It begins simply enough, a wizard will awaken to find a new spell inscribed in his spell book, or perhaps, a poet will find a new verse-form in her journal. The spell will be notated in EXACTLY the way the wizard would have done so; there is no chance of failure to learn this spell. The verse will be composed of words and themes unique to the poet in question.
Many assume that, somehow, they have written these things in strange somnambulatory sleep. It is not so; it is the work of a line gnome, hoping to gain your trust, hoping to make you dependent. The sleeping works will continue with increasing frequency, bringing about greater power, greater understanding, and/or greater artistic achievement.
Then it will stop. It will stop for a depressing length of time.
Once the subject is sufficiently tormented with their now-fruitless sleep, the gnome will appear to him/her. It is a thing of two dimensions, built of lines and arcs into the semblance of a face.
Geometry goblins may only exist upon and move across sufficiently flat, smooth surfaces. A scroll or a book is an obvious and natural place for them to be. A cobbled street is not. (As a rough rubric, if you could easily write upon a surface with chalk or a pencil, a line gnome may be there.) The goblin may choose to be any size contained within its current surface(from a god-like projection on a limestone cliff, to the size of a ink drop).It moves as fast as a frightened cat, and can cross onto any surface its current surface touches. Any purposefully drawn line is an impassible barrier to geometry goblins.
That of course makes them easy to trap if one thinks to do so. The gnomes are very, very aware and take great pains to insure their freedom.
But what do they want?
They want you, of course. They want you to be their meat puppet in this strange 3 dimensional world you inhabit. They want freedom, anybody’s freedom, yours will do quite nicely.
They will try to offer their victims anything to “let [them] on you, is all…”.
Once agreed, the goblin will flow onto their new home as an indelible tattoo. Then try to take the place over…
If someone is foolish enough to agree, have the player roll a d20 adding to it wisdom, intelligence, and charisma modifiers. Roll 1d100 for the gnome. The highest roll wins.
Should that be the geometry goblin, the PC’s personality and will are shunted into the ether. A completely amoral being now has a body with which to sate its incredible curiosity about the 3d world.
Should the PC win, the PC now has a permanent and petulant companion who knows much about magic (especially written or geometrical magics) and all forms of 2 dimensional art.
They can be destroyed simply by destroying the surface they occupy. If it's on wall, break the whole wall before the linear gnome can get to the floor. If it's on a page, circle it and throw the book into a fire.
Where do they come from?
No one knows. Some believe they are beings from a two dimensional world, cast out for crimes unthinkable. Some think they are devils. People think all sorts of fucking stuff. People are usually wrong about these sorts of things.