Re:Mathematicians Discover New Way for Spheres to 'Kiss'
by Cyber_Mobius on Thursday January 16, 2025 @02:01PM
(#42729416)
Just a tangent, but there's a nice trick for 8 x 12.
In algebra, you learn that (a - b)(a + b) = a^2 - b^2. It's not too hard to spot this when it's all variables with a little practice but it's easy to overlook that you can apply this to arithmetic too anywhere that you can rewrite a problem as (a-b)(a+b). This happens when the difference between the two numbers you're trying to multiply is even.
For a, take the halfway point between the two numbers, and for b, take half the difference between the numbers. So a = (8 + 12) / 2 = 10. b = (12 - 8) / 2 = 2.
Here, 8 = 10 - 2 and 12 = 10 + 2. So you can do something like (10 - 2)(10 + 2) = 10^2 - 2^2 = 100 - 4 = 96.
It's kind of a tossup if it's more useful on these smaller problems but it can be pretty fun to apply it to something like 17 x 23 which looks daunting on its own but 17 x 23 = (20-3)(20+3) = 20^2 - 3^2 = 400 - 9 = 391
In algebra, you learn that (a - b)(a + b) = a^2 - b^2. It's not too hard to spot this when it's all variables with a little practice but it's easy to overlook that you can apply this to arithmetic too anywhere that you can rewrite a problem as (a-b)(a+b). This happens when the difference between the two numbers you're trying to multiply is even.
For a, take the halfway point between the two numbers, and for b, take half the difference between the numbers. So a = (8 + 12) / 2 = 10. b = (12 - 8) / 2 = 2.
Here, 8 = 10 - 2 and 12 = 10 + 2. So you can do something like (10 - 2)(10 + 2) = 10^2 - 2^2 = 100 - 4 = 96.
It's kind of a tossup if it's more useful on these smaller problems but it can be pretty fun to apply it to something like 17 x 23 which looks daunting on its own but 17 x 23 = (20-3)(20+3) = 20^2 - 3^2 = 400 - 9 = 391