Author's note: Prussia/Hungary, Austria/Hungary, Russia/Hungary.

For DarkBlaziken who suggested this prompt months ago. I've been trying to figure out how I want to write it and finally sat down and just did it. I also thought I'd play with Hungary's name in the three parts; Erzsébet is my favorite but that's just cuz I'm a sucker for Hungarian and now vaguely know how to pronounce words in the language.

Math tells us of the
Three saddest love stories:

1. Tangent lines, who were together once then parted forever

Deep in the forrest, hidden by their tent, they hide away from the world as if they could stop it from tearing them apart.

"Come with me," Gilbert once more whispers in her ear, his hands threaded through her wild hair. Her body moves above his, flesh pressing into flesh, her eyes closed and her mouth open in a silent moan. "Come, my Hungarian beauty."

Erzsébet shakes her head, her lips pressing against his in an attempt to shut the Prussian up. "You don't want me," she mutters, her hands holding his face still. "Nothing would change if I went with you, even if I could."

"Marry me," he blurts out but fingers on his lips silence him.

"I am no man's wife," the Hungarian smiles, eyes falling closed as she loses herself in the feel of his body. When they're finished, Gilbert holding her close, Erzsébet elaborates. "I wouldn't be a good wife, and I love you but you wouldn't be a good husband. You can't marry and I can't leave and this is it Gilbert, we both know it." In the morning he'll leave; this is goodbye.

"I'll love you forever," he near-sings against her lips and that is enough for the Hungarian kingdom.

2. Asymptotes, who can only get closer and closer but never be together

He's been playing the piano for hours; a wife knows what that means. "Come back to bed Roderich," Elisabeth calls out from the door, holding her robe tightly about her body. The piece quietly finishes, allowing silence to envelope them as the Hungarian half of their empire walks forward to join her Austrian counterpart. "You are upset, I know-" a hand reaches out to rest on a tense shoulder.

"This is about more than being upset," Roderich manages through gritted teeth, looking away as his wife sits beside him on the piano bench. "I cannot do this, even if it is you who asks it of me."

"You must," Elisabeth presses on, her free hand resting on her husband's thigh. "This was never meant to be forever. We've had our time, you and I, to try and be together-"

"Was it enough?" Roderich turns to her suddenly, desperation in his eyes. "Were you happy? Was I a good husband, a good lover?" One of her hands reaches out to stroke a cheek, a hand that will soon no longer wear a wedding ring.

"These years have been priceless to me," she whispers, leaning in; Roderich leans towards her to match. "But you and I both know we were never meant to last."

"I love you," and their lips meet in a sweet kiss of approaching goodbye.

3. And parallel lines, who were never meant to meet

From the middle of the bed she watches him move in agony, his bare back tinged red as if healing, though he has not been injured this extensively in years and isn't healing at the moment but rather dying, his whole being in the midst of being torn apart. Finally the full weight of Ivan's body comes to rest on the side of the mattress, the Soviet's breathing labored.

Carefully Elizaveta rolls to her side, snapping up the bottle from the bedside table before rising to her knees and shifting to sit behind him. She warms the lotion between her hands before starting in on Ivan's back, making the strong man hiss in pain.

"Is it really that bad?" she whispers quietly because if she spoke any louder her voice would betray her fear. Not that Elizaveta didn't want to leave; she does with all that she is. And yet, though she should not feel for her captor what she does, it kills a piece of her to see Ivan like this. "I don't want to add to your burden."

"I've felt worst," the man mumbles in weak Russian; she doesn't doubt that he has. If anyone she's ever met has known pain, it would be Ivan. "I'll miss you," he mutters over his shoulder, "when this is over and you're gone."

"We were simply never meant to be," Elizaveta says, kissing at the base of his neck.

"Too bad I love you then," and that makes her sigh with a smile.