3 ms·
I 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 A
by CliffStoll 7y ago
I 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.