You know those mathematical novelties that math nerds like to toss out occasionally to astound and/or stultify us mere mortals? You know. Come on. A mathematical oddity. I know you know.
Many of the mathematical curiosities follow a pattern of take some parameters, apply some formulae, and you always get the same result no matter what the parameters are. You swear it’s not possible, but it nevertheless works. Or, at least, you swear it’s not possible if you, like me, are an advanced-math-challenged person.
Well, here’s an interesting, but little-known novelty torn from the pages of mathematics. (Please don’t tell the guy who’s textbook I tore it from that I was the thief.)
Feel free to try this little mathematical oddity for yourself and prove that it is true. But, to make sure you get the right answer, be certain to follow each step meticulously. Taking shortcuts will invariably lead you astray.
A mathematical oddity, just for you!
(Just for you only because you’re probably the only one who will find it. This site doesn’t get much traffic. If anyone else stumbles on this page you’ll have to share it with him or her. Sorry.)
And, no cheating. You can’t use a computer or an electronic measuring device to perform the following steps.
- Precisely measure the circumference of a circle—any circle—in hundredths of an inch. It may seem counterintuitive, but it doesn’t matter what size circle you use.
- Calculate the cube root of the circumference.
- Precisely measure the radius of the circle, but this time use the metric system and take the measurement in millimeters.
- Calculate the square of the radius.
- Divide the result of step 4 by the result of step 2.
- Draw a square enclosing the circle such that the center points of all four sides of the square just touch the circle.
- Precisely measure one of the diagonals of that square, again in millimeters. (Being a square, it doesn’t matter which diagonal you choose. They will all be equal.)
- Multiple the length of the diagonal by the result of step 5.
- Multiply the result of step 8 by the value of pi to 10 decimal places.
- Divide the result of step 9 by the square root of 1867, the year of Confederation in Canada, rounded down to the nearest whole number. (Round both the square root and the result of the division, that is, not the year of Confederation. But you probably figured out that you don’t have to round the Confederation year seeing as though 1867 is already a whole number. You’re clever that way. Or not. I don’t even know who you are.)
The Amazing Part
If you complete all of the above steps slowly, carefully and correctly, when you are done, if you did it right, you will find that you completely wasted one heck of a lot of time. And here’s the amazing part. If you perform the work meticulously, you’ll find exactly the same thing if you nevertheless made some mistakes. Weird, huh?
OK. Maybe it’s not that amazing. Sorry. It’s all I’ve got. I don’t have much of a life.