Just before I fell asleep a couple of nights ago, I made an interesting discovery. (A great first line of any post.)
Let me preface this by stating that I have no great interest in mathematics. With a bit of paper, I can add and subtract and multiply and divide. The longer the numbers, the less confidence I have in my results. By the time, I reached eighth grade, sitting in algebra class, I could never understand why all the fuss with the identity of x and y.
One thing that has always perplexed me- something my math teachers never gave a satisfactory answer to- was why are numbers called "squared" and "cubed." It is such a practical question that I am sure I must have been THAT one student who distracted everybody by asking. Then, lying on my bed, it suddenly the answer appeared to me in a visionary insight. And now, I shall share it with you.
First of all, you have to imagine yourself a teacher in ancient times without the use of a white board or a black board. You must explain some very high-minded concepts- a challenge. Now, imagine a sugar cube as a unit, representing the number one- a single item. Got that? Pretty easy. Take three of them and lay them side by side horizontally, and you now have- you guessed it- the number three. Lay another two on top of the first so that now you have three up and three across. Fill in the empty spaces of that "L" shape. Now, you have 3 x 3 which adds up to 9, forming a square, or 3 squared. See illustration.
So far this was only a theory until I came to the term, "cubed."
Now you must visualize in three dimensions. Take your 3-squared and make three of the same layers upwards. This shape represents 3 x 3 x 3 = 27 which is three-cubed. I guess there wasn't any other expression after that so they referred to 3 x 3 x 3 x 3 as three to the fourth power. I never had any problem with that, though.
Probably this was explained- exactly as I have here- in every other school in the world. Alas, my teachers parachuted in with both feet with x - 4 = y 4 . I'd stare at the blackboard until my eyes hurt and nothing happened. Apparently I need to begin at the sugar cube level.
And I wouldn't say I went to the best school in America and, in any case, I did everything in my power to avoid learning mathematics. So, blaming the school for gaps in my education is probably a bit unfair.
The school seemed modern and the teaching above standard. However, I distinctly recall in elementary school several of the students pointing out to our aging school teacher how the continents seemed to fit together if you could smooch them, like green and brown play-doh. The instructor stared at the map for a second and. with a dismissive nod. told us it was just a coincidence. Years later, individually all of the scattered members of Miss Humphrey's class of 1968 felt dismayed and not a little betrayed to learn all about plate tectonics.
Someday, if you are good, I will share with you my discoveries about the hidden mysteries of numbers.