Blog Post #152: Another small tribute to Srinivasa Ramanujan

As we step into a New Year, I wanted to take a moment to share a small tribute to the great mathematics genius, Srinivasa Ramanujan, whose 138th birth anniversary we celebrated on December 22nd. Although I am a few days behind in penning this post, the inspiration Ramanujan continues to bestow upon me remains timeless.

 

Ramanujan's profound contributions to the world of mathematics continue to be a guiding light for many, including myself. His unique ability to perceive numbers and patterns through an unconventional lens always fascinated me. Each time I delve into the world of mathematics and numbers, I find myself marveling at the seemingly infinite possibilities and the elegance of Ramanujan's insights.

 

His legacy encourages us to approach problems with a different perspective by breaking those down into smaller chunks, that could be solved to arrive at the big picture

 

I have made an attempt to look at some interesting patterns around Ramanujan's birth anniversary. Here we go!

 

a) 22-12-2025 was his birth anniversary - If we add the digits the resultant is 16 which is a perfect square of 4 which in turn is a perfect square of 2

 

b) Now add the "squares" of each digit of Ramanujan's birth anniversary - 2 ^ 2 + 2 ^ 2 + 1 ^ 2 + 2 ^ 2+ 2 ^ 2 + 0 ^ 2 + 2 ^ 2 + 5 ^ 2 and the output is 46. At first glance it looks like any other two digit even number but here's why it is unique - 2025 is the only perfect square of this century and the next perfect square year is 2116. Guess what - Square root of 2116 turns out to be 46!

 

c) Let's group the birth date into two 4 digit numbers - 2212 and 2025. Now subtract 2212 and 2025 which results in 187. 187 is a multiple of 17 and 11. When we draw a parallel to Ramanujan's birth year - 1887, it shows a very similar pattern - 1887 is a multiple of 17 and 111!

 

d) There is always a connection between Ramanujan number (1729) and the entire universe and this blog post is no exception - Here's why!

 

2025 is a perfect square year as we know by now and the next perfect square year is 2116. The difference between the two of them is 91 and when 91 is multiplied by its reverse (19) the output is none other than Ramanujan number - 1729!! It does not stop there... The previous perfect square year was 1936 (44 ^ 2) and difference between 2025 and 1936 is 89. 89 ^ 2 is 7921 and guess what - Anagram of 7921 is 1729 again :)

 

Numbers and patterns continue to amaze us and glad that i could contribute towards that in a small way on the occasion of Ramanujan's 138th birth anniversary - "The Man who Knew Infinity" continues to inspire me and many others!

 

Wishing everyone a very Happy, Healthy and Prosperous New Year!

Blog #151: All about 9/25/2025

There has been multiple posts/videos around the specialty of today's date - 9/25/2025 since the next similar sequence won't happen till 2116! 9 is 3 ^ 2, 25 is 5 ^ 2, 2025 is 45 ^ 2. 46 ^ 2 is 2116 and that's going to be close to 90+ years from now

 

While this is certainly unique, the date 9/25/2025 also exhibits other amazing patterns and that prompted me to write a short blog post pretty quickly after the OTP/Palindrome one i had shared few days ago

 

Let's see some of the patterns at play for 9/25/2025 - looks pretty simple but not so apparent. That's the beauty of Maths and Number patterns

 

1. 9 ^ 2 * 25 gives 2025 (Month ^ 2 * Day = Year)

 

2. Add the digits - 9 + 2 + 5 + 2 + 0 + 2 + 5 = 25 which is the Day as well as a perfect square

 

3. Let's alternate addition and subtraction - 9 + 2 - 5 + 2 - 0 + 2 - 5 and the resultant is 5 which is the square root of the Day!

 

4. Now multiple all non-zero digits and the resultant is 1800. 1800 + (9 * 25) = 2025 again! 1800 + (MM * DD) = YYYY

 

5. Next add the non zero digits in pairs - 92, 52, 25 and the resultant is 169 which is a perfect square again (13 ^ 2) and its reverse that is 961 is also a perfect square (31 * 2) - Note that 13 and 31 are also reverse of each other

 

6. The numbers 9 and 25 are part of the Pythagoras pair - 9 + 16 = 25 and there were even various social media posts last week around it when the date was 9/16/25. 2025 is not left far behind and it is also part of a Pythagoras pair - 729 + 1296 = 27 ^ 2 + 36 ^ 2!

 

So while 2116 is the next perfect square as far as Year is concerned and it is 91 years away, let's be at awe on what 9/25/2025 has to offer and live in the current moment :)

Blog Post #150: OTP and Palindrome!

Received an OTP as part of one of my regular online transactions and when i saw the number 347743, i told my wife that it is a palindrome. Ofcourse she gave me a surprised look and moved on with rest of the chores that she was focusing on!! 

Given my penchant towards numbers, I started analyzing this in more detail and it was pretty refreshing to unearth some of the obvious and not so obvious properties. 

347 and 743 are the two numbers in consideration and to draw a parallel to the corporate world, this is a great example of how complementary skillsets within the team can help galvanize everyone to come together to achieve a common goal

Let's start looking at some of the characteristics exhibited by the number

1. Both 347 and 743 are prime numbers to begin but 347743 has 11 as one of the factors given it was formed by 347 and its reverse!

2. Subtract 14 from 743 and it gives a perfect square (729). Now give whatever has been subtracted from 14 to 347 and the sum is again a perfect square! (361). Talk about balancing act!

3. 347, 349, 353, 359, 367 are successive primes and the difference between successive primes is 2, 4, 6, 8 (this is quoted in multiple mathematics articles). Now look at the reverse of these numbers - 743 is a prime as we already know, 943 is a product of two primes (23 and 41), 353 is a prime, 953 is a prime and 763 is again a product of two primes (7 and 109)!

4. From the original number 347743, let's do the following. Though some of these are pretty obvious in hindsight, it looks interesting on how it unfurls when we analyze deeper

a) Remove both 7s first and we get 3443 which is a multiple of 11 and 313 ( a palindrome). 

b) Remove both 4s and we get resultant number as 3773 which is a multiple of 343 and 11. 343 is a palindrome as expected but it is also 7 ^ 3 and unique in its own ways (3 + 4) ^ 3 is 343!!

c) Remove both 3s and we get resultant as 4774 or since we are dealing with odd numbers let's go with 7447. 7447 is again a product of two primes - 11 and 677

5. Now let's add 347 and 743 and the outcome is 1090. To begin with, 1090 looks pretty much like any other even number but here is the fun part 

a) It can be also written as Sum of two squares - 33 ^ 2 + 1 ^ 2.

b) What's more amazing is that it can be written as 32 ^ 2 + 66 and 34 ^ 2 - 66. 1090 exhibits such unique properties spread across 3 successive squares

6. Last but not the least when we multiply 347 and 743 the resultant is 257821. At first glance, there isn't much to look into except it is a 6 digit number and product of two primes. Dig a bit deeper - Take 821 and reverse it to get 128. 128 *2 + 1 is 257!

Numbers are fun as always and for me the trigger for this weekend post was a harmless OTP which turned out to be a very interesting palindrome showing lot of synergies just like we would all expect within a team in our corporate world!

Blog #149: The curious case of 15625!

Maths Blog #149: The curious case of the perfect square 15625, a versatile all-rounder!

Maths Blog #149: The curious case of the perfect square 15625, a versatile all-rounder!

Decided to pen a quick blog thanks to the message from my friend and ex-colleague Prasanna Aravamudhan over the week-end. He forwarded me a note that today's date in DDMMYY (if you ignore the zero!) format is a perfect square. 15/6/25.. 15625 and that acted as a trigger for me to write about 15625 - a true versatile allrounder that each one of us would like to have in our team!

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Here are some interesting stats about the number

1. As we know by now, 15625 is a perfect square of 125

2. Remove the leading number 1 and the resultant is 5625 which is also a perfect square of 75! 

3. Remove the first 2 digits (15) and the resultant is 625 which is also a perfect square of 25!!

4. Remove the first 3 digits (156) and the resultant is 25 which turns out to be a perfect square of 5!!!

5. 15625 also turns out to be a perfect cube of 25!

Now for some deeper insights on this perfect square

6. The reverse of 15625 (52651) turns out to be a product of two prime numbers - 37 and 1423. Unlike 15625 which has 5 and other factors, 52651 is a odd number with only two prime factors

7. Add 156 and 25 and the outcome is 181 while if we subtract 156 and 25, the resulting number is 131. Both 181 and 131 and palindrome primes!

8. 15625 is sum of multiple perfect squares - 100 ^ 2 + 75 ^ 2, 120 ^ 2 + 35 ^ 2

9. Sum of all the digits of 15625 is 19 which is a prime number

10. Sum of the squares of all the digits of 15625 (1+25+36+4+25) is 91 which is a product of two primes also reverse of 19 in the previous step!!