Blog #145: Welcoming 2024

As we step into a brand New Year, here's a short Mathematical note welcoming 2024

1. 2024 is a difference of two perfect squares - 2025 and 1 and #2 and #3 below illustrates that through alternate means

2. Add digits 1 to 9 and we get 45. (45 + 1) * (45 - 1) is 2024

3. Add the cubes of the digits from 1 to 9 and the resultant is 2025  (45 ^ 2). Subtract 1 ^ 2 as in #1 and we get 2024 again!

4. 2024 is also sum of 1936 + 88. In turn 1936 is nothing but a perfect square of 44. 

Hence 2024 can be written as (44 ^ 2) + (44 * 2). Look at how 2 and 4 which are the primary digits that make up 2024 come into play again! Add 20 and 24 and the resultant is 44 again!

5. Last but not the least..2024 x 2024 = 4096,576 where 4096 is a perfect square and 576 is also a perfect square (24 in action again!)

Wishing everyone a very Happy, Healthy and Prosperous 2024!

Blog #144: Tribute to the Maths Genius on his 136th birth anniversary

Today is 136th birth anniversary of Dr. Srinivasa Ramanujan, the Man who knew Infinity!

Here's a small Mathematical tribute to someone who loved Numbers and patterns and weaved magic and also why Year 2023 was special in that context

1. 1887 was his birth year and a multiple of three prime numbers 17, 37, 3

2. Coincidentally Year 2023 happens to be a multiple of 17 as well- 17, 17, 7 (all prime again)

3. 17 is the common thread across 1887 and 2023 and it is also the first 2 digits of Ramanujan's famous magic number 1729!

And for the grand finale!

Here's what makes both 2023 and Ramanujan's 136th birth anniversary year extra special. Look at the pattern below for 2023..

a)  2+0+2+3 = 7 is a prime

b) 2 ^ 2 + 0 + 2 ^ 2 + 3 ^ 2 = 17. Prime again!

c) 2 ^ 3 + 0 + 2 ^ 3 + 3 ^ 3 = 43. One more prime!

d) 2^4 + 0 + 2 ^4 + 3 ^4 yields 113 which is again a prime!!!

e) 2 ^ 5 + 0 + 2 ^ 5 + 3 ^ 5 = 307. Prime galore!

f) 2 ^ 6 + 0 + 2 ^ 6 + 3 ^ 6 = 857. Yes you guessed it right. Prime again 

g) 2 ^ 7 + 0 + 2 ^ 7 + 3 ^ 7 = 2443. Finally..We get a number which is a product of two primes! The streak is broken but not before displaying an amazing pattern

This is why numbers are so special and on that note, this is me signing off for 2023 with this humble tribute to the Man who achieved a lot in the field of Mathematics in a short span of time and continues to make a profound impact even today

#SrinivasaRamanujan #MathematicalGenius