Tricks, formulas, whateer…

Posted on July 12, 2015

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So the Washington Post runs this story at

http://www.washingtonpost.com/news/local/wp/2015/07/10/did-this-teen-spot-an-error-in-a-34-year-old-math-exhibit-at-a-boston-museum-not-exactly-but-hes-enjoying-the-ride/   …

math teachers — golden opportunity for “math in real life, well sort of” and exploring ratios and radicals, which arent’ *horribly* advanced.   (If you’re not one of my MTBoS buddies and don’t remember them — well, they are also *definitely* in the ‘no, you will almost certainly in fact never see or use this’ category).

Not dissing the kiddo for paying attention to stuff — but would suggest that *asking* why it wasn’t a plus sign would have made more sense, tho’ perhaps not in the “got him the fifteen minutes of fame” sense. (Update:   friend tells me that when he was being interviewed he had been unsure about it, so it’s the media which I forget is now completely incompetent that spun it as “corrected” the museum).  I am dissing people and our culture that deems him a “math whiz” because he noticed the formula.  What ?!?!?

The kiddo told the museum they had the formula wrong, because it wasn’t the one he memorized.   Somebody from the museum actually told him he was right and they’d be fixing it.  Then somebody did the arithmetic.

No. They *weren’t* both right — because he was saying the formula at the museum was wrong and it wasn’t. The formula he memorized was (sqrt 5 + 1)/2 and the one in the museum was (sqrt 5 -1)/2.
So he told ’em the sign was rwrong.

The article sort of implies that his “mistake” was not knowing the difference between capital phi and lower case phi but …
If you flip that first fraction over and then follow the weird rules for getting square roots off the bottoms of fractions (you can’t have radicals in your basement, you know), it ends up being equal to the second one. THey’re reciprocals like 2/3 and 3/2.

The museum in question showed the “golden ration” but showed it as short side / long side, so its formula with the minus sign was utterly correct.   Short/long would be the reciprocal of Long/Short.

One commenter noted that If the kid thought about the arithmetic, he’d have realized that (1 + the square root of five )/2 would be … bigger than one. The thing the museum said it was equal to was the ratio of the short side to the long side. A small number over a big number is … smaller than one. 3/4 is less than a whole. .
It wasn’t The Formula He Memorized, though, so it must have been wrong. Glad *somebody* knew the arithmetic to recognize what was happening.

Not surprising, the math is ‘way too advanced for most of the commenters –and that’s already filtering out prob’ly 75% of Amurricans who glazed over the mathiness — the commenters were full of “explanations,” including one guy who calculated the two reciprocals out to a mess of decimals and then stated that they were exactly the same.   Yup. 0.6 and a mess was exactly the same as 1.6 and a mess of decimals.

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