An event of some significance - perhaps rarity would be more precise - occurred yesterday. In fact, this event occurred twice that very day.
Sunday, you see, was July 8, 1990, and that date can be expressed by the numbers 7/8/90. Now at exactly 34 minutes and 56 seconds after the hours of midnight and noon on Sunday, the time and date were 12:34:56,7/8/90.I remember a similar day long ago - March 4, 1956, it was - because my father pointed out to me that it could be written 3/4/56 and that no other day would follow this pattern for 11 years. But that event started me thinking about interesting sequences of numbers that occur in the real world - numbers that reverse themselves, numbers that repeat themselves, telephone numbers, house numbers, ZIP codes.
Most children start their school experience being fascinated by numbers. Ask first-, second- or third-graders what their favorite subject is in school and you're likely to hear "arithmetic." But ask sixth-, seventh- or eighth-graders the same question and you'll find that "math" has fallen way down to the bottom of the list.
What happened during those middle years of elementary school? How did we manage to drive all the fun out of numbers? No one knows, and, unfortunately, very few are even trying to find out, but it is clear that children grow to see mathematics as a tedious and difficult subject that is useful only in school. They never learn to "play" with numbers, to see that numbers have some quirks and peculiarities that can entertain and delight anyone adventurous enough to poke at them a little and see how they behave.
Look at the numbers in the 9's column of the multiplication table, for instance. As we multiply 9 times 1, 2, 3 . . . and so on, the products are 9, 18, 27, 36, 45, 54, 63, 72, 81 and 90. I find it quite amazing that the sum of the digits in each of these products is 9 (9
9, 1 + 8
9, 2 + 7
9, 3 + 6
9. . .). And so it is for EVERY multiple of 9. (For example, 9 x 29
261, 2 + 6 + 1
9; 9 x 51
459, 4 + 5 + 9
18, 1 + 8
9.)
Today let me show you a couple of truly "magic" numbers that may prove entertaining to both you and your children. Grab a calculator (any size will do) because these "magic" numbers are rather large.
The first is the number 12345679 (the nine digits in order with the 8 removed). Now multiply this number by 9 and see what happens: 12345679 x 9
111111111. And when you use multiples of 9, the products jump up a notch: 12345679 x 18
222222222, x 27
333333333 and so on.
Or take the number 142857 and see what happens when you multiply it by 1, then 2, then 3, 4, 5 and 6. The answers (142857, 285714, 428571, 571428, 714285, 857142) show that the order of the digits remains unchanged, but the 142857 sequence begins at a different position each time. You could write the number clockwise around a circle, then start at any point, and the answers would follow. Now multiply 142857 by 7 and be ready for a surprise. Magic, isn't it? (If 142857 is hard to remember, just divide 1 by 7 - that's 1/7 expressed as a decimal - and watch 142857 repeat to infinity!)
Other "magic" numbers, along with calculator games and suggestions for ways to help you help your children rediscover the enchantment of numbers, can be found in the 510 and 793.74 sections of the juvenile collection in your local library. Several informative and inexpensive paperback books about number games and tricks can be found in the children's section of most bookstores.