Poem: "The Archetype of the Beauty"
Feb. 26th, 2018 12:43 am![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
ysabetwordsmithThis poem came out of the November 11, 2017 Poetry Fishbowl. It was inspired by prompts from technoshaman and peoriapeoriawhereart. It also fills the "homesickness" square in my 6-16-17 card for the ![[community profile]](https://www.dreamwidth.org/img/silk/identity/community.png)
hc_bingo fest, and the "hour" square in my 10-31-17 Time card for the Space and Time Bingo fest. This poem has been sponsored by EdorFaus. It belongs to the Shiv thread of the Polychrome Heroics series.
Note: Nothing bad happens in this poem, but the inside of Shiv's head is a mess, so he's angsting over things that would normally be enjoyable. Be patient with him.
"The Archetype of the Beauty"
Shiv hadn't meant to encourage Dr. G
by actually taking any of the classes,
but he couldn't resist Tactile Math
with its colorful crocheted frills.
He hopped a bus to the library,
kicking his toes against the seat
the whole way there and rocking
hard enough to make people glare.
He got there a good fifteen minutes early,
because the bus schedule in his neighborhood
wasn't as generous as some other places got.
The W. Dale Clark Library towered
over the Gene Leahy Mall, sleek stone
forming a block four stories tall.
Shiv slipped inside, hoping that
nobody would notice him, but he
was so stunned by the interior
that he stopped in his tracks
and people bumped into him.
Hastily he scrambled out of the way
so that he could stare up at the hole
through the middle of the building
which let him see all the floors.
A huge mural hung overhead,
showing a partial map of the Earth.
Nearby, a display advertised routes
for the Neighborhood Walk program.
Now that he thought about it, Shiv could
remember seeing the trailhead signs
and route markers around the area,
although he'd never followed any.
He found the art gallery, too,
full of paintings and sculptures,
its bulletin board plastered with
flyers for upcoming art classes.
There were books everywhere,
of course, but more than that,
there were tables and chairs
between the bookcases and
desks tucked under the windows.
One stairwell had a mural all over it,
not quite graffiti, but something that
reminded Shiv of graffiti. He liked it,
but he couldn't quite pin down why.
Shiv had been in libraries before,
of course, but never anything like this.
Field trips were for kids who could be trusted.
All he got were shitty school libraries and
neighborhood branches in dingy buildings.
He rarely stole from the Little Free Libraries
because those things were boring.
Today he wandered around in a daze
just looking at all the incredible stuff
until his vidwatch beeped a warning.
Then he had to hustle to the meeting room
so that he wouldn't be late, because that
would attract way too much attention.
Shiv slunk in through the door
and found a chair in the back corner
where hopefully nobody would notice
that he didn't belong here at all.
He stared at his toes and realized
that they finally stopped tapping.
Just to make sure, he tucked
his hands between his knees
to keep them out of trouble too.
When he snuck a quick peek
to check out the rest of the crowd
and see how badly he stuck out, Shiv
was surprised to see that most of them
were close to his age, and about half wore
some combination of red, black, and white.
An older woman came in carrying a basket
of yarn and big bags full of other things.
Sunglasses perched atop her graying hair,
and a wide smile flashed white against
the warm brown skin of her face.
She wore a nametag saying Cadenza
stuck on the front of her sweater.
Shiv hadn't taken a nametag.
He was generally better off if
nobody knew who he was.
The woman introduced herself
as Professor Cadenza Darden from
the University of Nebraska at Omaha.
Shiv scrunched down in his chair and
wondered if it was too late to escape.
He hadn't even realized that this was
supposed to be a college class.
Cadenza started talking about math
that was so far over his head, he could
hardly understand one word in ten.
She used a big white board on wheels
to write things with colored markers
that had more letters than numbers.
Shiv looked around the room for
a distraction, but there wasn't much
that could hold his attention for long,
just the chairs and the people in them.
When he shifted his focus to the metal
in the room, though, it got more interesting.
Cadenza had a bracelet on her right wrist,
a watch on her left wrist, and rings on
both ring fingers, so Shiv could feel
most of what she did with her hands.
She had a nice voice, dark and sweet
and smooth like chocolate frosting.
Shiv leaned back in his seat,
content to listen for now.
A nudge startled him upright.
"Hey man, you want this thing or not?"
said the guy in the next chair. "If you
don't, at least pass it to someone else."
Startled, Shiv looked over to see
one of the frilly things from the flyer,
and reached out to grab it eagerly.
It was made of plain yarn, but it was
a deep eggplant color in the center,
changing to violet, lilac, and finally
pale lavender along the edge.
It had kind of a cone shape, with
a hole going to a tail in the middle,
then spreading out to a circle, and
the rim curled into ruffles.
Shiv grinned as he ran his fingers
over it, trying to make it lie flat, but it
wouldn't since there was too much yarn.
"Pass that on now, and take this,"
he neighbor said, handing him
a purse made of sky-blue yarn.
Shiv did so, and discovered
that the purse opened to reveal
a whole set of tiny yarn things.
Laving them out along his leg,
Shiv found a little red nub, then
a red with a yellow ring, followed
by red rimmed in yellow and blue.
The one with the green rim
wouldn't lie flat anymore,
not even when Shiv tried
to iron it with his hands.
The next one had a border of
indigo almost the same shade
as the blue, and it ruffled.
The last two, with a hot pink rim
and a bright orange one, were
even frillier than the first few.
With the pieces laid in a row,
Shiv could see how they went
from flat to frilly, could trace
the spiral with his fingers
and feel how it changed.
The next thing to come around
the class was a pinkish frill.
Reluctantly Shiv stuffed
the colorful set back into
the purse and passed it on.
The pink thing had a tag on it
with numbers and letters that
made no sense to Shiv, but
it felt interesting to touch.
Every few stitches, there was
a sort of kink or a bump
where it got bigger.
He might not be able
to read the fancy math
written on the tag, but he
could grasp the yarn.
His neighbor handed him
another set, this time two frills.
One was red with yellow lines
stitched across it, and Shiv could
see how they ran side-by-side if he
folded the frill in different ways.
The other was purple with white lines
that made sort of a triangle except
the sides bent toward the center.
It almost made sense to him.
They looked like petunias.
Next he got a floppy oval,
yellow in the middle with
purple and then green along
the edges. It reminded him
of the sea slug pictures that
Aida had shown him.
After that came a long riffle
that he thought might be meant
as a scarf. Instead of colors in rows,
it was made of candy-colored yarn
that changed all the way through,
making it sort of speckled.
Shiv pulled it through his hands,
enjoying how the ripples tickled
against the skin of his palms.
The last was a ruffle so dense
that it curled itself into a ball,
the inside dark green with a glint
of metallic thread here and there,
the outer edge a bright red.
A loop of red yarn made him
realize that he was holding
a Christmas ornament.
Shiv sighed.
For a while, he had
stayed with a crafty family
that sucked way less than usual.
It hadn't lasted -- nothing in his life
ever lasted for long -- but still, it had
been almost nice for a while there.
He remembered their Christmas tree
hung with godawful handmade ornaments.
His foster grandmother had tried to coax him
into making one himself to add to it, but Shiv
had refused. He never made anything good.
Now he dug his fingers into the crinkly ball
and wished he could make nice things like this.
To make matters worse, the teacher
reminded him of his foster grandmother,
who he hadn't thought of in years.
He remembered his foster mother,
too, and the tangle of morning routines
as she sorted out hair care for kids with
all different colors and textures.
A twinge of homesickness
went through his chest, the pain
spiraling from one side to the other
as if pulling a riffle through his ribs.
Shiv huffed and shuffled in his seat,
trying to make the unfamiliar feeling
go away and leave him alone.
He tried paying attention to the lecture,
because if math couldn't put him
to sleep then nothing could.
Then he realized that Cadenza
was doing something with her hands,
and yeah, there was a steady flick-flick-flick
against his attention that he hadn't noticed
before, metal moving in a rhythm that
reminded Shiv of a metronome.
Looking closer, he saw that she
had a ball of light blue yarn and
a tool of some kind, like a long pin
with a blunt hook at one end of it.
Crochet hook, he recalled suddenly,
remembering his foster grandmother
in her rocking chair with a ball of yarn,
the bright metal dancing in her hands
as she made a pair of mittens.
Despite the awkward memories,
Shiv found Cadenza's crochet soothing
in a way that let him slump against
the back of his chair and let go of
some of the ever-present tension.
The soft chime at the end of class
startled Shiv out of his lull.
Had it really been an hour already?
Most of the other people got up and left.
A handful of those in the front row
clustered around the teacher,
pestering her with questions.
Eventually they drifted away, too,
leaving just Shiv and Cadenza.
"I haven't seen you here before,"
she said in her warm voice.
"Uh ... guy I knew gave me a flyer
for it," Shiv said, looking down to where
his hands still held the ruffle ball.
"Mind giving me a hand with
the cleanup, then?" she said,
waving a hand at the room.
Shiv looked up and saw
that everyone else had left
the yarn thingies scattered
all over everywhere.
"Okay, I guess?" he said.
Cadenza held out a bag.
"Just drop them in here."
Reluctantly Shiv gave up
the ruffle ball, then stuffed in
the floppy oval. "These are
really cool," he said. "I've never
seen anything quite like them."
"Hyperbolic planes are fun,"
she said. "They look so hard
to make, but they're easy --
it's just a basic stitch with
a lot of increases in it."
"I can't crochet," Shiv said,
"or do math, and I kind of
suck at school too."
"Handsy as you are, that's
no surprise," Cadenza said.
"I wish more people would
teach tactile math so that
touch-dominant students
could actually learn it."
"Huh?" Shiv said, baffled.
"People can learn things in
different ways, and most folks
have a favorite," she said as
she scooped up the lined frills.
"Like what?" Shiv asked. "School
is pretty much the same everywhere."
"Oh, not everywhere -- there are
different ways to teach," Cadenza said.
"You seem to favor touching things,
so if people tried to teach you with
just text or talking, that probably
didn't make a whole lot of sense."
"Well, but that's because I'm stupid,"
Shiv pointed out. He found the blue purse
and popped it open to make sure all of
the little bits were inside. They were.
"I don't usually see stupid people
in my hyperbolic math classes,"
Cadenza said in a dry tone. Then
she opened a new bag. "But here,
let me put the bottom rungs on
the ladder and see how you do."
This one held a bunch of flat shapes
and some that were like soft blocks.
Instantly Shiv put his hands behind
his back and held on tight enough
that his fingernails dug into the skin.
"You're not going to learn much
like that," Cadenza said. "Come here
and get a feel for these things. They're
made out of yarn, so they won't break."
Hesitantly, Shiv picked up the first one
and saw that it was a circle, pale pink
in the middle and darker at the edge.
There was a square, too, with
a sort of diamond pattern coming in
from the corners, another circle,
and a thing like a stop sign.
"How's come you got extras?"
Shiv wondered, stacking the circles.
"Take a closer look," Cadenza said
with a smile. "Poke at them to see
if you can feel the difference."
Shiv ran his fingers over
the soft ridges, tugging gently
to look at how the stitches went
together, but it wasn't until he
held them up to the window and
light shone through the holes
that he saw what she meant.
"Oh!" he exclaimed. "This one
here goes in rings, and then this one
goes around and around like a screw!"
"Exactly," said Cadenza. "One uses
concentric circles and the other a spiral.
Why don't you see what else you can find?"
Shiv scrabbled in the bag, looking for
more of the other shapes, and soon
he had a whole row laid out on chairs,
pairs of circles and triangles and squares
and other shapes he couldn't name.
That was okay, because Cadenza
identified each one as he took it out
if he didn't say the name himself.
"Here is a ball made using
a typical crochet pattern,"
she said, holding it out.
"That's not a very good ball,"
Shiv said, frowning at it. He
took it and looked closer. "See,
the blue ends are round but
the green middle is flatter."
"You have good eyes, too,"
Cadenza said, handing him
a yellow ball. "What do you
make of this one, then?"
"It's rounder," he said. "I
like it better than the first one."
"This is called an ideal sphere,"
she explained. "Here, let me
show you what that means."
She opened a folder and
pulled out a worksheet
full of fancy math shit.
"I can't read that," Shiv said,
shaking his head at the page.
"Sure you can," Cadenza said.
"Look, this curve is the ideal.
Then these blue dots illustrate
the old pattern. The new one
follows the curve more closely."
Shiv looked at the page, and
then looked at the two spheres.
"I guess, maybe?" he said.
"Here's an easy one," she said,
handing him a colorful pyramid.
"What do you think about this?"
Tilting it in his hands, Shiv saw
that it was actually made from
four different triangles sewn
together along the edges.
"So that goes with these,"
he said, putting it down
with the flat triangles.
"It sure does," she said.
"What about this one?"
The new pyramid was not
quite as sharp as the old one,
more like a ball with corners.
Shiv poked at it and said,
"Why is this one different?"
"Try looking at both pyramids
so you can compare them to
each other," Cadenza said.
Side by side, the difference was
clear, but it took a while before Shiv said,
"Oh! This one goes around and around
instead of side to side. But then how
do you make it pointy instead of round?"
"That's in the pattern of increases,"
Cadenza said. "You can make
almost any shape with crochet."
"Huh," Shiv said. He dug into
the bag and found some cubes.
This time it only took him a moment
to say, "This is the flat kind, and
this one is made in a spiral."
"Very good, you figured that
right out," Cadenza said in
a voice that made Shiv
wiggle in pleasure.
She didn't yell at him
for doing that, either.
Shiv found that he didn't
mind helping her pick up
the rest of the ruffles.
It felt different, helping
someone who was nice to him.
"I wish school made sense
like this," he sighed. "I would've
gotten into so much less trouble."
"If your teachers didn't explain
things so you could understand,
then that is their fault, not yours,"
Cadenza said in a firm tone.
"Didn't stop them from
taking it out on me, though,"
Shiv said with a shrug.
Cadenza grumbled something
that sounded rude as she put
the scarf thingy in her bag.
Then she picked up
the pale blue ruffle that
she had made during class
and handed it to Shiv.
"Here you go, a little token of
appreciation for staying after class
to help clean up," Cadenza said.
"Thanks," Shiv said quietly,
fingers playing with the soft folds.
It was beautiful and soothing.
"I still can't crochet, though."
"Would you like to learn?"
Cadenza said. She handed him
what was left of the light blue yarn
and the lavender hook that she
had been using to work it.
"But these are yours,"
Shiv said, staring at them.
"They were, and now they're
yours," Cadenza said. "Let's see,
you'll want basic instructions."
Shiv didn't bother explaining that
he sucked at following instructions.
When she handed him the little brochure,
though, it made perfect sense, because
it had pictures along with the text. Inside
was a cheat sheet for all the letter codes
and more pictures of basic stitches.
"I could maybe figure it out?"
he said, laboriously sounding out
some of the written descriptions.
At least the words were short.
"That's good," Cadenza said.
"Practice just making chains,
squares, and circles for a while.
When you've got that down, then
you can try your hand at this."
Shiv looked at the new brochure.
"How to Crochet Hyperbolic Corals,"
he read. The front had more ruffles,
and yep, there was a coral reef made
from about a million colors of yarn which
looked kind of like the snapshots that
Aida brought back from the Maldives.
He wondered if she knew anything
about crochet or hyperbolic planes or
how much coral really looked like
the sculpture in the brochure.
"Remember, these are much easier
to make than they seem at first glance,"
Cadenza said, patting him on the hand.
"They're just single crochet with increases."
The hairs on Shiv's skin stood up and
then slowly flattened again. He wasn't
used to people touching him so casually.
He tucked his hands behind his back
so that he could rub over the spot
without getting caught doing it.
"I guess I can give it a try,"
he said. "I'm still no good
at math or school, though."
"So?" Cadenza said. "This is
a different kind of math. Lots of
people who aren't great with
abstract numbers do fine when
they get into geometry, because
it has shapes that they can see.
It's a whole new form of art."
"Math isn't art," Shiv said at once.
"I may not be an artist, but I know
how to draw some stuff, and art
is so not made of numbers."
"No, it's made of shapes, and
shapes have numbers hidden
in them," Cadenza said. "How
many sides does a triangle have?"
"Well, three," Shiv said.
"Even I know that."
"So that's a number
that lies inside a shape,"
Cadenza said. "It's all
like that, the numbers just
get more interesting later."
"Huh," Shiv said. He could
count to three and recognize
a pyramid when he saw one,
and he certainly liked the frills.
"Guess I never thought of math
as going along with art before."
"Have you ever seen the pages
of art exercises that use shapes
to practice shading, or draw a frame
to make a person or animal?" she said.
"Oh yeah, I've done those," Shiv said.
"The shading stuff is relaxing."
"Well, that's some of what you
can do with geometry in art,"
Cadenza said. "I'm no expert
in that side of things, but if you
watch the museum newsletters,
some of my coworkers go out
to do presentations on that topic."
Shiv hadn't been a fan of museums,
but Tolli and Simon had dragged him
to one of their favorites, which had
been totally different from what he
remembered of museum trips.
Maybe this would be like that,
the way it didn't suck if you were
with someone who knew their shit
and also wouldn't hit you.
"I'll think about it," Shiv said.
"Well, good," Cadenza said.
"Geometry is the archetype of
the beauty of the world. Everyone
should get a chance to enjoy it."
Shiv fingered the ruffle that
she had given him and
wondered if it was true.
"You really think so?"
"Of course," said Cadenza.
"That's the whole point of
crocheting hyperbolic planes.
Super-Intellect Daina Taimina
came up with to make them
more accessible to people."
Shiv watched the soft ripples
move over his fingertips and
wished that all math could be
this easy. "That's neat," he said.
Another chime sounded,
soft in the hush of the library.
"Oh my goodness, would you
look at the time," Cadenza said.
"Where did that second hour go?"
Shiv had no idea either. He
thought the class just let out.
He scrambled to gather up
all the stuff that she'd given him.
"Here, take this," Cadenza said,
handing him an empty grocery bag.
Shiv put in the pale blue ruffle,
the ball of yarn, the crochet hook,
and the two how-to brochures.
"Thanks," he said. "This class
was way cooler than I expected."
"It's been my pleasure ... why,
I just realized I don't even
know your name," she said.
"Shiv," he said, looking down.
Sometimes people made fun of it,
but damned if he was going to change
his cape name because of dumbasses.
"No wonder you're so sharp,"
Cadenza said with a laugh.
She actually knew what it meant.
That wasn't something that happened
very often with college people.
"Come here and give me a hug,"
Cadenza said, squashing him
briefly against her side and then
letting go at his startled "Awk!"
"Don't worry, dear, one of
my grandbabies isn't much
of a hugger either," she said.
"I'd better go catch my bus."
"Yeah, me too," Shiv said,
although he'd already missed
the one he meant to take home
and had no idea when another
would head in his direction.
It didn't matter, really, because he
could get on any bus and figure out
the transfers from the route map.
Besides, it'd give him time to start
looking over the crochet brochures.
* * *
Notes:
Cadenza Darden -- She has medium-brown skin, brown eyes, and straightened gray hair to her chin. She has a broad nose in a rectangular face. Sensitive to cold, she often wears scarves and sweaters even in relatively mild weather. Cadenza teaches math in the University of Nebraska at Omaha. Although she presents the usual classes, she specializes in alternative teaching methods such as Tactile Math. In addition to her work at the university, she also volunteers to teach free classes at libraries and community centers. Cadenza enjoys cooking and crafting for her large family and many friends. Or anyone else who doesn't run away fast enough.
Qualities: Master (+6) Professor of Mathematics, Expert (+4) Fibercrafts, Expert (+4) Wisdom, Good (+2) Comfort Food, Good (+2) Gentle, Good (+2) Grandmother
Poor (-2) Cold-Sensitive
In Terramagne, the University of Nebraska at Omaha also offers a Pre-Zetetics concentration. Actually several fields feed into zetetic studies.
This is Cadenza's crochet basket.
* * *
"Geometry is the archetype of the beauty of the world."
-- Johannes Kepler
The W. Dale Clark Library lies just west of the Gene Leahy Mall. Its features include: ADA Accessible, Bike Racks, Computer Lab, Computers, Free WiFi, Meeting Room(s), Printing, Scanning, Copying & Faxing.
Library Neighborhood Walks
Local-Omaha has a set of maps showing neighborhood walking routes around the W. Dale Clark Library ranging from 1 to 3.5 miles. Terramagne-Omaha has routes throughout the city ranging from .25 to 10 miles.
In T-Omaha, a neighborhood walk customarily has a sign at the trailhead which shows the route, marks points of interest, and gives historic or cultural information about the trailhead itself. Along the route, turns are often marked with smaller signs, color-coded if necessary to distinguish overlapping trails, and the points of interest have larger signs. A few places have routes laid when the development first went in, marked with lines of colored concrete or brick along the edges of the sidewalks. People may walk the route at any time, but most routes have some times marked when free guided tours are available.
See the exterior of the library. This is the interior looking toward the Gene Leahy Mall in winter. This is a similar view in spring. Here you can look up and see the floors above. The Kingman Mural is painted on a giant canvas rather than directly on a wall. It has been displayed in various places before coming to the W. Dale Clark Library. The circulation desk overlooks an open area. The library has a break area that serves healthy snacks and beverages to reduce the frequency of patrons who forget to eat and then faceplant into the floor.
The library supports a variety of art. This graffiti-inspired mural hangs in the stairwell. The art gallery displays work from a variety of artists. This is an art class for homeless people.
The children's library has a colorful rug. The third floor Genealogy Room has books, study tables with chairs, and plugs for laptops or other devices. This is the non-circulating reference section. The reference section has study desks all along the wall by the windows.
The library offers multiple meeting spaces. The lecture room suits large groups. This meeting room is somewhat smaller, suited for classes like Tactile Math.
This is a map of the Metro bus routes in Local-America. Shiv took one look at this thing and said, "Where's the rest of it?" Because mass transit in Terramagne-Omaha is much better than this. There's a Beltway route around the Greater Omaha Area that connects to transit hubs in each of its 11 regions, instead of only the 6 shown here. Where that belt parallels the Missouri River, they actually put in an auxiliary line that just does the River Run, so tourists don't overfill the Beltway buses. There are bus routes within walking distance of almost every place within that belt, which is to say, every few blocks. Every park of neighborhood size or bigger, every major municipal or public building, and all the little residential neighborhoods have at least one bus stop at their hub or a corner. It's just that the less-good and less-populated areas have lower frequency of bus service. In a good, dense area there are buses every 5 minutes or so. In most neighborhoods it's 10-15 minutes. In Shiv's, you might have to wait half an hour to an hour. By the time you get out to the beltway, there may only be a morning bus and an evening bus, but they'll get you to and from work. And that's just the municipal stuff: most hospitals, grocery stores, malls, and other large businesses have a shuttlebus of their own, and many large employers have a commuter shuttle or even several. There are private touring buses for tourists too. That's why Shiv has no interest in a car: he doesn't need one. The boy that foster parents called "stupid" can glance at that spaghetti barf of a map and say, "We need to catch the Teal, transfer to the Black, and go east."
The body language of insecurity includes hanging back, downcast eyes, restless hands/feet, looking around bored, self-touch, fidgeting, hands in pockets, shrugging, hiding or pinning hands. Notice how much of that is said to be "disrespectful" or "disruptive" ...? Sure, Shiv can be disrespectful. But more often, he's just uncomfortable.
Students with behavioral disorders or other special needs are often excluded from field trips and other educational opportunities. Appropriate supports make it possible for such students to participate. Notice that when the Finns take Shiv anywhere, they make sure that he has things like food, sun protection, and something to do -- and they step in to help if he starts to overload, instead of pushing him over the edge.
Little Free Libraries are wonderful things, but local America seems to hate them. They're quite popular in Terramagne-America. Read about them and build your own. Shiv does not realize that he can't "steal" what is there for anyone to take. This one is near the W. Dale Clark Library, and the article includes a map.
Kinesthetic and tactile learners, along with visual-spatial learners, do poorly with conventional lessons based on listening or reading. Tactile techniques such as finger counting help students to develop early math skills. Shiv's teachers presented material in a format he could not absorb, and then smacked him for finding his own solutions. So of course he hates school.
Read about Super-Intellect Daina Taimina.
Crocheting the hyperbolic plane makes a good homework assignment. The purple ruffle is in this set. Here is the purse and its pattern. This set of pieces shows the anatomy of a hyperbolic plane crocheted around a point. Here is the mauve ruffle and its math. The red ruffle has parallel lines on it. The lavender one comes with a triangle. The sea slug is another crochet project. The fiesta scarf is a long riffle that you can crochet. The Christmas ornament is a simple pattern.
Geometric shapes may be worked in rounds, in concentric lines or in spirals. See the circle, square, and polygon.
Crocheting a ball is relatively easy to do. It's a serviceable ball, but not a very good sphere. For that you need the ideal sphere, with a more complex pattern.
This pattern produces flat pieces for a pyramid. Here's a matching pattern for a spiral pyramid.
The flat cube uses these crochet pattern blocks. For a spiral cube, you can use this pattern.
The front of Shiv's first brochure teaches crochet basics. The back shows more stitches.
The front of the second brochure is about crocheting a coral reef. There are more pictures here. The back shows more patterns for hyperbolic planes.
Math and art share much in common. Explore shapes, polyhedra, perspective, and frame. Compare math and geometry art projects. This worksheet teaches line drawing and shading, among Shiv's favorites. This figure drawing worksheet shows how geometric shapes combine to form a body.
technoshaman and peoriapeoriawhereart. It also fills the "homesickness" square in my 6-16-17 card for the hc_bingo fest, and the "hour" square in my 10-31-17 Time card for the Space and Time Bingo fest. This poem has been sponsored by EdorFaus. It belongs to the Shiv thread of the Polychrome Heroics series.Note: Nothing bad happens in this poem, but the inside of Shiv's head is a mess, so he's angsting over things that would normally be enjoyable. Be patient with him.
"The Archetype of the Beauty"
Shiv hadn't meant to encourage Dr. G
by actually taking any of the classes,
but he couldn't resist Tactile Math
with its colorful crocheted frills.
He hopped a bus to the library,
kicking his toes against the seat
the whole way there and rocking
hard enough to make people glare.
He got there a good fifteen minutes early,
because the bus schedule in his neighborhood
wasn't as generous as some other places got.
The W. Dale Clark Library towered
over the Gene Leahy Mall, sleek stone
forming a block four stories tall.
Shiv slipped inside, hoping that
nobody would notice him, but he
was so stunned by the interior
that he stopped in his tracks
and people bumped into him.
Hastily he scrambled out of the way
so that he could stare up at the hole
through the middle of the building
which let him see all the floors.
A huge mural hung overhead,
showing a partial map of the Earth.
Nearby, a display advertised routes
for the Neighborhood Walk program.
Now that he thought about it, Shiv could
remember seeing the trailhead signs
and route markers around the area,
although he'd never followed any.
He found the art gallery, too,
full of paintings and sculptures,
its bulletin board plastered with
flyers for upcoming art classes.
There were books everywhere,
of course, but more than that,
there were tables and chairs
between the bookcases and
desks tucked under the windows.
One stairwell had a mural all over it,
not quite graffiti, but something that
reminded Shiv of graffiti. He liked it,
but he couldn't quite pin down why.
Shiv had been in libraries before,
of course, but never anything like this.
Field trips were for kids who could be trusted.
All he got were shitty school libraries and
neighborhood branches in dingy buildings.
He rarely stole from the Little Free Libraries
because those things were boring.
Today he wandered around in a daze
just looking at all the incredible stuff
until his vidwatch beeped a warning.
Then he had to hustle to the meeting room
so that he wouldn't be late, because that
would attract way too much attention.
Shiv slunk in through the door
and found a chair in the back corner
where hopefully nobody would notice
that he didn't belong here at all.
He stared at his toes and realized
that they finally stopped tapping.
Just to make sure, he tucked
his hands between his knees
to keep them out of trouble too.
When he snuck a quick peek
to check out the rest of the crowd
and see how badly he stuck out, Shiv
was surprised to see that most of them
were close to his age, and about half wore
some combination of red, black, and white.
An older woman came in carrying a basket
of yarn and big bags full of other things.
Sunglasses perched atop her graying hair,
and a wide smile flashed white against
the warm brown skin of her face.
She wore a nametag saying Cadenza
stuck on the front of her sweater.
Shiv hadn't taken a nametag.
He was generally better off if
nobody knew who he was.
The woman introduced herself
as Professor Cadenza Darden from
the University of Nebraska at Omaha.
Shiv scrunched down in his chair and
wondered if it was too late to escape.
He hadn't even realized that this was
supposed to be a college class.
Cadenza started talking about math
that was so far over his head, he could
hardly understand one word in ten.
She used a big white board on wheels
to write things with colored markers
that had more letters than numbers.
Shiv looked around the room for
a distraction, but there wasn't much
that could hold his attention for long,
just the chairs and the people in them.
When he shifted his focus to the metal
in the room, though, it got more interesting.
Cadenza had a bracelet on her right wrist,
a watch on her left wrist, and rings on
both ring fingers, so Shiv could feel
most of what she did with her hands.
She had a nice voice, dark and sweet
and smooth like chocolate frosting.
Shiv leaned back in his seat,
content to listen for now.
A nudge startled him upright.
"Hey man, you want this thing or not?"
said the guy in the next chair. "If you
don't, at least pass it to someone else."
Startled, Shiv looked over to see
one of the frilly things from the flyer,
and reached out to grab it eagerly.
It was made of plain yarn, but it was
a deep eggplant color in the center,
changing to violet, lilac, and finally
pale lavender along the edge.
It had kind of a cone shape, with
a hole going to a tail in the middle,
then spreading out to a circle, and
the rim curled into ruffles.
Shiv grinned as he ran his fingers
over it, trying to make it lie flat, but it
wouldn't since there was too much yarn.
"Pass that on now, and take this,"
he neighbor said, handing him
a purse made of sky-blue yarn.
Shiv did so, and discovered
that the purse opened to reveal
a whole set of tiny yarn things.
Laving them out along his leg,
Shiv found a little red nub, then
a red with a yellow ring, followed
by red rimmed in yellow and blue.
The one with the green rim
wouldn't lie flat anymore,
not even when Shiv tried
to iron it with his hands.
The next one had a border of
indigo almost the same shade
as the blue, and it ruffled.
The last two, with a hot pink rim
and a bright orange one, were
even frillier than the first few.
With the pieces laid in a row,
Shiv could see how they went
from flat to frilly, could trace
the spiral with his fingers
and feel how it changed.
The next thing to come around
the class was a pinkish frill.
Reluctantly Shiv stuffed
the colorful set back into
the purse and passed it on.
The pink thing had a tag on it
with numbers and letters that
made no sense to Shiv, but
it felt interesting to touch.
Every few stitches, there was
a sort of kink or a bump
where it got bigger.
He might not be able
to read the fancy math
written on the tag, but he
could grasp the yarn.
His neighbor handed him
another set, this time two frills.
One was red with yellow lines
stitched across it, and Shiv could
see how they ran side-by-side if he
folded the frill in different ways.
The other was purple with white lines
that made sort of a triangle except
the sides bent toward the center.
It almost made sense to him.
They looked like petunias.
Next he got a floppy oval,
yellow in the middle with
purple and then green along
the edges. It reminded him
of the sea slug pictures that
Aida had shown him.
After that came a long riffle
that he thought might be meant
as a scarf. Instead of colors in rows,
it was made of candy-colored yarn
that changed all the way through,
making it sort of speckled.
Shiv pulled it through his hands,
enjoying how the ripples tickled
against the skin of his palms.
The last was a ruffle so dense
that it curled itself into a ball,
the inside dark green with a glint
of metallic thread here and there,
the outer edge a bright red.
A loop of red yarn made him
realize that he was holding
a Christmas ornament.
Shiv sighed.
For a while, he had
stayed with a crafty family
that sucked way less than usual.
It hadn't lasted -- nothing in his life
ever lasted for long -- but still, it had
been almost nice for a while there.
He remembered their Christmas tree
hung with godawful handmade ornaments.
His foster grandmother had tried to coax him
into making one himself to add to it, but Shiv
had refused. He never made anything good.
Now he dug his fingers into the crinkly ball
and wished he could make nice things like this.
To make matters worse, the teacher
reminded him of his foster grandmother,
who he hadn't thought of in years.
He remembered his foster mother,
too, and the tangle of morning routines
as she sorted out hair care for kids with
all different colors and textures.
A twinge of homesickness
went through his chest, the pain
spiraling from one side to the other
as if pulling a riffle through his ribs.
Shiv huffed and shuffled in his seat,
trying to make the unfamiliar feeling
go away and leave him alone.
He tried paying attention to the lecture,
because if math couldn't put him
to sleep then nothing could.
Then he realized that Cadenza
was doing something with her hands,
and yeah, there was a steady flick-flick-flick
against his attention that he hadn't noticed
before, metal moving in a rhythm that
reminded Shiv of a metronome.
Looking closer, he saw that she
had a ball of light blue yarn and
a tool of some kind, like a long pin
with a blunt hook at one end of it.
Crochet hook, he recalled suddenly,
remembering his foster grandmother
in her rocking chair with a ball of yarn,
the bright metal dancing in her hands
as she made a pair of mittens.
Despite the awkward memories,
Shiv found Cadenza's crochet soothing
in a way that let him slump against
the back of his chair and let go of
some of the ever-present tension.
The soft chime at the end of class
startled Shiv out of his lull.
Had it really been an hour already?
Most of the other people got up and left.
A handful of those in the front row
clustered around the teacher,
pestering her with questions.
Eventually they drifted away, too,
leaving just Shiv and Cadenza.
"I haven't seen you here before,"
she said in her warm voice.
"Uh ... guy I knew gave me a flyer
for it," Shiv said, looking down to where
his hands still held the ruffle ball.
"Mind giving me a hand with
the cleanup, then?" she said,
waving a hand at the room.
Shiv looked up and saw
that everyone else had left
the yarn thingies scattered
all over everywhere.
"Okay, I guess?" he said.
Cadenza held out a bag.
"Just drop them in here."
Reluctantly Shiv gave up
the ruffle ball, then stuffed in
the floppy oval. "These are
really cool," he said. "I've never
seen anything quite like them."
"Hyperbolic planes are fun,"
she said. "They look so hard
to make, but they're easy --
it's just a basic stitch with
a lot of increases in it."
"I can't crochet," Shiv said,
"or do math, and I kind of
suck at school too."
"Handsy as you are, that's
no surprise," Cadenza said.
"I wish more people would
teach tactile math so that
touch-dominant students
could actually learn it."
"Huh?" Shiv said, baffled.
"People can learn things in
different ways, and most folks
have a favorite," she said as
she scooped up the lined frills.
"Like what?" Shiv asked. "School
is pretty much the same everywhere."
"Oh, not everywhere -- there are
different ways to teach," Cadenza said.
"You seem to favor touching things,
so if people tried to teach you with
just text or talking, that probably
didn't make a whole lot of sense."
"Well, but that's because I'm stupid,"
Shiv pointed out. He found the blue purse
and popped it open to make sure all of
the little bits were inside. They were.
"I don't usually see stupid people
in my hyperbolic math classes,"
Cadenza said in a dry tone. Then
she opened a new bag. "But here,
let me put the bottom rungs on
the ladder and see how you do."
This one held a bunch of flat shapes
and some that were like soft blocks.
Instantly Shiv put his hands behind
his back and held on tight enough
that his fingernails dug into the skin.
"You're not going to learn much
like that," Cadenza said. "Come here
and get a feel for these things. They're
made out of yarn, so they won't break."
Hesitantly, Shiv picked up the first one
and saw that it was a circle, pale pink
in the middle and darker at the edge.
There was a square, too, with
a sort of diamond pattern coming in
from the corners, another circle,
and a thing like a stop sign.
"How's come you got extras?"
Shiv wondered, stacking the circles.
"Take a closer look," Cadenza said
with a smile. "Poke at them to see
if you can feel the difference."
Shiv ran his fingers over
the soft ridges, tugging gently
to look at how the stitches went
together, but it wasn't until he
held them up to the window and
light shone through the holes
that he saw what she meant.
"Oh!" he exclaimed. "This one
here goes in rings, and then this one
goes around and around like a screw!"
"Exactly," said Cadenza. "One uses
concentric circles and the other a spiral.
Why don't you see what else you can find?"
Shiv scrabbled in the bag, looking for
more of the other shapes, and soon
he had a whole row laid out on chairs,
pairs of circles and triangles and squares
and other shapes he couldn't name.
That was okay, because Cadenza
identified each one as he took it out
if he didn't say the name himself.
"Here is a ball made using
a typical crochet pattern,"
she said, holding it out.
"That's not a very good ball,"
Shiv said, frowning at it. He
took it and looked closer. "See,
the blue ends are round but
the green middle is flatter."
"You have good eyes, too,"
Cadenza said, handing him
a yellow ball. "What do you
make of this one, then?"
"It's rounder," he said. "I
like it better than the first one."
"This is called an ideal sphere,"
she explained. "Here, let me
show you what that means."
She opened a folder and
pulled out a worksheet
full of fancy math shit.
"I can't read that," Shiv said,
shaking his head at the page.
"Sure you can," Cadenza said.
"Look, this curve is the ideal.
Then these blue dots illustrate
the old pattern. The new one
follows the curve more closely."
Shiv looked at the page, and
then looked at the two spheres.
"I guess, maybe?" he said.
"Here's an easy one," she said,
handing him a colorful pyramid.
"What do you think about this?"
Tilting it in his hands, Shiv saw
that it was actually made from
four different triangles sewn
together along the edges.
"So that goes with these,"
he said, putting it down
with the flat triangles.
"It sure does," she said.
"What about this one?"
The new pyramid was not
quite as sharp as the old one,
more like a ball with corners.
Shiv poked at it and said,
"Why is this one different?"
"Try looking at both pyramids
so you can compare them to
each other," Cadenza said.
Side by side, the difference was
clear, but it took a while before Shiv said,
"Oh! This one goes around and around
instead of side to side. But then how
do you make it pointy instead of round?"
"That's in the pattern of increases,"
Cadenza said. "You can make
almost any shape with crochet."
"Huh," Shiv said. He dug into
the bag and found some cubes.
This time it only took him a moment
to say, "This is the flat kind, and
this one is made in a spiral."
"Very good, you figured that
right out," Cadenza said in
a voice that made Shiv
wiggle in pleasure.
She didn't yell at him
for doing that, either.
Shiv found that he didn't
mind helping her pick up
the rest of the ruffles.
It felt different, helping
someone who was nice to him.
"I wish school made sense
like this," he sighed. "I would've
gotten into so much less trouble."
"If your teachers didn't explain
things so you could understand,
then that is their fault, not yours,"
Cadenza said in a firm tone.
"Didn't stop them from
taking it out on me, though,"
Shiv said with a shrug.
Cadenza grumbled something
that sounded rude as she put
the scarf thingy in her bag.
Then she picked up
the pale blue ruffle that
she had made during class
and handed it to Shiv.
"Here you go, a little token of
appreciation for staying after class
to help clean up," Cadenza said.
"Thanks," Shiv said quietly,
fingers playing with the soft folds.
It was beautiful and soothing.
"I still can't crochet, though."
"Would you like to learn?"
Cadenza said. She handed him
what was left of the light blue yarn
and the lavender hook that she
had been using to work it.
"But these are yours,"
Shiv said, staring at them.
"They were, and now they're
yours," Cadenza said. "Let's see,
you'll want basic instructions."
Shiv didn't bother explaining that
he sucked at following instructions.
When she handed him the little brochure,
though, it made perfect sense, because
it had pictures along with the text. Inside
was a cheat sheet for all the letter codes
and more pictures of basic stitches.
"I could maybe figure it out?"
he said, laboriously sounding out
some of the written descriptions.
At least the words were short.
"That's good," Cadenza said.
"Practice just making chains,
squares, and circles for a while.
When you've got that down, then
you can try your hand at this."
Shiv looked at the new brochure.
"How to Crochet Hyperbolic Corals,"
he read. The front had more ruffles,
and yep, there was a coral reef made
from about a million colors of yarn which
looked kind of like the snapshots that
Aida brought back from the Maldives.
He wondered if she knew anything
about crochet or hyperbolic planes or
how much coral really looked like
the sculpture in the brochure.
"Remember, these are much easier
to make than they seem at first glance,"
Cadenza said, patting him on the hand.
"They're just single crochet with increases."
The hairs on Shiv's skin stood up and
then slowly flattened again. He wasn't
used to people touching him so casually.
He tucked his hands behind his back
so that he could rub over the spot
without getting caught doing it.
"I guess I can give it a try,"
he said. "I'm still no good
at math or school, though."
"So?" Cadenza said. "This is
a different kind of math. Lots of
people who aren't great with
abstract numbers do fine when
they get into geometry, because
it has shapes that they can see.
It's a whole new form of art."
"Math isn't art," Shiv said at once.
"I may not be an artist, but I know
how to draw some stuff, and art
is so not made of numbers."
"No, it's made of shapes, and
shapes have numbers hidden
in them," Cadenza said. "How
many sides does a triangle have?"
"Well, three," Shiv said.
"Even I know that."
"So that's a number
that lies inside a shape,"
Cadenza said. "It's all
like that, the numbers just
get more interesting later."
"Huh," Shiv said. He could
count to three and recognize
a pyramid when he saw one,
and he certainly liked the frills.
"Guess I never thought of math
as going along with art before."
"Have you ever seen the pages
of art exercises that use shapes
to practice shading, or draw a frame
to make a person or animal?" she said.
"Oh yeah, I've done those," Shiv said.
"The shading stuff is relaxing."
"Well, that's some of what you
can do with geometry in art,"
Cadenza said. "I'm no expert
in that side of things, but if you
watch the museum newsletters,
some of my coworkers go out
to do presentations on that topic."
Shiv hadn't been a fan of museums,
but Tolli and Simon had dragged him
to one of their favorites, which had
been totally different from what he
remembered of museum trips.
Maybe this would be like that,
the way it didn't suck if you were
with someone who knew their shit
and also wouldn't hit you.
"I'll think about it," Shiv said.
"Well, good," Cadenza said.
"Geometry is the archetype of
the beauty of the world. Everyone
should get a chance to enjoy it."
Shiv fingered the ruffle that
she had given him and
wondered if it was true.
"You really think so?"
"Of course," said Cadenza.
"That's the whole point of
crocheting hyperbolic planes.
Super-Intellect Daina Taimina
came up with to make them
more accessible to people."
Shiv watched the soft ripples
move over his fingertips and
wished that all math could be
this easy. "That's neat," he said.
Another chime sounded,
soft in the hush of the library.
"Oh my goodness, would you
look at the time," Cadenza said.
"Where did that second hour go?"
Shiv had no idea either. He
thought the class just let out.
He scrambled to gather up
all the stuff that she'd given him.
"Here, take this," Cadenza said,
handing him an empty grocery bag.
Shiv put in the pale blue ruffle,
the ball of yarn, the crochet hook,
and the two how-to brochures.
"Thanks," he said. "This class
was way cooler than I expected."
"It's been my pleasure ... why,
I just realized I don't even
know your name," she said.
"Shiv," he said, looking down.
Sometimes people made fun of it,
but damned if he was going to change
his cape name because of dumbasses.
"No wonder you're so sharp,"
Cadenza said with a laugh.
She actually knew what it meant.
That wasn't something that happened
very often with college people.
"Come here and give me a hug,"
Cadenza said, squashing him
briefly against her side and then
letting go at his startled "Awk!"
"Don't worry, dear, one of
my grandbabies isn't much
of a hugger either," she said.
"I'd better go catch my bus."
"Yeah, me too," Shiv said,
although he'd already missed
the one he meant to take home
and had no idea when another
would head in his direction.
It didn't matter, really, because he
could get on any bus and figure out
the transfers from the route map.
Besides, it'd give him time to start
looking over the crochet brochures.
* * *
Notes:
Cadenza Darden -- She has medium-brown skin, brown eyes, and straightened gray hair to her chin. She has a broad nose in a rectangular face. Sensitive to cold, she often wears scarves and sweaters even in relatively mild weather. Cadenza teaches math in the University of Nebraska at Omaha. Although she presents the usual classes, she specializes in alternative teaching methods such as Tactile Math. In addition to her work at the university, she also volunteers to teach free classes at libraries and community centers. Cadenza enjoys cooking and crafting for her large family and many friends. Or anyone else who doesn't run away fast enough.
Qualities: Master (+6) Professor of Mathematics, Expert (+4) Fibercrafts, Expert (+4) Wisdom, Good (+2) Comfort Food, Good (+2) Gentle, Good (+2) Grandmother
Poor (-2) Cold-Sensitive
In Terramagne, the University of Nebraska at Omaha also offers a Pre-Zetetics concentration. Actually several fields feed into zetetic studies.
This is Cadenza's crochet basket.
* * *
"Geometry is the archetype of the beauty of the world."
-- Johannes Kepler
The W. Dale Clark Library lies just west of the Gene Leahy Mall. Its features include: ADA Accessible, Bike Racks, Computer Lab, Computers, Free WiFi, Meeting Room(s), Printing, Scanning, Copying & Faxing.
Library Neighborhood Walks
Local-Omaha has a set of maps showing neighborhood walking routes around the W. Dale Clark Library ranging from 1 to 3.5 miles. Terramagne-Omaha has routes throughout the city ranging from .25 to 10 miles.
In T-Omaha, a neighborhood walk customarily has a sign at the trailhead which shows the route, marks points of interest, and gives historic or cultural information about the trailhead itself. Along the route, turns are often marked with smaller signs, color-coded if necessary to distinguish overlapping trails, and the points of interest have larger signs. A few places have routes laid when the development first went in, marked with lines of colored concrete or brick along the edges of the sidewalks. People may walk the route at any time, but most routes have some times marked when free guided tours are available.
See the exterior of the library. This is the interior looking toward the Gene Leahy Mall in winter. This is a similar view in spring. Here you can look up and see the floors above. The Kingman Mural is painted on a giant canvas rather than directly on a wall. It has been displayed in various places before coming to the W. Dale Clark Library. The circulation desk overlooks an open area. The library has a break area that serves healthy snacks and beverages to reduce the frequency of patrons who forget to eat and then faceplant into the floor.
The library supports a variety of art. This graffiti-inspired mural hangs in the stairwell. The art gallery displays work from a variety of artists. This is an art class for homeless people.
The children's library has a colorful rug. The third floor Genealogy Room has books, study tables with chairs, and plugs for laptops or other devices. This is the non-circulating reference section. The reference section has study desks all along the wall by the windows.
The library offers multiple meeting spaces. The lecture room suits large groups. This meeting room is somewhat smaller, suited for classes like Tactile Math.
This is a map of the Metro bus routes in Local-America. Shiv took one look at this thing and said, "Where's the rest of it?" Because mass transit in Terramagne-Omaha is much better than this. There's a Beltway route around the Greater Omaha Area that connects to transit hubs in each of its 11 regions, instead of only the 6 shown here. Where that belt parallels the Missouri River, they actually put in an auxiliary line that just does the River Run, so tourists don't overfill the Beltway buses. There are bus routes within walking distance of almost every place within that belt, which is to say, every few blocks. Every park of neighborhood size or bigger, every major municipal or public building, and all the little residential neighborhoods have at least one bus stop at their hub or a corner. It's just that the less-good and less-populated areas have lower frequency of bus service. In a good, dense area there are buses every 5 minutes or so. In most neighborhoods it's 10-15 minutes. In Shiv's, you might have to wait half an hour to an hour. By the time you get out to the beltway, there may only be a morning bus and an evening bus, but they'll get you to and from work. And that's just the municipal stuff: most hospitals, grocery stores, malls, and other large businesses have a shuttlebus of their own, and many large employers have a commuter shuttle or even several. There are private touring buses for tourists too. That's why Shiv has no interest in a car: he doesn't need one. The boy that foster parents called "stupid" can glance at that spaghetti barf of a map and say, "We need to catch the Teal, transfer to the Black, and go east."
The body language of insecurity includes hanging back, downcast eyes, restless hands/feet, looking around bored, self-touch, fidgeting, hands in pockets, shrugging, hiding or pinning hands. Notice how much of that is said to be "disrespectful" or "disruptive" ...? Sure, Shiv can be disrespectful. But more often, he's just uncomfortable.
Students with behavioral disorders or other special needs are often excluded from field trips and other educational opportunities. Appropriate supports make it possible for such students to participate. Notice that when the Finns take Shiv anywhere, they make sure that he has things like food, sun protection, and something to do -- and they step in to help if he starts to overload, instead of pushing him over the edge.
Little Free Libraries are wonderful things, but local America seems to hate them. They're quite popular in Terramagne-America. Read about them and build your own. Shiv does not realize that he can't "steal" what is there for anyone to take. This one is near the W. Dale Clark Library, and the article includes a map.
Kinesthetic and tactile learners, along with visual-spatial learners, do poorly with conventional lessons based on listening or reading. Tactile techniques such as finger counting help students to develop early math skills. Shiv's teachers presented material in a format he could not absorb, and then smacked him for finding his own solutions. So of course he hates school.
Read about Super-Intellect Daina Taimina.
Crocheting the hyperbolic plane makes a good homework assignment. The purple ruffle is in this set. Here is the purse and its pattern. This set of pieces shows the anatomy of a hyperbolic plane crocheted around a point. Here is the mauve ruffle and its math. The red ruffle has parallel lines on it. The lavender one comes with a triangle. The sea slug is another crochet project. The fiesta scarf is a long riffle that you can crochet. The Christmas ornament is a simple pattern.
Geometric shapes may be worked in rounds, in concentric lines or in spirals. See the circle, square, and polygon.
Crocheting a ball is relatively easy to do. It's a serviceable ball, but not a very good sphere. For that you need the ideal sphere, with a more complex pattern.
This pattern produces flat pieces for a pyramid. Here's a matching pattern for a spiral pyramid.
The flat cube uses these crochet pattern blocks. For a spiral cube, you can use this pattern.
The front of Shiv's first brochure teaches crochet basics. The back shows more stitches.
The front of the second brochure is about crocheting a coral reef. There are more pictures here. The back shows more patterns for hyperbolic planes.
Math and art share much in common. Explore shapes, polyhedra, perspective, and frame. Compare math and geometry art projects. This worksheet teaches line drawing and shading, among Shiv's favorites. This figure drawing worksheet shows how geometric shapes combine to form a body.
