So I need to divide a rectangle into 3 equals parts, but without fractions. It's one of those old "You have two jars of two sizes and need to get an exact amount of some other size" type problems, except a real world example and I don't think I can do much in the way of pouring back and forth.
Here is what I can do:
I can place the 3 parts into 3 "slots" of a larger set, so long as the larger set can be evenly divided using a non-repeating decimal (1/4, 1/5, 1/10, etc) and then set the size of the pieces to exceed their slots by a percentage greater than 100 so that they overflow, pushing each other along the way, to fit 100% of the total slots.
So if I have 4 slots, I would have to set the size of the pieces to 133.(3)%, so not an option. 5 slots requires 166.(6)%, so that's out.
I'm wondering if there is either a basic equation/function I'm not thinking of to solve this or if it's provably impossible.
If it's any help, there's no reason (other than futility if it's impossible and sanity if requires a significant depth), why I couldn't put slots within slots with the pieces at varying depths. I just can't think of the math to pull if off (if it can be).