Image via WikipediaToday I ended up walking home from downtown. I’m a fanatical little record keeper in some ways and I was wearing my pedometer, so I felt especially virtuous hearing its little click-click sound.
When I got home I checked my pedometer: 7623. What a cool number! Think about it:
7-1=6, the number right next to the 7.
2+1 (the difference between 7 and 6)=3 (the number next to the 2).
Working back right to left, 3x2=6 (the number that comes right before the 23 combination).
6/2=3 (yes, this is just another way of expressing 2x3=6. Isn’t math cool that way?!).
7x6=42, which utilizes the 2 that’s in this number, and if you take 2 times itself you get 4, which is the other digit in 42. And 4/2=2.
6x2=12. If you take the 4 from the 42 you create with 6x7, you can put it with the 3 that’s in our original number, and 3x4=12.
Of course, once you’ve gotten that 12, you recognize that it uses the 2 from the figure and the 1 you get whether you take the difference between 7 and 6 or the difference between 2 and 3--and 1+2=3.
Isn’t this fun? But wait—there’s more!
Add all the digits: 7+6+2+3=18. The first digit, 1, is of course our old friend, the difference between 7 & 6 and between 2 & 3 (to say nothing of being a number that belongs in the sequence 1-2-3, which is the first thing we learn about numbers).
If you multiply 2 times the 4 you created with 7x6 or with 22, you get the 8 from our 18.
8+1=9, which is the 3 times itself.
Add just a couple of them: 7+6=13; we know about the 1, the 3 is in the full number, 1+3=4 again, and among all these numbers you've used the first four odd primes: 1-3-7-13. (The missing prime that would complete the sequence, 2, is hidden between the 1 and the 3.)
Try some more subtraction. 7-2=5 which equals 2+3. 6-3=3 which is already there.
I’m not finished, but I’ll stop. (Thank heavens! You think to yourself. This is an elective course, after all.)
When Younger Daughter was a little girl, she started this game by looking at the microwave and noticing the relationships among the numbers. She especially liked numbers like 11:11, 2:22, 1:23, 9:10—something with a clear pattern.
I started pointing out the arithmetical relationships one could see in the numbers, including the relationships outside the actual digits that we could create through manipulation (like my 42 above that gave us a 4 to throw in). (Oh, and if you add our invented 4 to the 7 you get 11 and if you add the digits in 11 you get the 2.)
This game has been fun for me too, as someone who majored in English and linguistics and didn’t really dig into math until college, only to realize then that I was pretty good at it.
This aha took place way too late to let me go into the sciences, which I might have done; as a kid I planned to be a marine biologist and study dolphin language, which may explain the linguistics degree.
I couldn’t say whether “Microwave Math” has anything to do with it, but Younger Daughter is getting an A as a high school freshman taking a junior-level course. It’s not her favorite but she does really well.
Seen any good math lately?
P.S.: I know the equations here are simple arithmetic. Microwave Math uses alliteration, which is one of my favorite word things. Perhaps another time I’ll tell the story about how I came to realize I prefer odd numbers to even.