I posted this on /r/math but it got removed sorry if this is the wrong subreddit.
I’ve been drawing algebraic relationships as graphs and I can’t figure out if this is already a well-known thing that I just don’t know the name of. I don’t really have a maths background so very possible I’m just reinventing something obvious.
I’ll explain how to read the drawings and then the pictures will hopefully make more sense than my explanation.
Every number is a node. When I’m saying two things are equivalent I draw lines from each of them that join into a single line going to the other side. So like if 7 and 3 are equivalent to 10, I draw a line from 7 and a line from 3 and those two lines join together into one line that goes to 10. It’s a branching structure. You can read it in either direction, 10 splitting into 7 and 3 is the same drawing as 7 and 3 joining to make 10. There’s no input or output, it’s just saying these things are equivalent.
Every number also has a negative version, and when a number and its negative are on the same side of a line they cancel to zero.
For multiplication I’m treating it as the same thing but where every branch carries the same value. So 2 times 8 would be eight lines each carrying the value 2, all joining together into one line going to 16. Obviously I’m not going to draw eight separate lines every time so the shorthand I use is drawing the first branch and the last branch with three dots in between, and writing the total number of branches next to it. So you’d see a line labelled 2 at the top, a line labelled 2 at the bottom, dots in the middle, and the number 8 to indicate there’s eight branches total. Division is just reading the same picture the other way.
I’ve been drawing these for fractions, exponents, bracket expansion, sign rules, and a bunch of other things, and it keeps seeming to work using just the stuff I described above without adding any new rules. I honestly don’t know if that’s the graph doing something interesting or if it’s just how algebra already works and I’m just drawing it instead of writing it. Attached a bunch of pictures, the fraction addition one is probably the clearest. Any help figuring out what this is or what to search for would be great, the closest I’ve found is string diagrams in category theory but I don’t understand those enough to tell if it’s the same idea.