• Published 2nd Sep 2014
  • 1,120 Views, 47 Comments

Ponies Learn Calculus - Lopsy

Can the mane six discover calculus fast enough to win a flying competition, counter a deadly parasite, and destroy a tornado? A fanfic slash calculus tutorial.

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Chapter 1 - Speed Limit

Rainbow Dash blasted through the window into Twilight’s library. “Twilight! Twilight! Are you there?”

“Mmrmph,” said a muffled voice from below her.

Rainbow looked down. Twilight Sparkle was sprawled on the floor under her. “Whoops,” she said sheepishly, removing her hoof from Twilight’s mouth. “Sorry about that. I thought I had a clear landing.” Dash helped Twilight to her hooves.

“Don’t worry, I’m not hurt,” Twilight said. “My window, on the other hoof—”

“There’s no time for that, Twilight. Take a look at this!” The colorful flier handed her the colorful flyer.

“Oh? What about it?”

“The Wonderbolts are gonna be watching this like hawks,” Dash said. “I have to snag first place tomorrow.”

Twilight flipped over the flyer and started reading the fine print. “I see. It appears that this competition focuses less on speed, and more on maneuverability and complex tricks.”

“Exactly. And to be a Wonderbolt, you’ve gotta be the best at both.”

“Good luck, Rainbow! I’ll be there to cheer you on. Have you planned out your act yet? Maybe you should rehearse it tonight. I’ll pretend to be a judge, and—”

Rainbow raised a hoof to stop her. “Thanks. But what I really need right now is — well — Twilight, do you have any kind of speed-measuring spell?”

Twilight stroked her chin. “Speed-measuring? I can’t say I’ve heard of any spells like that. Why?”

“Wellllll, I kinda found out today that the stadium’s really small, and they’re judging style over speed, so… the competition has a 20 ponylengths per second speed limit.”

“Yes, it says that right here.” Twilight pointed to a sentence written in tiny font on the back of the flyer. “Wait. You mean you didn’t read the rules until today?!”

Rainbow turned away, embarrassed. “Look, it’s fine, okay? I threw together a new act today. I just need to know whether it follows the rules. But if you don’t have a speed-measuring spell, I guess I’ll leave…” Rainbow trailed off. She opened the library’s door and sulked out.

Twilight galloped outside. “Rainbow! Wait!” she said. “I may not have a spell, but I’ll try my best to help you out. Can I see your act?”

Dash grinned. “Not here. This series of awesome tricks is top secret. We have to go somewhere nopony will ever find us.”

“Where is that?”

“Just follow me.”

* * * * *

Later, in a clearing deep in the Everfree Forest…

“The fastest part of this trick,” Rainbow Dash lectured, “is at the very bottom of this loop-the-loop.”

As Twilight watched, Dash spread her wings and took to the sky. She started to flap her wings erratically. Slowly, she turned herself upside-down.

This is no simple task.

Both bird wings and pegasus wings are built for pushing their owners upward. If anypony tried flying upside down normally, they’d rocket towards the ground.

As such, Dash had to jitter her wings up and down in an irregular, alien-looking pattern, just to stay afloat. Most pegasi never bothered learning this trick. And there was nopony else lunatic enough to try what Rainbow did next.

She dipped her head downwards, and started to fall.

She accelerated towards the ground.

“No!” Twilight yelled. Her horn glowed as she prepared to catch Rainbow with her telekinesis.

Would her magic have caught Rainbow Dash in time? We’ll never know. A split second before she hit the ground, Dash pumped her wings. She contorted her sleek body, wrenching herself into a hairpin turn.

For a split second, Dash was right-side up, her stomach skimming the grass. Then she soared upwards, leaving Twilight’s magic with nothing to grasp but thin air, and her jaw nowhere to go but down.

Dash grinned. “So. How was it?”

Twilight gaped. “Wow. I wouldn’t call it ‘elegant,’ but… before seeing it, I also wouldn’t have called it biologically possible.”

“No, I mean the speed! On the turn, was I going over 20 ponylengths per second or under?”

Twilight put her hoof to her chin. “Hmm… I’m not sure. Mind showing me again?”

“No problem.” Rainbow darted up into the sky and flipped herself upside-down.

* * * * *

Seventy minutes later…

Twilight shuffled through a sheaf of paper in front of her, filled with numbers and graphs. “Let’s see…” she said. “I’m 90% confident that your top speed is somewhere between 15 and 25 polylengths per second. Mind doing ten or twenty more trials?”

Rainbow Dash was slumped on the ground. “Sure… *pant*… thing… *wheeze*… Twilight…” She groaned. “Why is this… *pant*… taking so many tries? I’m totally doing the same thing… *pant*… every time,” she said.

“Sorry,” said Twilight. “It’s just so hard to gauge your speed by looking.”

Dash sighed. “Rats.”

“Maybe you can do the trick without any turning or accelerating? If you were moving at a constant speed in one direction, we could use speed=distance/time to find the answer.”

Rainbow rolled her eyes. “Duh. I don’t think the judges will be impressed… *pant*… by your ‘fly in a straight line’ trick, Twi.”

Twilight turned away. “Sorry, Rainbow. I wish there was something I could do.”

“Why don’t’cha use this?”

Twilight did a double-take. Pinkie Pie had suddenly appeared beside her, holding an odd black rectangular device.

“Um, Pinkie… what’s that?” Twilight asked.

Rainbow let herself flutter to the ground, thankful for the chance to catch her breath. “More importantly, how did you find my hyper-secret hiding place?”

Pinkie showed them the front of the device. It had a small rectangular screen. The screen showed an image of Dash hovering upside-down in the air.

“It’s a camera, silly! Don’t you see them following us around every Saturday? I saw one heading into the Everfree Forest, and I just knew it had to be following up on something fun!”

Rainbow took a sidelong glance at Twilight. They both shook their heads, mentally agreeing not to pry into Pinkie’s mind.

“So… how does this ‘camera’ work?” Twilight asked.

“It’s easy-peasy-lemon-squeezy.” Pinkie pressed a button on the device, and the screen jumped into motion, showing a video of Dash’s trick.

Dash stared at the screen, transfixed. “I knew I looked awesome, but I didn’t know I looked that awesome…”

Twilight pushed her aside. “Pinkie Pie, this technology is amazing. I have to study this.”

“Gooooood luck! They go away once you start doing boring stuff.”

“That doesn’t make any –” Twilight stopped herself, remembering the Pinkie Sense incident. “Ugh. Fine.”

“Cameras can do tons of other stuff too! You can watch Rainbow’s trick zoomed super way in, or even go through it frame-by-frame.”

“Frame-by-frame?” asked Dash.

“Yepper-doodle! Cameras record footage at 30 frames per second. But usually you only watch frame-by-frame if you’re looking for Easter eggs or animation errors.”

Twilight started playing with the camera, ignoring Pinkie Pie’s nonsense outburst.

You can play with it too, here. You’ll need Flash Player.

If you don’t have Flash Player (maybe you’re reading this on a phone), here’s a quick description of what Twilight and Rainbow Dash discovered.

- The camera let them watch Dash’s trick as many times as they wanted.
- They could also pause and zoom in.
- In addition, they could step through the action, frame by frame. The camera records footage at 30 FPS.
- The footage also shows a small stick on the ground. This is Twilight’s measuring stick. It is one ponylength long, and has markings every 1/10 of a ponylength.

Twilight and Dash want to determine whether Dash’s speed is above or below 20 ponylengths per second, when she’s at the very bottom of her loop.

Using just the information you have so far, you should be able to figure this out!

(If you don’t have Flash Player, you won’t be able to figure out the answer yourself. But maybe, if you think hard, you can figure out a method Twilight and Rainbow can use to find the answer.)

Author's Note:

Next time on Ponies Learn Calculus: Lightbulbs! Onion skins! And maybe even... some actual math?

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