An Itch That Could Never Be Satisfied (Until Now!)

My math teacher back in AP calc told our class to 1) memorize our squares up 25 and 2) that we should see a pattern. This was years back too (I've recently graduated from uni!!!). The insight may be rudimentary to a sophisticated math person, but i don't care about that, because this bring me sheer joy :')

The first thing i noticed: if 4 squared is 16, any other number whose last digit is also 4 will have a square that ends with a 6 as well. For example, 14^2 is 196, 24^2 is 476, and so on.

After tutoring math, and spending a lot of time with students looking at pascals triangle, sequences/series, and summation techniques, I finally found a better algorithm / pattern that makes mental math for squares easier, and less memorization based.

For squares 1-10, you can add 1+3+5+....+19 or just memorize the outcome (the latter being preferred to make subsequent squares easier)

For squares 11-20, this get beautiful....

ex 11^2 = 10^2 + (10)x2x1 + 1^2 = 100 + 20 + 1 = 121

ex 17^2 = 10^2 + (10)x2x7 + 7^2 = 100 + 140 + 49 = 189

For squares 21-30, its the same idea!

27^2 = 20^2 + (20)x2x7 + 49 = 729

I'm actually not a formal mathematician but still I found this very rewarding to come across. If I wasn't pursuing medicine, I'd dedicate more time to math. Still, math remains a small part of my life :)