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.)
My prayers have been answered!
This is an interesting premise. I hope that this fic will teach me a little bit about the basics of calculus.
I see someone uses WolframAlpha. Definitely a good read for someone in calc, like me.
u nobe smart and make us have math here
Oh wow. Teaching calculus with ponies? I see nothing wrong with this idea. And you've even included some Flash animation. This is awesome.
It's been a few years since I've taken any math classes, so we'll have to see what I remember.
As for the answer (assuming I remember how to do math correctly):
It looks to me that at the bottom of her loop, her cutie mark travels from the 0pl marker to the 0.6pl marker in one frame (1/30s).
(0.6pl)/(1/30s) = (0.6*30)pl/s = 18pl/s
That's lower that Twilight's prediction, and it seemed surprisingly easy. Did I mess something up?
I was kind of hoping that Pinkie's box would be a calculator. I'm not even sure I know how to do math without one anymore.
For those who are too lazy to watch the animation, it's clear that Rainbow takes more than one frame to traverse the length of the ruler.
If she were moving faster than 30 ponylengths/sec then she would pass the stick in a single frame, since the camera takes 30 frames per second.
Hence she's not breaking the speed limit.
Very cool idea, and it's even accompanied by a flash animation! Definitely watching this one.
4941214
I came to the same conclusion. At first, I measured from her front hoof, which in one frame went from .3 pl to .8 pl (.5 pl) but after reading your comment I looked at the cutie mark. Her speed then does appear to be 18 pl/s
This seemed way to easy, even for entry level Calc.
4941366
Yeah, I got that measurement at first too. But since the result from doing it that way (15pl/s) seemed too small, I looked for alternatives that would give a better result. Though admittedly, this result isn't that much better.
The apparent simplicity of this question did throw me off too. But I suppose that most math classes, at least in high school, do tend to start with a super-simple overview of everything you should already know that the rest of the class will then build on.
4941264
And here we have the clever guy who figures out the answer the easy way.
4941495
This week it's Pony Calculus Answers: brought to you by The Letter J !
God Dang you, cellphone. I'd love to figure it out by myself. I'm a math freak myself so... aaaaaaahhhhhhhh. Frustration.
This is relevant to my interests!
Liked and faved!
Also, typo detected:
Should be ponylengths.
I hate maths, but I like this.
4941495
As my first-year calc prof said, "Mathematicians are lazy". Go for the elegant proof!
and I'm on my laptop. lets say 0.8 ponylenghts in two frames. so 0.8 PL in four seconds. multiplied by fifteen is (four sec*15 = 60) and 0.8 * 15 = 12.
so I say 12 PL/S
the trick is slow enough for the competition.
New all-time favorite fanfic 4th wall breach.
W-why would you make this? YOU MONSTER!!! *cries* *sobs*
*full-on weeping*
I was going to use this to remember my calculus ... but so far it's a question and not a study-help.
Lead us through a problem. THEN present a similar problem. Then present a dissimilar problem.
Really hoping this works out, I'd love to remember my calculus ...
4942248
That's the exact same thing they've been telling me since my first year in secondary school.
4942598 *wraps arms around you murmuring consoling words*
4945177 *gets soothed enough to talk* W-why would you do this?
4945198 It's okay. Shhh. Go read something fluffy and happy.
4945409 I cannot feel... Only pain, and sadness... No Empathy, no Compassion... Just pain...
4945418 just read this.
4945480 ...Still nothing.
I don't think that I've seen an author attempt to weave a mathematical word problem into a (relatively fleshed-out) fanfic narrative before, and I'm impressed with just how well it works.
The only similar concept to this which I can recall ATM is Pineta's "The Tao of Two Pie" story, which explains some fundamental mathematical *principles* through pony narrative, but doesn't have an actual 'problem' to solve, per se. Come to think of it, Pineta has quite a few good edu-tainment pony stories. The two of you ought to share notes and collaborate on something IMHO.
You've got my attention. Great to see another writer playing my favourite game of mixing ponies and science. This was well written and the animation worked well. I look forward to reading more.
I once created an analogy which explained certain aspects of chemistry and nuclear physics via people on rocket powered roller skates(protons, with the rollerskate settings being heat) trading the scarves that were their only clothing(electrons) between the groups that clung together for social purposes (atoms), and were themselves held together by monkeys (neutrons).
Alas, for this text is lost to the mists of time. It was pretty good.
My point, however, is that however good your work is, you are setting your (initial) goal too high by suggesting that people should ask their teachers to make this (when and if finished) an actual text... now something they refer students who are having problems to, or even if you could get a DVD ROM version available (or CD ROM for older school computers), that might be of use as a supplemental teaching method. When and if this is wildly successful, THEN you could start thinking "textbook".
I look forward to seeing this thing's progress.
Thanks for the comments!
Quick edit - the speed limit in chapter 1 was supposed to be 20, not 30. Of all the things I could get wrong, of course it'd be a math error
Chapter 3 will go up this Saturday.