TASTE OF INDIA PART II
I hope you had a good time learning Vedic maths in the 1st part of this series.Today we will speak of mathematics and Hemachandra numbers ( the series of recurrences) 
Mathematics is, in large part, the search & study of patterns and for the explanations as to why those patterns exist. We will see the use of these patterns in day to day life.
Example: Patterns in motion of planets led to theory of gravitation or patterns in genomes help in curing disease.
Lets start the math with the universe of Whole Numbers:
What are whole numbers :
……-4,-3,-2,-1,0,1,2,3,4,…..
Lets see some number sequences below:
1,1,1,1,1,1,1,1,1,…. All 1’s
1,2,3,4,5,6,7,8,9,….Counting numbers
1,3,5,7,9,11,13…. Odd numbers
2,4,6,8,10,12,14…Even numbers
1,4,9,16,25,36,….squares
1,8,27,64,125,…..cubes
1,2,4,8,16,32,64,128,….Powers of 2
1,4,16,64,256,1024,4096….Powers of 4
Lets see now how sequences are related:
Example 1: Odd numbers and Square numbers are related
How ?
When you add up the odd number sequence you get the square number sequence
1=1
1+3 =4
1+3+5=9
1+3+5+7=16
Formula : 1+3+5+…..(2n-1) = n square
Example 2: Counting numbers and square numbers are related
How?
When you add up the counting numbers sequence to a point N and back to 1 , you get the square numbers sequence.
1=1
1+2+1 =4
1+2+3+2+1 = 9
1+2+3+4+3+2+1 = 16
Formula : 1+2+3 + ….+ n +…..+ 3+2+1 = n square
Now lets see the Hemachandra number series : (Hemachandra (1150 AD) number series also written by Gopala ( 1135 AD ) also known as Fibonacci( 1200 AD))
Write down 1 and 2
The next number is the sum of the previous two numbers
1,2,3,5,8,13,21,34,55,……..
Formula: Hn= H (n-1) + H ( n-2)
So which is the 7th number in the series , look up and count , its 21. and so on.
Where is it applied ?
Hemachandra numbers in Sanskrit Poetry :
Poetry has 2 syllables – Long ( 2 beats) And Short ( 1 beat)
The number of ways you can fill up 8 beats:
Long Long Long Long = 2+ 2+2+2 = 8
(Short Short ) X 4 = 8
Short Long long Short Long = 1+2+2+1+2 = 8
So answer to the question that in how many ways can you fill up 8 beats , see the 8th number in the Hemachandra sequence : answer is 34.
Hemachandra numbers in Nature:
a) Daisies ( flower) have 13 , 21, 34 petals – all Hemachandra numbers
b) Pine Cones have 8,13,21,24 etc spirals – again all in the Hemachandra numbers series
Now , lets evaluate some others mathematical concepts.
Prime Numbers
2,3,5,7,11,13,17,…….
Prime numbers have only two factors , 1 and itself
You cannot have two numbers multiplied to get that number – that is a prime number.
So lets see for example the number 13 = 1X13 = 13 = two factors only , 1 and 13.
But these prime numbers were discovered way before humans by nature.
You know Cicadas ? These are insects ( bugs)
Cicadas live underground and emerge only once every N years , where N tends to be a prime number like 13 or 17
Why ?
The hypothesis is that then N is least likely to be a multiple of the length of the predators population cycle which could kill them off.
Indian Cicadas come out every 7 years and some every 19 years
In America , they come out every 13 years and 17 years.
It was observed that those coming out in years other than prime numbers were predated and lost their lives so this pattern has become common that they come out only in prime number years , based on their predators life cycle!!
Prime numbers in everyday life
Suppose you have two 200 digit prime numbers
Give them a computer , and it can multiply them in a fraction of a second and give the answer which will be a 400 digit answer.
Now take this 400 digit answer and give it another computer , and ask to find the original two 200 digit prime numbers.
The best known algorithms , working on all the worlds computers , would still take billions of years to find those two 200 digit prime numbers !!!!
Which means A multiply by B = C – here finding C is very easy A XB but to reverse find the factors A and B which result in C is impossible !
So basis this , it is easy to multiply two large prime numbers but hard to do the reverse process , is the basis of the world’s encryption !!!!
Often when we submit private information on the internet , prime numbers are what are being used to encrypt the information and protect it since no one knows how to find factor numbers ( or so we think ) this method of encryption is presumably secure !
The thesis is that it is difficult to go backwards and find the factor or find a quick way to find the factor. So the problem of factoring is the basis of encryption technology.
(Opposite of multiplication is factoring – 10X10 = 100
100 is multiplication and factoring is to know 10 and 10 are the factors)
142857 :
Example of 142857 – a 6 digit number – so we will multiply it till 6 and see:
142857 X 1 = 142857
142857 X 2 = 285714
142857 X 3 = 428571
142857 X 4 = 571428
142857 X 5 = 714285
142857X 6 = 857142
Look closely , the same numbers get interchanged in the answers , observe carefully!!!!!!!
Are there such n digit numbers so the if you can multiply by 1 through n , the number just cycles around ?
Yes example is 0588235294117647 ( 16 digits)
Try multiplying this 16 digit number with 1 and till 16 and the answers will be the same numbers just circling around.
Are there infinitely many such numbers ? No one knows ….
Reasons for this pattern is Self similarity and Fractals:
Examples of self similarity and fractals in Nature are as follows:
Fern leaves – each leaf is just the same as another of its leaf.
Similar fractals are snowflakes , leaves , clouds , coastlines , mountains , lightening ……
Another example of Fractal architecture is The Kandariya Mahadev Temple in Madhya Pradesh
Self similarity in man made art :
Fulani wedding blanket from Nigeria
M.C. Escher the Dutch artist who made mathematically influenced graphic art – zoom a picture and you keep seeing the same picture in the picture.
In todays times , Princeton University even has a Fractal broccoli !
Thanks for taking the time to read this ancient power of Indian sciences and now you can go back to WhatsApp university to learn and argue on what NDA did or UPA did which is our current obsession !
Pride is a result of complex. So if you are already feeling proud that it was an Indian who discovered these patterns and not the Italian Mathematician Fibonacci , it has nothing to do with Hemachandra or Fibonacci , it is to do with your own complex. And yes , I purposely didn’t mention that Hemachandra was a Jain monk born in Gujarat so as not to let any artificial pride get in the way of understanding the subject for what it is. Happy Easter!
PS: This article is directly influenced from the lectures and work of the current generation mathematician at Princeton University , Professor Mr Manjul Bhargava!



Companies are made-up of management and staff that are invariably a unique combination of brains and personalities. Being able to bring all their talents together, in order to achieve success, is a paramount challenge.
CSS Group recently received Ms. Lilia Garcia, Foreign Sales Manager of IFS Spain at the Regional Headquarters of CSS Group in Dubai. Her visit was as part of a strategic sales campaign initiative to CSS Offices in the Middle East. Along with the subjects of mutual interests and business development, the current market scenario -too- was brought in to the discussion table by both companies. It was mutually agreed to work more closely to enhance business in 2019 through the trade lanes which are already open.
“In IFS, we believe that the close and continued contact with our partners is the way to improve our common service to the freight forwarders and to understand their needs” mentioned Lilia to Lighthouse.
Breakbulk Middle East provided opportunities to interact on several platforms, for the participants. The event was well attended by CSS delegates and participated at the networking dinners. One such was organized by Höegh. Head of Country (UAE), Finn Roden from Höegh invited for a presentation of their Breakbulk cargo handling initiatives, followed by a Customer Appreciation Dinner at the -“Bliss 6” Restaurant-The Conrad Hotel Dubai on the 11th of February.

Now take 1000 as the base
The ability to produce through imaginative skill, to make or bring into existence something new.”
The United Arab Emirates is essentially a civil law jurisdiction heavily influenced by French, Roman, Egyptian and Islamic law. Common law principles, such as adopting previous court judgments as legal precedents, are generally not recognized. In 2004, Dubai’s ruler at that time established The Dubai International Financial Center (The DIFC) Courts, providing an independent administration of justice in DIFC, attempting to ensure that Dubai would offer to its players the highest international standards of justice administration, and efficiency, flexibility and certainty that is usually provided by the Common Law.
Multitude types of sound – office chatter, crowds cheering, car horns blaring, babies crying, dogs barking, birds singing and waves breaking on the shore, all affect us in different ways. Often we fail to recognise their impact as we relegate them to the backdrop hubbub of what we are doing. However all these sounds influence us, and the way we feel within our environment, especially when we are unable to control them.
The CSS Group’s annual Strategy Meet 2018 was held at the Cinnamon Lakeside Resort, Colombo, Sri Lanka from the 15th to 17th November. Time to evolve continued to be the theme this year for the meet, which invariably declares the need for strategically design new plans and programmes to enhance the business performance in this most challenging time. The meeting was inaugurated by Sasikala (SK), Manager- Corporate communications, CSS Group.
Consolidated Shipping Services Group, has attained a reputable position in the industry with specialized operations in cargo consolidation (LCL), both in Ocean export and import. The reliability of world class transcontinental partnerships qualifies CSS Group to be amongst the leading NVOCC service providers from the GCC and the South Asia. Personalized client handling and global standards in cargo management has made CSS the most trusted partner in consolidation activities in the region where they operate, that too made possible with an enviable global network of partners.
Commencing in 2003, the combined efforts of both CSS Group and FPS Rotterdam has made them the market leaders today in the NVOCC industry. Mr. Jean-Paul van Munster, the CEO of FPS Rotterdam, spoke with Lighthouse on more about the mutual relationship. “It started when Mr. Kala and I visited Mr. Alvin Tan that time director of FPS Singapore at the same time. It was Mr. Alvin Tan who knew me since 1995 and figured that CSS and FPS Rotterdam had a lot to offer to each other, and he was absolutely right!”
While discussing about the industry and business, Jean-Paul mentioned about the beginning and growth of FPS Rotterdam. He was full of excitement when he narrated the story. “FPS, Famous Pacific Shipping B.V. originated from the 1992 founded forwarder TOP Trans Ocean Pacific forwarding. With the growing consolidation activities within TOP it was in 2001 when we decided to separate the consolidation activities from TOP and continue fully independently as a neutral consolidator under the name of FPS Famous Pacific Shipping Rotterdam, successfully led by its present director Ms. Saskia de Jong. During the past 17 years FPS Rotterdam has grown from its humble start to one of the leading consolidators in Rotterdam”.
In today’s world, where technology seems at times to be taking over our lives and where external noise is getting louder and louder, it’s becoming increasingly more difficult to maintain focus. Especially at work.
Whatever you set your goals at, remember that at the end of the day you need to be satisfied about what was accomplished and not waste it as we often do not controlling our own time and actions and spending the day doing only clerical tasks.
As part of its global expansion CSS Group is proud to announce the opening of its Sri Lanka enterprise. Consolidated Shipping Services, Sri Lanka – commenced operations from Colombo, on the 1st of December 2018