When multiplying any two numbers, for example 15 * 18, the value is the same as:
x * y = avg(x,y)2 - (avg(x,y) - min(x,y))2
Which simplifies to:
x * y = 2 * avg(x,y) * min(x,y) - min(x,y)2
so 15 * 18 =
= avg(15,18)2 - (avg(15,18) - min(15,18))2
= 2 * avg(15,18) * min(15,18) - min(15,18)2
= 2 * 16.5 * 15 - 152
= 270
So the value of any multiplication is the same as the average of the two sides squared minus the distance from the numbers to the average squared.
For example (reload page for more random examples):
-12 * 6 = -72
avg(-12,6) = -3; min(-12,6) = -12
-32 - (-3 - -12)2 = -72
2 * -3 * -12 - -122) = -72
11 * 1 = 11
avg(11,1) = 6; min(11,1) = 1
62 - (6 - 1)2 = 11
2 * 6 * 1 - 12) = 11
14 * 3.1111111111111 = 43.555555555556
avg(14,3.1111111111111) = 8.5555555555556; min(14,3.1111111111111) = 3.1111111111111
8.55555555555562 - (8.5555555555556 - 3.1111111111111)2 = 43.555555555556
2 * 8.5555555555556 * 3.1111111111111 - 3.11111111111112) = 43.555555555556
10 * 4 = 40
avg(10,4) = 7; min(10,4) = 4
72 - (7 - 4)2 = 40
2 * 7 * 4 - 42) = 40
-13 * 1.125 = -14.625
avg(-13,1.125) = -5.9375; min(-13,1.125) = -13
-5.93752 - (-5.9375 - -13)2 = -14.625
2 * -5.9375 * -13 - -132) = -14.625
-12 * 4 = -48
avg(-12,4) = -4; min(-12,4) = -12
-42 - (-4 - -12)2 = -48
2 * -4 * -12 - -122) = -48
-11 * 14 = -154
avg(-11,14) = 1.5; min(-11,14) = -11
1.52 - (1.5 - -11)2 = -154
2 * 1.5 * -11 - -112) = -154