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The caption "The equation 1⁰² + 1¹² + 1²² = 1³² + 1⁴², whose answer is that both sides equal 365, was immortalized in a different form in this 1895 painting: “M
by jimhefferon 7y ago
The caption "The equation 1⁰² + 1¹² + 1²² = 1³² + 1⁴², whose answer is that both sides equal 365, was immortalized in a different form in this 1895 painting: “Mental Arithmetic. In the Public School of S. Rachinsky.” (NIKOLAY BOGDANOV-BELSKY)" has funky exponents. Medium requires that I make an account to say that, so I am saying it here.
- mkl 7y agoThat formatting error is repeated in at least one other place too.
- jkinudsjknds 7y agoOn the subject of that painting, can anyone tell me what the kids are wearing on their feet?
- CliffStoll 7y agoMuckluks. Or the 1890 Russian version
- norrius 7y agoThese are bast shoes [0], known in Russian as lápti, which were the typical footwear in villages until the 20th century. They are strapped to the leg so that they don't fall off. [0]: https://en.wikipedia.org/wiki/Bast_shoe https://en.wikipedia.org/wiki/Bast_shoe
- CliffStoll 7y agoI think the equation on the board is ( 10^2 + 11^2 + 12^2 +13^2 + 14^2 ) / 365 which solves for 2. The students are expected solve this with "Mental Arithmetic". Try that in your head!
- jimhefferon 7y agoThanks. I cannot see that on my screen. The powers of 1 caught my eye, though.
- CliffStoll 7y agoHappy Pi-Day!
- CliffStoll 7y agoLet a=12 then (a-2)^2 + (a-1)^2 + a^2 + (a+1)^2 + (a+2)^2 /365 and a binomial a+b squared yields a^2 + 2ab + b^2 so a^2 + 4 + a^2+1 + a^2 + a^2+1 + a^2 + 4 add up all those a^2 's to get 5a^2 + 10 replace a by 12 and 720 + 10 yields 730 Divide by 365 2 That's what the sharp kid in the foreground is doing at the moment of the painting.
- delhanty 7y agoAssuming one's memorized a table of squares already. 10^2 = 100 11^2 + 13^2 = 121 + 169 = 290 12^2 + 14^2 = 144 + 196 = 340 100 + 290 + 340 = 730 730 / 365 = 2
- lonelappde 7y agoYou can also "walk it up" if you haven't memorized them: 10^2*5 + (10+11)*4 + (11+12)*3 + (12+13)*2 + (13+14) ------------ 500 + 84 + 69 + 50 + 27 ----- 730 It's a bit of detail to juggle in your head but not too bad if you hang on to your current subtotal and remember where you are in the sequence to compute the next addend, and you know it's easier to add multi-digit numbers left-to-right than-right to-left. You only carry from the ones place twice.
- stevespang 7y agoFUCK MEDIUM, assholes