The Tao of Two Pie

by Pineta

Rating: everyone
Tags: Comedy, Maud Pie, Pinkie Pie, Slice of Life, My Little Pony: Friendship is Magic
Length: 1914

Once upon a time on a rock farm, two sisters bond over a piece of geometry.

Once upon a time on a rock farm, two sisters bond over a piece of geometry.
Written for tau day (τ = 2π = 6.28) following a suggestion from Walabio

Published 2014-06-28 13:20:05 UTC
Last updated 2014-06-28 13:20:05 UTC

Easy as two pi

“Will you read me a story?”

The little pink filly, tucked up in bed, clutching a stuffed toy alligator, looked up at her older sister with large hopeful eyes and an adorable pleading expression. However Maud Pie was gifted with a strong natural resistance to attacks of epic cuteness. She had exams coming up and wanted to read through her crystallography notes before going to bed.

“No,” she said.

They were alone that evening, as Mom and Dad had gone, with their sisters Limestone and Marble, to visit Granny Pie at her farm in the next valley. They had left their eldest daughter with a list of chores: to check the rocks were safe for the night, lock up the farm, and put her little sister to bed.

“Pleasepleasepleasepleasepleasepleasepleaseplease! I'm not tired yet.”

“You could play with Rockie.”

Pinkie brought her head down to the level of her pet rock, sitting on a table beside her bed, and stared intently for a short moment before reaching a decision. “Rockie doesn't have anything to say tonight. He told me that he was tired out after playing all day with his rock buddies.”

Rockie didn't contradict this. Maud felt this was a bit unreasonable. Her preliminary geological studies had taught her that every rock had a fascinating life story. But it was true, they were not very good at telling them to young foals. They didn't talk. They were rocks.

“I don't know any stories.”

“But you can read one—you've got all those books in your room.”

“They're not story books.”

“Will you read me a not-story?”

Maud sighed, then walked out of the room and across to her own bedroom. Whereas Pinkie had painted her room with bright pictures of balloons and cupcakes, Maud's room had a plain blue and grey décor. It contained a bed, small closet, a study desk with her pencils and notebooks neatly arranged, and a large book shelf. On the wall was pinned her revision schedule, with highlighted study periods for physics, chemistry, geology and double maths.

She looked at the shelf searching for something which might be suitable for Pinkie. Maud read exclusively non-fiction. She ran her hoof across the spines reading the titles: Story of the Earth—that was a bit too violent for a little filly... Tectonic Tales, maybe...

No. That was the wrong approach. She needed to make it quite clear to Pinkie that she had no books which could possibly interest her. They were quite different ponies, and the sooner she learnt that and stopped pestering her for bedtime stories, the better. She could read Pinkie some of her poetry. Then she had a better idea. She prised a copy of Euclop's Elements off the shelf and ran a hoof lovingly across the cover. This was one of her favourites.

Maud had discovered the work of the ancient Pegasus mathematician in a dusty old volume on a shelf of the mobile library which visited the rock farming region once-a-month. The librarian had said it was never read by any other pony, so she may as well keep it. Maud had then spent many hours reading through the definitions, axioms, and theorems. At first, it was a fascination with the language—a new sort of poetry to her—so beautiful, and hinting at a deeper meaning. As she grew older and learnt more mathematics and science, the fascination turned to veneration of the ancient text. The foundation of all knowledge. The rocks she knew and loved around her could be understood through chemistry and physics, based on mathematical laws, and ultimately everything stood on the foundations laid by the scholar of ancient Pegasopolis, over two thousand years ago.

She had quickly learnt that this admiration was not shared by other ponies. After brief attempts to explain it to her family, she realised that they were simply not the slightest bit interested. So Elements became a private pleasure, and she spent many an evening reading it to herself, or to Boulder, her pet rock. Although fond of her family, Maud had always spent most of her time in private study, which suited her fine. There were not many opportunities for socialising on the rock farm. Her sisters Limestone and Marble were happy to play together and let her be. But her younger sister Pinkie was growing increasing hyperactive since she gained her cutie mark, and had an excessive enthusiasm for parties. Well, a few pages of Elements would calm her down.

Maud walked back into Pinkie's room carrying the book and Boulder. She sat down on the bed, opened the book and started reading.

“A point is that which has no part.”

“No part of what?” said Pinkie.

“It means it has no length, width or breadth. It's indivisible.”

“Like a cake sprinkle! No, that does have a length, just very short. Like a grain of sugar! No. Like a really small grain of sugar!”

“A line is a length without breadth. The ends of a line are points.”

“A streamer without breadth? That would be silly, it would just be a piece of string. No thinner than string...”

“A straight line is a line which lies evenly with the points on itself.”

“Straight lines are boring. Wiggly lines are far more fun. Well I think so. Like whenever I go across the south field to the outhouse—some ponies just go in a straight line—but I take the interesting route...”

“A surface is that which has length and breadth only. The edges of a surface are lines. A plane surface is a surface which lies evenly with the straight lines on itself.”

“Can you touch the tips of your ears with your tongue? I've been trying to do it for weeks now, and I've just about got it, at least for my left ear, my right ear seems to be more difficult, which is a bit odd don’t-cha think? Surely it should be the same distance from your mouth to either ear?”

Pinkie's reaction to Elements was unique. On previous occasions when Maud had read it to another pony, she had just received a blank look of incomprehension. She had never had a commentary before.

“A plane angle is the inclination to one another of two lines in a plane which meet one another and do not lie in a straight line.”

“Angle is a really cool word. It rhymes with bangle, and jangle, and wrangle, and tangle. My mane has been getting into a real tangle every time I go outside when it’s windy. Doesn’t bother me but Mom seems to think it’s a problem and she attacked me with a comb this morning, which hurt! And it didn’t do any good as two minutes later my mane was just the same as it had been before she started. I don’t know why she always picks on me. She never goes after you, or Marble or Limestone with a comb!”

Of course it didn't matter that it was Elements, Pinkie would have given an equally enthusiastic random commentary if she had read a chapter from Fairy Tales for Young Foals, or something from The Rock Farmers' Almanac, the Table of Radioactive Isotopes, or the dictionary.

“A boundary is that which is an extremity of anything. A figure is that which is contained by any boundary or boundaries.”

“Like that fun thing we did at school last week when we all got sheets of paper with line drawings of our favourite ponies and we got to colour them in, and almost everyone tried to colour in them all accurate and lifelike, but I coloured mine in completely different as it's more fun that way, and I thought Princess Celestia looked really cool with a yellow and orange coat and black and red mane, but everyone else said that's not how you're supposed to do it...”

“A circle is a plane figure contained by a single line, such that all of the straight-lines radiating towards the circumference from one point amongst those lying inside the figure are equal to one another. And the point is called the centre of the circle. And a diameter of the circle is any straight-line, being drawn through the centre, and terminated in each direction by the circumference of the circle. Any such line also cuts the circle in half.”

Suddenly Maud had an idea. She jumped up and trotted over to her room, and returned a moment later carrying a notebook, a pencil, and a piece of string. She then sat down next to her sister and placed the notebook between them. She tied one end of the string to the pencil, and then placed the other end in the middle of a blank page.

“Hold it there, in the middle,” she said to Pinkie.

Pinkie obligingly placed a hoof on top of the loose end. Maud then pulled the pencil until the string was taut, and used it to trace out a loop on the paper.

“That's a circle!”

“...a plane figure contained by a single line—that's the circumference—such that all of the straight-lines radiating towards the circumference are equal to one another.” Maud pronounced the definition with due reverence. “Now can you tell how many times this line—the radius—goes around the circumference?”

Pinkie closed one eye, focussed intensely with the other, and stuck out her tongue to aid her concentration. With two hooves, she moved the piece of string around the edge of the circle counting the number of times the length would fit.

“It's about six,” she said.

“It's actually a bit more than that,” said Maud.

“Six and a half?” guessed Pinkie.

“Not quite that much.”

“How much?”

“6.283185307179586—roughly speaking.”

“How rough?”

“It has an infinite number of digits, which follow an apparently random string of numbers.”

“I LOVE apparently random strings of numbers! Teach me! Teach me! Teach me!”

“6.283...” Maud repeated the digits of the irrational constant slowly, and Pinkie, with the aptitude of a young child for memorization, learnt them all, up to twenty decimal places.

“It's a special number,” said Maud, “so we give it a special symbol – the Pegasus letter tau.”

She wrote this symbol in the centre of the circle in her notebook: τ.

“And that's just one way to do it. We can also look at the ratio of the circle circumference to the diameter, which is half of tau, or about 3.142. We label this number with the letter pi. So tau is equal to two pi.” She wrote τ = 2π and underlined it.

Pinkie yawned, and closed her eyes, as the excessive number memorization routine had finally tired her out. As her little sister drifted off to sleep, Maud tip-hooved out of the room. Back in her own room she pushed Elements back into its rightful place on the shelf (under E), then sat down at her desk and opened her notebook, and started reading her notes on the crystalline structure of basalt.

But her mind was now on other things. She wondered what she and Pinkie could do together tomorrow morning, before the rest of the family returned. Putting her notes to one side, she picked up a stack of magazines, and flipped through an old copy of Junior Equestrian Rock Scientist. She started reading an article she had noted a while ago, but not paid any further attention at the time, entitled 'Rock Candy Recipes'.

Author's Note

Euclid's Elements
Tau Day