Blog Post #122: Tribute to the Maths Genius Srinivasa Ramanujan on his 133rd birth anniversary

As we near the end of an unprecedented year, here's a short blog post on the occasion of the birthday of an eminent personality whom I admire and revere the most - Mathematician Srinivasa Ramanujan

Dec 22nd 2020 marks the 133rd birth anniversary of the Mathematical genius and needless to say this day won't be complete without looking at some incredible number patterns

Let's look at few of them

a) 1887 + 2020 is 3907 which is a Prime number

b) 2020 - 1887 is 133 which is the product of two prime numbers - 19 and 7!

c) Add the digits of today's date in pairs - 22 + 12 + 20 + 20 and the resultant number is 74. Reverse of 74 is 47 and when you add both we get 121 which is a perfect square and a palindrome!

d) Now add the individual digits of the date - 2 + 2 + 1 + 2 + 2 + 0 + 2 + 0 which gives us 11 - square root of 121 in the previous step!

e)  Extract the 1st and last digits of both 1887 and 2020 - 17 and 20. Sum of these two numbers is 37 and difference is 3. Now multiply 17 with 37 and 3 - the resultant is 1887!!

f)  It does not stop there.. Hold on! 

133rd birth anniversary is special as well in many sense

- 133 is a product of two primary numbers as we saw earlier

- 133 is also a sum of two cubes - 125 and 8 (5 ^ 3 + 2 ^ 3)

- 133 is difference of two perfect squares - 169 and 36 (13 ^ 2 - 6 ^ 2)

I am sure we can go on and on as there are infinite possibilities when we start talking about the Mathematical genius and humble tribute to "The Man who knew Infinity"!

Blog Post #121 - 12/12/2020

 Time flies and we are already in December in an year which has been unprecedented in nature and we continue to look for positives before we step into 2021

12/12/2020 is a bit unique many ways and today's blog post is around some of the patterns that we see around this date which also coincides with the Computer Science Education Week (Dec 7th to 13th)

1. 12 + 12 + 20 + 20 is a perfect square (64) which is a core number in computer/digital world and it is a sheer coincidence with Computer Science Education Week 

2.   12 * 12 gives 144 and 20 * 20 is 400. Difference of the two is again a perfect square (256) and square of 256 is 65536 which again is a most familiar number in Computer world

3. The best is always reserved for the last

Sum of the digits - 1+2+1+2+2+0+2+0 = 10

Sum of the squares of the digits - 1 + 4 + 1 + 4 + 4 + 0 + 4 + 0 = 18

Sum of the cubes of the digits - 1 + 8 + 1 + 8 + 8 + 0 + 8 + 0 = 34

Sum of the fourth power of the digits - 1 + 16 + 1 + 16 + 16 + 0 + 16 + 0 = 66

Notice the sequence - 10, 18, 34, 66

The difference between successive numbers is 2 ^ 3, 2 ^ 4, 2 ^ 5 and you could guess what would be the next number in the series without doing any further complex maths!

Maths is fun and 12/12/2020 is just another reason why we can feel more optimistic as we move towards 2021

Blog Post 120: Fascinating world of Prime factors

The world of prime numbers and prime factors has been always fascinating and always amazes me with interesting patterns.

As we start a new week after the Diwali long week-end, 17th November being the first working day for many of us in this part of the world, here's a short but interesting sequence starting with the number 1711 (dd-mm format for 17th Nov)

- To start with, 1711 is made up of two prime numbers - 17 and 11

- 1711 itself is not a prime but a product of two prime numbers - 29 and 59

- Next form a 4 digit number combining 29 and 59 which gives us 2959. 2959 is not a prime but again a product of two primes! - 11 and 269

- Let's go a step further and form a 5 digit number with 11 and 269 which gives us 11269. What's interesting is that 11269 follows the same pattern - It is not a prime but again it is a product of two primes - 59 and 191 (As a side trivia, check how 59 appears across multiple numbers here)

- Next in line - the 5 digit number 59191 (59 and 191 together). Voila - 59191 is also a product of two primes 11 and 5381!!

Tempted to go one step further

- 115381 - this is a product of 7 and 16483 while 16483 in turn is a product of 53 and 311

Though in some sense the sequence is "broken" as 115381 is a product of three prime numbers instead of two but we could see the sheer beauty of prime factorization in play through this example

What could we learn from Prime factors - the need to have a differentiated offering in whatever we do and create something unique

Dedicated to some of my colleagues, friends who are celebrating their work anniversaries or birthdays or other events on 17/11!

Blog Post #119: Dedicated to M S Dhoni

As a keen follower of cricket and someone who watched MSD in awe soaking in pressure time and again and still maintain a calm and cool head, here's a small Mathematics note for the Man who gave enough for Indian fans world over to cheer over the last decade

1929 hrs is the time when he announced his retirement. 

a) As Mayank mentioned in another post, he always had 7 as his lucky number and so 1+9+2+9 adds up to 21 which is a multiple of 7

b) 2020 - 1929 is 91 which is again a multiple of 7 and in spite of our misgivings about Year 2020, MSD probably scored a perfect score there as well and let's remember that he scored 91* in the 2011 World Cup final!

c) 1929 is also 7:29 P.M - 729 is a perfect square and MSD almost always set himself for a perfect finish

d) The number equivalent of the letters in his name M S DHONI (13 + 19 + 4 + 8 + 15 + 14 + 9) adds up to 82 and 1929 + 82 is 2011 which was the year when we won the World cup again under his captaincy!

e) Last but not the least he was fondly called MSD in short - Number equivalent of MSD (13+19+4) adds up to 36 which is "sixer" squared - Yes the helicopter shot was worth 36 always and not a simple 6!

#ThankYouDhoni #MSD #ThankYouMahi #MSDhoni

Blog Post #118: Dissecting 2020!

Year 2020 has been in the news for various reasons and has been the trigger for memes, jokes among others and needless to say most of them reflected a pessimistic outlook till now

I have attempted to take a more optimistic view of the Year as we step into the month of August and what better way to do it - Combination of Numbers through two different scenarios!

Scenario 1:

To illustrate this, I am going to express 2020 as a sum of two different perfect squares

Combination 1:

1764 + 256 = 2020 (42 ^ 2 + 16 ^ 2)

Combination 2:

576 + 1444 = 2020 (24 ^ 2 + 38 ^ 2)

What's unique about this as there are quite a few numbers which can be expressed as sum of two squares

Let's get a bit deeper at Combination 1 to start with

1764 ==> 17 + 64 is 81 (yes it is a perfect square)

256 ==> 2+5+6 is 13 (prime number)

Combination 2

576 ==> 5 + 76 is 81 (same as above)

1444 ===> 1+4+4+4 is 13! (same as above)

Remember that I have used the same principle for Combination 1 and Combination 2 to highlight the unique pattern

Conclusion: If your team starts with a specific goal in mind, the path taken by each sub-groups could be different but the broader principle they follow (aka rules & regulations) can still be intact.

2020 is a pretty good example for that!

Scenario 2:

2020 could be expressed as 1000 + 729 + 100 + 81 + 19 + 91

In turn this can be written as 10 ^ 3 + 9 ^ 3 + 10 ^ 2 + 9 ^ 2 + (10 ^ 2 - 9 ^ 2) + (10 + 9 ^ 2)

or

10 ^ 3 + 9 ^ 3 + 10 ^ 2 + 9 ^ 2 + (10 + 9) + (10 ^ 2 - 9)

Amazing to see how 2020 can be expressed as a combination of two numbers 10 and 9 using different set of operators

Conclusion: We could start with smaller building blocks and once we figure out the right tools and techniques, we can achieve the target in multiple ways. Again 2020 is a prime example of that

We still have 5 months left this year and if someone has the right attitude and work towards a clear goal as target, there are multiple ways to achieve that !

Let's spin some more optimism around 2020 and move forward!

#2020 #Optimism #Positvity #AnandMathsBlog