Applejack had heard the things that Pinkie had said about her father, and they went best unrepeated. Applejack had also heard the things that Pinkie deliberately hadn't said, and they'd given her nightmares for a solid month. No pony should act in that way to another pony.

So, when Igneous comes by looking for Pinkie, Applejack has to find a way to send him away again...

(This story is based on an incident referenced in the backstory of Estee's excellent Triptych Continuum, and is an interpretation of how the confrontation between these two ponies could have gone in a very slightly different universe. It may contain spoilers for Triptych. You have been warned.)

(Erfworld crossover)

Erfworld is a world ruled by Numbers, a world that runs as if on the mechanics of a turn-based strategy game. How far can you travel in a day? A number of hexes equal to your Move. When enough fights and you will level up, growing stronger. Magic is well known; from Predictamancers to Mathamancers, Foolamancers who fool the senses to Dollamancers who make clothes and golems. Home to giant firebreathing dwagons, hulking twolls, eight-legged spidews, most sides are ruled by the two-legged, Language-speaking tribes of Men.

Most sides.

(Previously published on the Erfworld site. Reposted here in its entirety.)

It started over tea. Twilight and Starlight agreed to each invite one friend; and then the conversation turned to the question of what if the world around them was nothing but a work of fiction?

When a visitor from the future appears out of nowhere in Twilight's new castle, he triggers a series of events that sends Twilight back and forth through history...

For other takes on the same prompt, see Stopped Clock, by Carabas, and From Forever, With Love by Monokeras

Rainbow Dash tries to write a story. Twilight tries to read it.

Then Discord decides to be helpful...

Tirek has, undoubtably, thoroughly, completely, won.

He has all six former bearers of the Elements tied to his (formerly Celestia's) throne.

He has the other three alicorns trapped in Tartarus.

He's absorbed every scrap of magic from every pony in Equestria.

And nopony will ever get a cutie mark, ever again.

Three certain fillies are going to do something about that. And if they can somehow rescue their sisters in the process, all the better...

For another take on the same idea, see Crusade at Midnight Castle by Carabas; or, for a story that takes the idea in a completely different direction, see Der Unter-gang by Monokeras.

The Banach-Tarski Theorem describes how to split a sphere and re-arrange the pieces to make two spheres of volume equal to the original sphere.

Turns out it works on dragons, too.

(Cover taken from http://mlp.wikia.com/wiki/File:Spike_ID_S3E05.png and slightly modified)

For other stories of similarly duplicated characters, take a look at Second Sun by Carabas and Amphelion by Monokeras.

This story is a sequel to Roaming

Applejack goes home for Christmas.

She has news to tell her parents... about the fact that there's a portal, open three days every thirty moons, to an alternate universe in the courtyard of Canterlot High. But that can wait until tomorrow.

Today, Clementine Apple has a perfectly innocent question to ask her daughter...

This story is a sequel to Skywriter's excellent story Roaming.

Every now and then, something happens that Twilight feels the need to question. Why didn't Celestia tell her about the Elements, when she asked before Nightmare Moon's return? Why does Ponyville allow pegasus or earth pony magic during Winter Wrap-up, but not unicorn magic? Why were there no stallions at the Running of the Leaves?

And, like any good student, when Twilight finds a need to ask a question, she asks it.

Trivial Knowledge was a unicorn with a gift of near-perfect recall of minor information. He was also one of the first five ponies sent by Princess Celestia to leave the comfort of Equestria, seeking new horizons, new worlds to explore, new friends to meet, aboard a space-travelling construction known as the Friendship.

These are a sample of her voyages.