3 ms·

Out of curiosity, in what situations does knowing the squares benefit someone later in mathematics / life? Actually curious.

• Someone 11y ago
  Short version: it is fun. If you do mental math, it makes exercises way more fun if you know more interesting numbers. The 16x18 example is an example. For another example, consider 42x49 When primed by 16x18, one might consider writing it as (45-3)x((45+3)+1) = 45^2-3^2 + 42 = 2025 - 9 + 42 = 2058 (This works for many pairs of numbers that are relatively close together, only requires one 'large' multiplication, and that one is simple, as stated in the article) But of course, half-way through, one may realize it is 6x7 x 7x7 = 7^4 - 7^3 Now, 7^3 = 343 (easy to remember in combination with 3^5 = 243), but 7^4 = 2401, for me, doesn't pop out (when you say 2401, I know it's 7^4, but not vice versa) Meanwhile 49 is close to 50, so we have 42x50 - 42 = 2100 - 42 = 2058 That is faster, but somewhat dull. Meanwhile, as far as we know, the savant calculator just takes the dull road, adding 40x40, 40x(2+9), and 2x9, doesn't get distracted, and produces the right answer in a tenth of the time I take. He has less fun, though, because I take detours to visit tourist attractions. It also can make taxi rides more fun.
• deleted 11y ago
  [deleted]