you certainly do not need algebra or a special computer program to create a quilt with out a pattern-
i'm always guilty of not doing the math ---and very seldom use a pattern-
sometimes i do sit down with some graph paper & try to sketch out what i want to do---but in the end i've never actually used that graph paper sketch and made anything.
piano key borders are one of the easiest---for not knowing what size you want/need- you just start sewing strips together(mine are always different widths like 1", 1 1/2", 2", 2 1/2") since its a border the center- to be bordered is done- just lay it out- then sew strips together until they are as long as you need them & stop adding strips---you can cut them what ever width you want your border to be as you go along- or after you have it the width you want-
sometimes people just (over-complicate) things- it is possible to make a whole quilt with very little math involved- i do it everyday.
i usually put them together in rows- so will lay out pieces i want to use in the row- if they are not the same size i measure the largest one then figure out what i need to add to others to get them (up to that size) figure out what to add around them to make the row the length i want---
don't make it harder than it is- make up some blocks- lay them out---and start adding as you go until you have a quilt top put together- if you want to frame it decide what size border you need to add to make it the size you want (such as you have 54" top---and you want it to be 72"----which is 18"---so you would need 9" of border per side---which you could make any number of ways---if you wanted piano keys-but not that wide- you could add a 2 1/2" strip of plain-then your piano keys (5 1/2") then another 2 1/2" outside border---then you have your 9" (finished size) border to add---
once you jump in and make your first one you will have so much of it figured out- you will find it is not difficult-you just had yourself convinced it was hard.