How good you were in Maths !! - Tables !!!

 

How good were in you Maths !!  ~ remember that when we were young, we were taught Tables !  - upto 16 – in the class, students in chorus 1 x 8 = 8, 2x 8 = 16, 24,32,40,48,56,64,72,80,88,96 ………. 

This morning SYMA conducted a Medical camp at Chennai Middle School, Ramnagar, Triplicane – the infrastructure, class rooms, cleanliness all impressed me beyond a point ! [that will be subject matter of another post] – this about a blackboard containing tables ..  do children glued to mobiles and calculators still learn Tables ?!?!?

Perhaps  there isn't a single person who invented them. They developed gradually in ancient civilizations.  Some references put that the  earliest known multiplication tables come from ancient Mesopotamia. Babylonians wrote mathematical tables on clay tablets, using their base-60 (sexagesimal) system.   Egyptians had sophisticated methods for multiplication, but generally used doubling rather than memorising a complete set of tables. For example, to multiply by 13, they could successively double and add the required quantities.

                Indian mathematicians developed and used multiplication tables extensively. The decimal place-value system and zero, which emerged in India, made arithmetic and multiplication much easier. By the early medieval period, Indian mathematical texts contained systematic multiplication methods and tables. Chinese mathematics: China also developed multiplication tables very early. The famous “Nine-Nine Table” (九九表) was traditionally memorised as a sequence of products from 1×1 through 9×9.  

Nobody can really be called the inventor. Multiplication itself is thousands of years old, and tables evolved as a practical shortcut for repeated multiplication. The  “2 to 20 tables” tradition familiar in Indian schools is much more extensive than the standard 1–10 tables commonly taught in many Western countries. Aryabhata, Brahmagupta and Bhaskaracharya did not invent the school multiplication tables as such. They developed and codified arithmetic methods that made systematic calculation possible..

Before Aryabhata — multiplication was repeated addition -  5 × 4 = 5 + 5 + 5 + 5 = 20.  Indian mathematicians explicitly regarded multiplication as a form of repeated addition. The terminology was quite sophisticated: the number being multiplied and the multiplier had specific Sanskrit names, and the result had its own terminology.  Calculations were sometimes performed on a board covered with dust, hence the term dhūlikarma (“dust work”).  

Aryabhata, in his Āryabhaṭīya, gave a systematic treatment of mathematics (gaṇita) alongside astronomy. His importance to the later tradition is not that he created “2 times table, 3 times table…” but that he codified mathematical procedures in a highly systematic form. His work became the foundation for generations of Indian commentators and mathematicians. An important point is that these texts were written in compact Sanskrit verse, partly because mathematical rules were intended to be memorised. So there was already a strong tradition of learning numerical rules by heart—something that eventually fits very naturally with the school practice of reciting multiplication tables.

About a century later came Brahmagupta. His Brāhmasphuṭasiddhānta, written in 628 CE, contains an extensive treatment of arithmetic, including multiplication, division, fractions, negative numbers and zero.  Consider: 347 × 26. Today we instinctively understand that:

6 × 347 = 2082

20 × 347 = 6940

therefore 2082 + 6940 = 9022.

That depends on understanding place value — units, tens, hundreds — and the decimal numeral system. Indian mathematicians developed increasingly sophisticated arithmetic using this system. Historical descriptions of Indian multiplication methods show procedures remarkably close in principle to the long multiplication taught in schools today.   

Much later in the 12th century,  Bhaskaracharya’s famous Līlāvatī, part of the Siddhānta Śiromaṇi, contains extensive arithmetic and specifically discusses methods of multiplication and squaring. Bhaskara II gives methods of multiplication that involve arranging numbers in particular positions and multiplying their individual digits—methods that are recognisably related to the algorithms used later in traditional arithmetic teaching. And Līlāvatī is particularly interesting because it doesn't merely give rules. It presents problems for students to solve, including arithmetic progressions, interest, fractions, geometry and other numerical problems.

The modern Indian school tradition of Maths tables  is not something we can attribute to Aryabhata or Brahmagupta individually. Rather, it grew out of the broader Indian tradition of: number → place value → repeated addition → multiplication rules → memorised computational rules → school arithmetic. The fact that Indian mathematical texts were composed in concise, memorable verses also encouraged oral memorisation. Over centuries, this developed into the familiar practice of children reciting tables aloud.

The traditional Indian method of multiplication was so influential that medieval Europeans sometimes referred to Indian arithmetic as “modus Indorum” — the method of the Indians.  So when an Indian child today confidently rattles off “13 ones are 13, 13 twos are 26…”, there is a very long mathematical ancestry behind that apparently simple school exercise.

Interesting ! – back to Basics ! – back to schools !!

 

Regards – S Sampathkumar

4.10.2026

If ships end up at breaking (grave)yards ... aircrafts at boneyards...

In 1979, when we were at school, the film ‘Ninaithale Inikkum’ directed by K Balachandar, starring Kamal Rajni, Jayapradha opened with rave reviews.  The story moves to Singapore and my friends remarked that aeroplane taking off is being shown and great one at that.  Those were the days, when most had never seen a plane closer.

Davis–Monthan Air Force Base  is a United States Air Force base located within the city limits of downtown Tucson, Arizona. It was established in 1925 as Davis-Monthan Landing Field. The base has been named in honour of World War I pilots Lieutenants Samuel H. Davis and Oscar Monthan (1885–1924), both Tucson natives. Davis, who attended the University of Arizona prior to enlisting in the Army in 1917, died in a Florida aircraft accident in 1921. Monthan enlisted in the Army as a private in 1917, later became a pilot; he was killed in the crash of a Martin bomber in Hawaii in 1924.

Away from air, looking at the sea, the sight of a very large vessel floating on water, carrying goods from one place to another offers imagination beyond dreams. Man has conquered the ocean sailing across with the aid of ships and boats which developed alongside mankind. Vessels have borne the key in history’s greatest explorations. The cargo - from slaves to modern day containers, dry and wet, live, frozen and refrigerated, big machineries, bulk cargo, liquid cargo – the variety is endless.  But just as most things have a shelf life, ships also have a limited span of life. These vessels who have outlived its existence are sold and dismantled to recover the valuable steel – that is all about ‘ship breaking’ at yards where the majestic creature gets reduced to a skeleton and eventually wiped out of existence.

It is written that down South Kolb Road in the Arizona city of Tucson,  just like one sees concrete structures on any modern city, one would find rows of military aircraft, still and silent, spread out under the baking desert sun. On and on, everything from enormous cargo lifters to lumbering bombers, Hercules freighters and the F-14 Tomcat fighters made famous in Top Gun ~ and that is Davis-Monthan Air Force Base, run by the 309th Aerospace Maintenance and Regeneration Group (309 AMARG). It’s home to some 4,400 aircraft, arranged over nearly 2,600 acres (10.5 sq km). Some look like they were parked only a few hours ago, others are swathed in protective coverings to keep out the sand and dust.

….. and the reason for they being there inside the facilities' hangars – stand reduced to crates of spare parts  waiting to be sent out to other bases in the US or across the world to help other aircraft take to the air again. ….. they call it ‘boneyard’. Davis-Monthan is not the only aircraft boneyard in the world; it is by far the biggest. The climatic conditions in Arizona – dry heat, low humidity, little rain – mean aircraft take a lot longer to rust and degrade.

A BBC report puts it that another post-Soviet boneyard is in the Chernobyl Exclusion Zone – the area evacuated after the 1986 nuclear disaster in Ukraine. The vehicles used to help clean up the disaster area were contaminated with radiation. A line of giant Soviet helicopters has been left to rust in the fields. BBC News pictures editor Phil Coomes visited the site in 2006, on the 20th anniversary of the disaster. “After the nuclear accident at Chernobyl, many of the contaminated vehicles used in the clean-up operation were placed in graveyards in the vast exclusion zone around the reactor.  Though they remain at the largest graveyard, souvenir hunters would be wise to keep away as there could be still contamination from radiation.  Despite the danger of radiation poisoning, many of the helicopters have been stripped of useful parts; their skeletal remains dwindle with every passing year.  In eastern California, Mojave Airport carries out a similar role for civilian aircraft that have reached the end of their operational lives. Airliners have been flown here for decades, and stored in the dry desert heat until broken up for scrap.

Aircraft boneyard (Aircraft graveyard) is a term for a storage area for aircraft that are retired from service. Most aircraft at boneyards are either kept for storage or turned into scrap metal. Deserts, such as those in the Southwestern United States, are good locations for boneyards since the dry conditions reduce corrosion.  It could be surrealistic view to see so many aircrafts lined up in one place, factual is that those aircrafts constructed spending thousands of dollars are idling with no productive use. 

As it turns out, the airline industry goes in cycles. The boneyards first filled up after WWII when the military downsized and converted to jet aircraft.  The next wave of idle planes happened during the oil crisis in 1974. With the  travel shock of the 1991 Gulf War, thousands of airliners were sent to the desert.  The 9/11 attack  and continued terrorist threats, high cost of fuel, and passenger concern, the boneyards continued to fill up.  Ironically, some aircraft that were on order as of 9/11 were rolled off of the assembly line, and flown directly to storage in Mojave without carrying a single paying passenger.

With regards – S. Sampathkumar

25^th Sept. 2014

Many thanks to BBC from which most of boneyard report is reproduced.

another Amma brand ..... CM Ms J Jayalalithaa launches 'amma cement'..

For ages, the dream of middle class is to have a house of their own … The first things that comes to mind when one thinks of construction is – cement – the binder, a substance that sets and hardens and can bind other materials together. The word "cement" traces to the Romans. Cements used in construction can be characterized as being either hydraulic or non-hydraulic, depending upon the ability of the cement to be used in the presence of water.  The most important uses of cement are as a component in the production of mortar in masonry, and of concrete, a combination of cement and an aggregate to form a strong building material.

Portland cement (thought it was a brand by itself) is the most common type of cement in general use around the world, used as a basic ingredient of concrete, mortar, stucco, and most non-specialty grout. It developed from other types of hydraulic lime in England in the mid 19th century and usually originates from limestone. It is a fine powder produced by heating materials in a kiln to form what is called clinker, grinding the clinker, and adding small amounts of other materials. Portland cement is caustic so it can cause chemical burns. 

India is the second largest cement producer in the world. However, it is way behind China, where the capacity is more than five times larger. In India, it has a high rate of excise duty and accounts for 5% of total excise duty collection.   The major raw material required is limestone gypsum, coal & power. India is having a huge deposit of limestone.  Limestone is available in  Andhra Pradesh, Karnataka, Gujarat, Rajasthan and Madhya Pradesh. Gypsum is another important material which is required along with clinker.

Back home in Tamil Nadu, the 'Amma brand' is doing great.  One would nurse different views on what Govt should be doing – but Tamil Nadu CM J. Jayalalithaa took a giant leap forward when in her poll manifesto, she announced distribution of free mixers, grinders, fans, milch cows and goats, laptops to students, bus passes, free bicycles and more.    In a metropolis replete with hotels and restaurants – big and small, individual outlets, big chains and franchisees of International brands…..  the State Government forayed in to food industry setting up Amma Unavagams in all wards in the city, which instantaneously became a very big hit. Then came another master stroke - the packaged drinking water project ……. ‘the amma water scheme’ formally launched on 15th Sept. 2013.   ~ and in the State of famed Vedaranyam where Rajaji and others fought British with salt – Ms Jayalalithaa launched ‘amma salt’….. not stopping with the success,  Tamilnadu Chief Minister aspired to provide all kinds of medicines, from routine to life saving drugs at affordable costs to the common man.  And  ‘Amma Marunthagam (medical shops)’ came into being.   

There is no stopping of ‘success tidal waves’ - The Tamil Nadu government has today announced a populist ‘Amma Cement Scheme’ under which it will procure cement from private manufacturers and sell them at Rs. 190 per bag in the wake of possible increase in rates of the key construction component. The scheme, named after Chief Minister Jayalalithaa, who is addressed as ‘Amma’ (Mother) by her supporters, follows similar efforts  which have been all low-cost initiatives.

Ms. Jayalalithaa said she had recently discussed with officials the situation regarding production of cement from the State and supply from outside. The erstwhile united Andhra Pradesh contributed about 4-4.5 lakh tonnes of cement for Tamil Nadu’s monthly average use of 17-18 lakh tonnes, but the companies there had now hiked the prices by Rs. 80-100 per bag, she said. “Subsequently, the supplies to Tamil Nadu had reduced to around 1.50 lakh tonnes to 3 lakh tonnes, creating a favourable situation for the private manufacturers here to increase price of cement,” she said in a statement.

Therefore, she had directed officials to roll out the “Amma Cement Scheme” aiming to benefit the lower and middle classes, wherein the government will procure two lakh tonnes of cement from private manufacturers every month and sell them through all urban and rural local bodies at Rs. 190 per bag. Beneficiaries are eligible for a maximum of 750 bags for 1500 sqft, and the cement could be bought by submitting the government approved building plan or the road plan, she said. Those wanting to buy cement for repair and renovation are eligible for 10 to 100 cement bags, she said.

Tamil Nadu Cement Corporation will be the nodal agency while the scheme will be implemented by Tamil Nadu Civil Supplies Corporation and Rural Development Department through their 470 godowns, the Chief Minister said. The scheme will also cover the state’s Green House and Central government’s Indira Awas Yojana, she said adding, it will help ease the burden of lower and middle class in constructing a house.

Here is the price list of cement 50 kg bags as on 25^th Sept. 2014: source :  http://www.livechennai.com/cement_Price_List_Chennai.asp

Cement Price List
Items	Prices (Rs.)
Dalmia Vajram	350.00
Dalmia PPC	350.00
Ramco Super Grade	350.00
Ultratech	350.00
White Cement	865.00

With regards – S. Sampathkumar

26^th Sept. 2014.

Selfie ..... Elfie.... Theftie ........... the list grows !!!!

I have posted earlier on Selfies; on what was dubbed as ‘sickest selfie’ of all times by the Newyork Post; an International selfie that was decried….and more….  I had also posted on the news of ‘British women spending  a  month of their lives taking selfies... some climb the ladder of success through ‘Selfie’ too in the mould of Triana Lavey  who had a chin implant, nose job, cheek-defining fat grafts and Botox ~ now  makes a living help others to make money using selfies.  Heard of ‘elfie’ or  ‘theftie’ ……. Read on ……

Daily Mail reports of the moment an elephant at a wildlife park used an iPhone to take the world's first ‘elfie’. Visitor Scott Brierley, 23,  of Birmingham, had been traveling in the West Midlands Safari Park’s drive-through elephant zone in Bewdley, Worcestershire, taking pictures of the African animals. But as Mr Brierley, took one photograph on Bank Holiday Monday he dropped his mobile phone and the keepers ordered him to stay in his car and keep moving. Staff later retrieved his iPhone and Mr Brierley was stunned to see 22-year-old elephant Latabe had touched the screen with her trunk - and taken a picture of herself.

The events manager said he has now got the world's only elephant selfie, adding: ‘I live quite close to the park so I've been there a few times. The elephants are my favourite along with tigers. He is quoted as saying that when the phone fell down on the grass, the elephant was all over it - I think he thought it was food. I didn't dare get out the car to get it. I just drove to one of the workers I could see and he went to get it.  ‘I really couldn't believe when the iPhone came back, I pressed the centre button to check it was still working and “wow”, there it was. Me and my friend were in shock.

Though the elephant had taken two pictures, only one was good.  The keeper said, he was proud of the elephant named Latabe. The 200-acre West Midlands Safari Park was opened in April 1973 and admission is £18 for adults.

On a more serious note, here is something that technology can offer again linked to ‘selfie’ ……… this post in Daily Mail is about an application developed by San Francisco-based company Lookout that takes 'theftie' photos and emails  the lost phone's location to help track down a stolen mobile.  The theftie - a selfie accidentally by a thief - will be accompanied by a map.  Phone's front-facing camera is triggered by a thief entering a wrong password, taking out the SIM card, turning it off or engaging 'airplane mode'

With that innovative app of San Francisco-based security firm – ‘selfies’ are no longer so intentionally taken – but include accidentally taken ones of hapless thieves.  They provide users with alerts when suspicious activity occurs on their iPhone or Android handset. Thieves often remove a SIM card and turn off a device after stealing it to prevent the owner from tracking it. So the Theft Alert service sends the victim an email with a photo of the thief and a map of the device's location within minutes, to give the victim the best chance of recovering their handset - and with it, private information. Lookout, the company behind the idea, added the new 'Theft Alert' to its premium service, which is designed to be used on iPhones and Android handsets. The premium version of Lookout costs $3 a month or $30 for the year and includes features such as backing up data, virus protection and finding lost phones. Wait gentlemen, it is not available in our land ~ nor is it available on Apple devices because the operating system won't allow it.  One in 10 smartphone users in France, UK, Germany and the U.S. have had their phones stolen, according to a report by IDG Research on behalf of Lookout.

Interesting and useful technology indeed….

With regards – S. Sampathkumar