I’ve mentioned in a previous posting that I have complex dreams. I woke up yesterday morning with something in my head that wasn’t necessarily related to a dream, but it’s interesting — and I’m going to map it out now.
Easy Square Process
I came to the realization that it’s easy to figure out the square of a number if it’s near another number: Take the square of the nearby number, and add both that number and the adjacent number to it.
Example: 11 Squared
To determine 11 squared, you do the following:
10 squared is 100. To find out what 11 squared is, you start with 100, and add 10 to it, and then add 11 to it. You end up with 121.
11 squared isn’t that exciting, because many people may already know that it is 121. This process is more useful with larger numbers.
Example: 101 Squared
Say you wanted to know what 101 squared. This is the way to do it:
100 squared is 10,000. Add 100 and 101 to it, and you get 10,201 — which is what 101 squared is.
Example: 99 Squared
You can do it in the other direction too. If you want to know what 99 square is, start with 10,000 subtract 100 from it and then subtract 99. You end up with 9801. That is what 99 squared is.
Example: 102 Squared
If you’re looking to find a number that is farther away than just one digit, you need to do more addition or more subtraction. As an example, 102 squared is going to be 10,000 plus 100+101 plus 101+102. Which equals 10,404. Essentially you need to do the addition or the subtraction as many times as the number is different.
Proof
To validate this process, you can see it through algebra:
(X+1)2 = X2 + 2X + 1 — which can be organized as:
X2 + X + (X+1) — which is the logic I mentioned above
Summary
It’s a little silly for me to write this down and put it on my writing site, but it is interesting to me that I woke up with this in my head. This simple way of getting the square of certain numbers is interesting, and potentially useful.
I also wake up from complex dreams — I should document these, and use them as plots for written stories.