Euler brick

An Euler brick is a special kind of 3D shape that has three different lengths for its sides, just like a rectangular prism. The special thing about an Euler brick is that all of its edges (the lines where two sides meet) have whole number lengths, and the lengths of the edges, when cubed (multiplied by themselves three times), can be added together to get the cube of another whole number.

That might sound complex, so let’s try to break it down. Think about a rectangular box like a shoebox. If you measure the length, width, and height of the shoebox, you end up with three different measurements. These measurements are what we call the sides of the box. Now, what if we could make a box that has edges that are whole numbers (like 1, 2, 3, etc.)? That box would be called an Euler brick.

To be called an Euler brick, though, there’s one more condition that the edges have to meet. If you take the length of each edge, cube it (multiply it by itself three times), and add up those three numbers, you should get another perfect cube (like 8, 27, 64, etc.).

So, an Euler brick is a 3D shape that has edges of whole number lengths and also satisfies a mathematical equation that makes the lengths of the edges special. It’s like a really cool, fancy math game!