Have you ever needed to know what’s the max width for a particular length on your printer bed?
Or wondered what the biggest rectangle is that can fit inside your 3D printer bed?

That’s where geometry helps.

When a rectangle is centered and rotated 45 degrees inside a square with side length s, its sides x (width) and y (length) are related by this simple formula:

y = s√2 - x

This means that as one side gets longer, the other must get shorter so the rectangle still fits perfectly inside the square.

For example, if your 3D printer bed has a size of s = 256 mm, then:

y = 256√2 - x ≈ 362.04 - x

This means any rectangle with sides that follow this equation will fit exactly inside the square print area when rotated 45 degrees.

So next time you’re setting up a print or adjusting your layout, use this formula to quickly find the maximum width for a given length (or the other way around) and make the most of your printer bed space.

by MrWays