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posted by
Fnord666
on Friday September 13 2019, @08:26PM
from the for-all-values-of-everything<113 dept.
from the for-all-values-of-everything<113 dept.
Submitted via IRC for chopchop1
The problem of 42 — at least as it relates to whether the number could be considered the sum of three cubes — has finally been solved. The question of whether every number under 100 could be expressed in this fashion has been a long-standing puzzle in the world of mathematics. Now, two mathematicians, Andrew Sutherland of MIT and Andrew Booker of Bristol, have jointly proven that 42 is indeed the sum of three cubes.
In the equation x3+y3+z3 = k, let x = -80538738812075974, y = 80435758145817515, and z = 12602123297335631. Plug it all in, and you get (-80538738812075974)3 + 804357581458175153 + 126021232973356313 = 42.
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Life, the Universe, and Math: 42 Proven to be the Sum of 3 Cubes
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(Score: 3, Informative) by martyb on Saturday September 14 2019, @09:54AM
Why not?
A cube is a number that has been multiplied with itself 3 times, just as a square is a number that has been multiplied with itself 2 times.
so, just as the square of 5 is 5x5 (i.e. 25), the cube of 5 is 5x5x5 (i.e. 125), and the cube of -5 is (-5)x(-5)x(-5) which is -125
Example 1: take one cube that is 10 units on a side and another cube that is 5 units on a side. Let's assume each cubes is made of lead. Now imagine a bucket that is 30 units in diameter and 20 units tall, filled with water. I place both blocks in the bucket. How much water is displaced?
(10^3) + (5^3) = (1000) + (125) = 1125 cubic units of water are displaced. We have simply combined the volumes of each of these cubes.
Example 2: Imagine another pair of cubes. Like before, we start with a cube that is 10 units on a side. Now we remove a chunk of that cube by measuring 5 units in from a corner. We now place this single (reduced-in-size) cube into a fresh bucket filled with water. How much water is displaced?
(10^3) + (-5^3) = (1000) + (-125) = 875 cubic units would be displaced. The removed 5x5x5 chunk could be considered to have negative volume when compared to the original 10x10x10 cube.
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