| Do you know that numbers are the key to life? | | | | A "one" number is simply a number whose digits |
| Indeed numbers form the foundations of | | | | consist entirely of 1's. Thus 1 11 111 1111 11111 are all |
| mathematics from number theory all the way up to | | | | "one" numbers. Because 1 is such a special number--in |
| partial differential equations. Without these curious | | | | fact one of the most important constants in |
| creatures, we could not calculate, estimate, or | | | | mathematics, much like water is one of the most |
| compute (as in computer); nor could we transact any | | | | important compounds in chemistry--its presence as |
| of the business that occurs daily throughout the | | | | the sole digit in forming numbers--the "one" |
| known world. Yet most people find these most | | | | numbers--makes squaring these numbers such an |
| interesting entities just a bothersome part of life. | | | | easy task. Watch what I mean. |
| Why should this be so? Well maybe a person's | | | | To multiply the number 11 by itself, something called |
| ambivalence towards numbers derives from childhood | | | | "squaring 11" or taking the square of 11, we obtain |
| frustrations experienced when struggling to learn the | | | | 121. Stepping up to 111, squaring we have 12321. If |
| basics of arithmetic and the rote calculations | | | | we square 1111, we get 1234321. I think by now the |
| associated with this discipline. | | | | pattern has become clear to you and we can thus |
| Lacking an appreciation for numbers can be a sad | | | | form a rule for squaring any "one" number: write |
| state of affairs for any person since such a condition | | | | down the digits consecutively from 1 to the number |
| often leads to mathematical illiteracy. As parents we | | | | represented by the number of 1's forming the "one" |
| should try to instill a love and curiosity for numbers | | | | number and then count backwards from this number |
| into the minds of our children so that they never | | | | to 1. So in 1111, we have four 1's. To square this |
| arrive at this blighted condition. One way we can do | | | | number write the numbers from 1 to 4 consecutively, |
| this is by teaching our children early on the amazing | | | | and then back from 4 to 1 so as not to repeat the 4 |
| properties of numbers and some of the magical | | | | twice: 1 2 3 4 3 2 1 to get 1234321 or one million two |
| calculations that can be performed with them. Indeed | | | | hundred and thirty-four thousand three hundred and |
| the Teenage Number Trick, the Nifty Five Square | | | | twenty-one. That's all there is to it. Want a bigger |
| Technique (see my other articles on these topics), | | | | example. Try 11,111 x 11, 111. How many 1's? Five. So |
| and the techniques laid out in this article should | | | | we get 123454321 or one hundred twenty-three |
| suffice to arouse and stimulate curiosity even in the | | | | million four hundred fifty-four thousand three hundred |
| most torpid learners. Thus here we go on to | | | | twenty-one. |
| introduce a calculation that permits one to square any | | | | If you show your kids how to do these calculations |
| "one" number with blinding speed. In a future article | | | | so that they can multiply and square numbers which |
| we will learn how to multiply any two arbitrary "one" | | | | produce results in the hundreds of millions, do you |
| numbers with no difficulty at all. | | | | think they might have a new outlook on mathematics |
| But in order to begin this short educational journey, | | | | and their ability to master this subject? I think you'll |
| we need to understand what we are talking about in | | | | agree that the answer to this question is self-evident. |
| the first place. What is a "one" number. Take a stab | | | | Stay tuned for Part II which is even more amazing |
| at it before reading further. Okay, now the definition. | | | | than this one. |