

3 Apr 2016 logo 0 comments


The living things are classified into plant kingdom and the animal kingdom (including birds, fishes, etc.) respectively. There are some microorganisms, which do not fit precisely into the either. About 20 fruits and fruit bearing plants have been identified in the Holy Qur’ān.  The 20 plants mentioned in the Holy Qur’ān include: date palm, fig, ginger, grape, garlic, henna/camphor, lentil, manna, olive, onion, pomegranate, summer squash, sweet basil, athel tamarisk, tooth-brush tree, arak, mustard, acacia, cucumber, gourd, leek, cedrus (cedar or Lote-tree) and Euphorbia.  The Bitter Thorn and Blessed Tree are yet to be identified. The Bitter Thorn is the tree in the Jahannum (hell) and is mentioned in Surah Al-Ghashiyah (88, meaning The Overwhelming Event): 6-7.  The Blessed Tree is mentioned in Surah Al-Ra`d (13, meaning The Thunder): 29.  

The Qur’ānic botany continues to be an active area of research.  Likewise, over 40 animals and a dozen animal products (such as milk, wool, honey, leather, pearl, silk, musk, etc.) are mentioned in the Holy Qur’ān.  In this article, we shall focus on the honeybee and the honey.  The honey bee and honey are mentioned in the following Ayaat (English Meaning by Muhammad Asad from  

1.    And [consider how] thy Sustainer has inspired the bee: “Prepare for thyself dwellings in mountains and in trees, and in what [men] may build [for thee by way of hives]; and then eat of all manner of fruit, and follow humbly the paths ordained for thee by thy Sustainer.” [And lo!] there issues from within these [bees] a fluid of many hues, wherein there is health for man. In all this, behold, there is a message indeed for people who think! [Surah Al-Nahl, 16:68-69]
2.    [And can] the parable of the paradise which the Allah-conscious are promised – [a paradise] wherein there are rivers of water which time does not corrupt, and rivers of milk the taste whereof never alters, and rivers of wine delightful to those who drink it, and rivers of honey of all impurity cleansed, and the enjoyment of all the fruits [of their good deeds] and of forgiveness from their Sustainer – can this [parable of paradise] be likened unto [the parable of the recompense of] such as are to abide in the fire and be given waters of burning despair to drink, so that it will tear their bowels asunder? [Surah Muhammad, 47:15]  

Biologically bees belong to the class of insects. There are about six to ten million types of insects. Very few insects have been studied in detail. Millions are yet to be named! There are over 20,000 known species of bees. Bees are found in all continents except Antarctica! They are identified by their wing veins, structure of the moth parts and other micro-features related to behavioural peculiarities. A honey bee (or honeybee), in contrast with the stingless honey bee, is any bee member of the genus Apis, primarily distinguished by the production and storage of honey and the construction of perennial, colonial nests from wax.

Currently, only 11 species of honey bee are recognised, with a total of 44 subspecies. Honey bees represent only a small fraction of the roughly 20,000 known species of bees. Some other types of related bees produce and store honey, but only members of the genus Apis are true honey bees. The study of bees is known as melittology. The study of honeybees is called Apiology/Apidology and this term is often used interchangeably with melittology.  
Honey is a sweet food made by honey bees foraging nectar from flowers. Honey is as old as history is itself. The Romans used honey to heal their wounds after battles. The ancient Egyptians not only made offerings of honey to their gods, they also used it as an embalming fluid and a dressing for wounds. Honey use and production has a long and varied history. Honey collection from the wild bees is a widely practised ancient activity, and there are records that are over 15,000 years old.

Beekeeping (or apiculture) is the maintenance of honey bee colonies, commonly in hives, by humans.  A beekeeper (or apiarist) keeps bees in order to collect their honey and other products that the hive produces (such as: beeswax, propolis, pollen, and royal jelly). Beekeeping in pottery vessels began about 9,000 years ago in North Africa. Domestication of honeybees is shown in Egyptian art from around 4,500 years ago. Now bee farming is an established science and widely practised because of the economic returns.  

The possible health benefits of consuming honey have been documented in early Greek, Roman, Vedic, and Islamic texts and the healing qualities of honey were referred to by philosophers and scientists all the way back to ancient times. Because of its rich chemical content the honey has been used in all civilizations since ancient times.
Honey contains a treasure chest of hidden nutritional and medicinal value for centuries.  Hence, it is also called as liquid gold. The sweet golden liquid from the beehive is a popular kitchen staple loaded with antibacterial and antifungal properties that has been used since the early days of Egyptian tombs. Honey’s scientific super powers contribute to its vastly touted health benefits for the whole body. The healthy natural sweetener offers many nutritional benefits depending on its variety.  

Honey Nutritive Value per Cup (339 grams)
Principle    Nutrient Value    Percentage of RDA
Energy    1031    52%
Water    58 g    
Carbohydrates    279 g    93%
Protein    1 g    2%
Total Fat    0    0
Cholesterol    0    0
Dietary Fibre    0.7 g    3%
Sugars    278g    
Ash    0.7g    
Vitamin A     0.0 IU    0%
Vitamin C    1.7 mg    3%
Vitamin D    –    –
Vitamin E (Alpha Tocopherol)    0.0 µg    0%
Vitamin K    0.0 µg    0%
Thiamin    0.0 mg    0%
Riboflavin    0.1 mg    8%
Niacin    0.4 mg    2%
Vitamin B6    0.1 mg    4%
Folate    6.8 µg    2%
Vitamin B12    0.0 µg    0%
Pantothenic Acid    0.2 mg    2%
Choline    7.5 mg    
Betaine    5.8 mg    
Sodium    13.6 mg    1%
Potassium    176 mg    5%
Calcium    20.3 mg    2%
Copper    0.1 mg    6%
Iron    1.4mg    8%
Magnesium    6.8 mg    2%
Manganese    0.3mg    14%
Phosphorus    13.6 mg    1%
Zinc    0.7 mg    5%
Selenium    2.7 µg    4%
Fluoride    23.7 µg    –
RDA: Reference Daily Intake or Recommended Daily Intake, which is considered sufficient to meet the dietary requirements of most individuals.  

Honey offers incredible antiseptic, antioxidant and immune boosting properties for our body and health. It not only fights infection and helps tissue healing but also helps reduce inflammation and is often used for treating digestive problems such as indigestion, stomach ulcers and gastroenteritis.  

The individual behaviour and organisational behaviour of several insects has drawn the human attention since ancient times. The colonies of ants and bees are prime examples of strong social behaviour among the insects. The 1973 Nobel Prize in Physiology or Medicine was awarded jointly to Karl von Frisch, Konrad Lorenz and Nikolaas Tinbergen ‘for their discoveries concerning organisation and elicitation of individual and social behaviour patterns’ in insects.  Karl Ritter von Frisch’s work centred on investigations of the sensory perceptions of the honey bee and he was one of the first to translate the meaning of the waggle dance.  Waggle dance is a term used in beekeeping for a particular figure-eight dance of the honey bee.  By performing this dance, successful foragers can share, with other members of the colony, information about the direction and distance to patches of flowers yielding nectar and pollen, to water sources, or to new nest-site locations.
Researchers from around the world are discovering new and exciting medical benefits of honey and other healing items produced in the hive such as propolis, royal jelly and bee pollen.  As stated in the Hadīth, the Holy Prophet (peace and blessings of Allah be to him) said, Narrated Ibn ‘Abbas: (The Prophet said), “Healing is in three things: A gulp of Honey, cupping, and branding with fire (cauterising).” But I forbid my followers to use (cauterisation) branding with fire.” [Sahih Bukhari, Book #71, Hadith #584].  Nutritious, health, medical and industrial value of the honey is not fully recognised. The researchers all over the world are searching and investigating in the matter.
[HAJIRA KHAN studies at Indian School Salalah, Salalah, Sultanate of Oman & SAMEEN AHMED KHAN teaches at Department of Mathematics and Sciences, College of Arts and Applied Sciences (CAAS), Dhofar University, Salalah, Sultanate of Oman,]

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Lost ‘N’ Found

31 Jan 2016 logo 0 comments


Once a boy named Mike was travelling alone to Chicago, USA, from Salalah, Oman. He was travelling as an unaccompanied minor. While returning from there, he was on the last leg of his long journey: flight from Qatar to Salalah. At Qatar he suddenly realised that his passport was not with him. He searched and searched through his pockets and the bags. He then told the airport staff that he has lost his passport. Then, he thought that he must have left his passport in the aeroplane. That plane was searched before it left for Dubai. The passport was not found in the plane. Mike phoned his relatives in Chicago and his parents in Salalah.

There was a huge panic fearing that Mike will be sent to his motherland, India. In such an event he would have to make a new passport in India. The plane returned from Dubai to Qatar. On the telephonic request of Mike’s parents, the airline staff did a second search. Lo and behold the passport was found stuck between to the legs of two seats several rows away from the seat on which Mike had travelled from Chicago to Qatar. It was a miracle of sorts!
The aeroplane had made two flights and nobody else noticed the passport! Otherwise it would have landed in the hands of some person and ended up somewhere else! Finally, he took the scheduled flight to Salalah. The long wait which Mike had planned to spend exploring the Qatar airport was lost in the passport lost ‘n’ found incident. Mike was given a huge welcome at the Salalah Airport by his anxious parents and their well-wishers.

Mike had travelled from Salalah-Qatar-Chicago as an unaccompanied minor. But while returning the staff at Chicago treated him like an adult and Mike was compelled to keep the passport with himself. This was the root-cause of the problem. The unconcerned staff should have checked his age from the passport and treated him like a minor as in the onward flights.

What happened with Mike can happen with anybody irrespective of age: losing the passport during travel. The moral of the incident is to keep the passport secure so that it may not slip or fall. One should also keep some photocopies and digital copies.

Nonetheless, Mike had an adventure of sorts. Now, he has an adventurous incident to describe to one and all again and again. [This is based on a true incident.]

[The writer studies at Indian School Salalah, Salalah, Sultanate of Oman]

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Eidgah Preparations

12 Jul 2015 logo 0 comments


Eidgah is a place meant for offering the Eid Salaat (prayers). It is usually a ground with a small structure in the direction of Qibla (facing Makkah), and hence not much in use rest of the year. Every night preceding the Eid, my father and our close neighbour Iqbal Uncle along with some other volunteers go to the Eidgah after the Isha Salaat. They clean the ground and then remove the stones, which may come under the carpets. Then, they mark lines using the white chalk powder. They also ready the wooden platform and the microphone for the Imam affectionately known as the Qari Saheb even though he is a Hafiz and an Alim. The volunteers are given water and sometimes juices.

In the morning immediately after the Fajr Salaat, Iqbal Uncle rushes to the Eidgah for final inspection. Then with the help of volunteers the long sheets of cloth are laid on the ground. In the Masajid (Mosques) the Eid Salaat is at 7 a.m. but in the Eidgah they keep it at 8. This helps the people who miss the Salaat in the Masajid and particularly those sections of the society which have long queues for the bathrooms.

The Qari Saheb gives a good Bayan (speech) before the Salaat and makes an announcement for his Madrasa (Islamic Seminary). Some money is also collected for the Madrasa as well as the needy. Qari Saheb makes a special Dua (Supplication) for all those who helped with the various Eidgah arrangements. Last year, it was raining lightly and Iqbal Uncle also arranged tents. My father had held an umbrella over the Qari Saheb during the Bayan and the Khutbah (Sermon) after the Salaat.

After the Salaat, people meet one another in the Eidgah and drink the water and juices provided. The volunteers again work hard to pack the cloth sheets and other things. Then the volunteers of the Eidgah preparations along with Qari Saheb proceed to the residence of Iqbal Uncle. Then, in his house everyone has his breakfast with many items. It is more like a full lunch and breakfast combined! Iqbal Uncle hosts another party for the Families, usually next day of the Eid.

[HAJIRA KHAN studies at Indian School Salalah, Salalah, Sultanate of Oman]

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Iftaar Party with a Significant Difference

5 Jul 2015 logo 0 comments


The holy month of Ramadan-ul-Mubarak was going on. The little girl, Maryam used to get up for Suhoor (the pre-dawn meal) every morning and join everybody in the meal. But was yet to have her first Siyaam (Fast) as the elders felt she was too young to fast. One fine day, she woke up or Suhoor as usual. She ate more than the usual, with the intention to fast. She also drank a good quantity of water. She also had some Zamzam and made a Dua. She did the Fajar Salaat as usual and slept.

When she woke up, it was midday! Usually she used to wake up at nine or ten. But all the same she was very happy. Now, she would be able to fast for the whole day. She went to her neighbour’s house for some time. After returning home, she told her parents about it. Her parents felt that it is too late to break the fast! They also felt very excited about her fasting. Soon the preparations began for the Roza-Rakhai (also called the Roza Kushai, a function to mark the first fast of a person). The guests were invited; shopping was done for the food and a lot more.

The invitees also included the elder brother of Maryam’s father. He was affectionately called Hajji-Abba by Maryam and other kids in the family. Hajji Abba had earlier discouraged Maryam from fasting but now realized that little kids can also fast!

When it was time for Iftaar, the guests arrived, with gifts for Maryam. Then after hearing the Maghrib Azan, everybody ended their fast. Hajji Abba gifted Mayram a big note. Maryam was the happiest of them all. She again had some Zamzam. That Ramadan, she kept two more fasts.

This article is based on a true incident.

[HAJIRA KHAN studies at Indian School Salalah, Salalah, Sultanate of Oman]

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Ramadan-ul-Mubarak and Children

21 Jun 2015 logo 0 comments


There once lived a girl named Maryam. She was very excited as the month of Ramadan-ul-Mubarak was approaching. She was planning to fast in the holy month. She had seen her friends and neighbours’ kids fast the previous Ramadan. Her parents had agreed. They were also looking forward to it. One fine evening, just before the Ramadan her father’s elder brother visited them. He was affectionately called Hajji-Abba by Maryam and other kids in the family. Hajji-Abba enjoyed a lot of respect and at times dominated the whole clan. When he learned that Maryam was about to fast, he forced her parents saying that do not allow Maryam to fast this Ramadan as she is young.

Eventually, the month of Ramadan arrived to which Maryam was eagerly looking forward for more than a year. In the previous Ramadan she used to get up almost every day for the Suhoor (the pre-dawn meal). She used to eat well along with her brother and parents hoping to keep fast. Her parents would request her to have lunch if not the breakfast. They had assured her that the half-day exercise of not eating will prepare her to fast completely. The previous Ramadan Maryam had attended the Roza-Rakhai (also called Roza Kushai, a function to mark the first fast of a person) of several of her classmates. But alas! All the preparations and eagerness are yet to be materialised into her first fast. Thanks to the domination of Hajji-Abba.

The irony in the episode is that elders at times are overprotective and consequently, delay the activities of children whom they love; fasting and school admissions are prime examples of the delayed activities.

This article is based on the sad situation of the writer’s classmate.

[HAJIRA KHANstudies at Indian School Salalah, Salalah, Sultanate of Oman]

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World of Satellites

11 Jan 2015 logo 0 comments


A satellite is any object that orbits around another, larger body. The Moon, for example, is a natural satellite of the Earth. An artificial satellite is a manufactured object that continuously orbits the Earth or some other body (moon, planets or sun) in space. Such satellites are used for gathering information about the other heavenly bodies. Most artificial satellites orbit the Earth. In this article, we shall discuss the artificial satellites in detail.

The British physicist, Sir Isaac Newton (1643-1723) in 1687 presented his theory of gravitation. An object when thrown up is pulled back to the earth. He formulated the equations governing the motion of bodies. He also calculated the speed required to launch a body into an orbit around the earth. It is about eight kilometres per second. The famous Russian physicist, Konstantin Tsiolkovsky (1857-1935) formulated the details of the space travel and rocket design towards the end of the 19th century. In his works, he described the future of satellites and even human travels into space. The works of Newton and Tsiolkovsky remained an academic exercise till the rocket technology was developed in the latter half of the 20th century.

On 4 October, 1957, the Soviet Union launched Sputnik 1, the first artificial satellite. It circled Earth once every 96 minutes and transmitted radio signals that could be received on Earth. On 3 November, 1957, the Soviets launched a second satellite, Sputnik 2. It carried a dog named Laika, the first animal to soar in space. The United States of America launched its first satellite, Explorer 1, on 31 January, 1958, and its second, Vanguard 1, on 17 March, 1958. This started the space age. Now there are thousands of satellites playing key roles in the communications industry; in military intelligence; and in the scientific study of both earth and outer space. Engineers have developed many different types of satellites designed to serve specific purposes. We shall briefly describe some of them below.



The communications satellites serve as relay stations, receiving radio signals from one location and transmitting them to another. A communications satellite can relay several television programmes or thousands of telephone calls at once. Communications satellites are usually put in a high altitude, geosynchronous orbit (an orbit that keeps the satellite over the same spot above the earth) over a ground station. A ground station has a large dish antenna for transmitting and receiving radio signals. Countries and commercial organisations, such as television broadcasters and telephone companies, use these satellites continuously. If not for the telecommunication satellites, our life would have been very different without the numerous television channels and the affordable telephone networks.



Navigation satellites help in locating the positions of ships, aircraft, and even automobiles that are equipped with special radio receivers (global positions systems or GPS). A navigation satellite sends continuous radio signals to earth. These signals contain data that a special radio receiver on earth translates into information about the satellite’s position. The receiver further analyses the signal to find out how fast and in what direction the satellite is moving and how long the signal took to reach the receiver. From this data, the receiver can calculate its own location. Some navigation satellite systems use signals from several satellites at once to provide even more exact location information.



Weather satellites have special cameras and other equipment pointing to analyse the earth’s atmosphere. The data collected from these satellites is relayed to the meteorological centres on the earth. These centres use the data to make weather forecasts. These are particularly useful in predicting and tracking of storms.



Military satellites include weather, communications, navigation, and earth observing satellites used for military purposes. They are designed to observe (using very powerful cameras) the number and location of the ships, tanks, airplanes and military equipment. They can even detect the launch of missiles, the course of ships at sea, and the movement of military equipment on the ground. Thus the satellites used for spying gives an advantage to the countries, which have access to the satellite data.



Scientific satellites enable in studying the earth in detail. They enable in knowing the size and shape of the earth in great detail, mapping its magnetic field, dynamics of the oceans and the atmosphere. There are many satellites for studying the moon, planets, sun and the cosmos. Some satellites are also searching for life in outer space.



The Aryabhata spacecraft, named after the famous Indian mathematician and astronomer from the 5th century, was India’s first satellite. It was completely designed and fabricated in India by the Indian Space Research Organisation (ISRO, It was launched by a Soviet Kosmos-3M rocket from Kapustin Yar on 19 April 1975. The success of the launch was celebrated by issuing a postage stamp on 20 April 1975! Aryabhata spacecraft was also commemorated by stamping its imprint on the Indian two rupee bank note from 1976 to 1977. ISRO’s vision is to harness space technology for national development, while pursuing space science research and planetary exploration. India has launched numerous satellites.

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Chandrayaan-1 was India’s first mission to the Moon. It was launched on 22 October 2008 from Satish Dhawan Space Centre, Sriharikota. Chandrayaan-1 became the first lunar mission to discover existence of water on the Moon. Mars Orbiter Mission known as Mangalayaan is India’s first interplanetary mission to planet Mars with an orbiter craft designed to orbit Mars in an elliptical orbit. Mangalayaan was launched into Earth orbit on 5 November 2013 by ISRO and entered Mars orbit on 24 September 2014. Only the US, Russia and Europe have previously sent missions to Mars, and India has succeeded on its very first attempt!

Since the dawn of space age in 1957, about 6,600 satellites have been launched. The latest estimates are that 3,600 remain in orbit, of which about 1,000 are operational. The rest have lived out their useful lives and are part of the space debris. Over the last six decades the artificial satellites have changed our way of life in many ways. It is difficult to predict the influence of satellites on our lives in times to come.

[HAJIRA KHAN studies at Indian School Salalah and SAMEEN AHMED KHAN teaches at Engineering Department, Salalah College of Technology, Salalah, Oman.]

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Floating Magnets Revisited

23 Nov 2014 logo 0 comments


Most of us are familiar with magnets. They are used in everyday life. Very simple applications are such as the magnets used for sticking decorations on fridges. Magnets are also used for lifting small objects such as pins and clips. The tips of many tools such as screwdrivers are magnetised so as to lift the nuts and screws. Importantly, magnets are used for knowing the direction. This is because a freely suspended magnet shows the north and south direction of the Earth. This forms the basis of the magnetic compass. A graduated compass can be used to locate the Qiblah, the direction of Makkah Mukarramah required for offering Salaat (Namaz or Prayers).

The study of the magnets dates back to ancient times. The ancients were fascinated by their ability to attract iron and show direction. In modern understanding, we say that every magnet has two poles: “north seeking pole” and a “south seeking pole” which we simply call the north-pole and the south-pole respectively. The opposite-poles attract and the like-poles repel. When a magnet is broken, we obtain a pair of magnets. It is not possible to separate the poles. They always occur as a pair within a single magnet. The Earth behaves as if it has a huge bar magnet inside it. The Earth’s magnetic field is a mystery, which is an active field of research. Geological studies point to the fact that the direction of the Earth’s magnetic field reverses after few million years.

In the 19th century two discoveries were made: (1) a wire carrying electric current behaves like a magnet; and (2) a moving magnet induces current in a coil of wire near it. The first discovery led to the invention of very powerful electromagnets, with controlled properties by changing the current. The second discovery gave birth to the dynamo and the transformer. These discoveries revolutionised the technological applications of magnetism and electricity. It will be difficult to imagine a life without electricity and magnetism. Many applications of magnetism include motors, loudspeakers, variety of measuring instruments. Magnetic memories are used in making videos, compact discs, flash memories and computer storage devices. High magnetic fields are used in medical diagnostics from high resolution images obtained using techniques such as the MRI (magnetic resonance imaging). Such techniques have certain advantages over traditional X-Rays.



Like-poles of two magnets repel. This property can be used to float magnets. This is easily achieved using two-ring magnets. Ring magnets are cylindrical magnets with a hole in the centre. The diameter is usually much larger than the height of the magnets. The ring-magnets are present in speakers and microwave ovens. A wooden dowel (rod or pole) or a pencil is vertically attached to a wooden block by a screw. The first ring-magnet is placed over the wooden dowel. The second magnet is brought close to the first magnet to feel the magnetic forces and decide which of the two poles repel. After identifying the repelling pole the second magnet is placed over the dowel in such a way that the like-poles face each other. This makes the second magnet float. In a similar manner, the third ring-magnet is also placed over the dowel.

The procedure can be repeated to place several more ring-magnets on the dowel. The force of gravity pulls the magnets down and closer to each other. The force of repulsion between the like-poles overcomes the force of gravity and makes the magnets float. The distance between the first and the second magnet is the least, followed by the second and the third, followed by the third and the fourth, and so on. The first magnet has to bear the weight of all the magnets; hence the distance is the least. The assembly of magnets on the dowel behaves very much like a spring.

If the magnets are pushed down, they resist, just like a spring. Care needs to be taken while bringing the unlike-poles of the magnets together. The force is strong enough to cause injury and damage. One can also attach a pan on the topmost magnet on the dowel and make a weighing device. The numbers can be marked on a scale attached to the dowel.

Magnets have numerous applications in our life. The force of repulsion between the like-poles can be used to levitate the magnets. It would be an interesting exercise to study the pattern of the increasing gaps between the ring-magnets on the dowel.

[HAJIRA KHAN is studying at Indian School, Salalah, Oman &SAMEEN AHMED KHAN is on the Engineering Department, Salalah College of Technology (SCOT), Salalah, Oman.]

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