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penfullofwordsaheadfullofstories · 5 years

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Bruises- Pt.8 (A Peter Pevensie Fanfic)

AN: everything disappeared suddenly today! Now everything is back up! Thank you to everyone following this crazy brain child of mine. :) gifs belong to @eternalroleplay

Previous chapters: Pt1 Pt2 Pt3 Pt4 Pt5 Pt6 Pt7

Chapter note: This was a fun one to write!

A nobleman from some island comes to visit in the following days, and I don’t see Peter for a week and a half. Not that I’m counting.

Not that I’m necessarily saddened by it either. My brain is still shaken to the bone by a number of things, and the time to think is much needed.

With the castle’s visitors to talk about, the talk around me dies down, and I’m able to return to the maid’s quarters, despite Mrs. Dolie’s insistence that I hadn’t overstayed my welcome.

The maids that I’m not particularly close to give me side glances laced with poison, and the ones I did have an acquaintance with give me a half forced smile at any eye contact. Even if they didn’t mind my current... affiliation… with the High King, they likely don’t want the affliction sure to come their way with any association with me.

It’s my own fault, really. I’ve been a quiet, aloof lass long before they had a reason to have distaste for me.

Just as well: I have a book to read. I sit in the hallway outside the quarters, under a torch so I can see. Then I devour the pages until my eyelids begin to droop before reluctantly forcing myself to my bunk.

Midweek, I get to take another trip into town, this time accompanied by Adonis. I smile at the thought of Peter taking my comfort level with the centaur into account when assigning the guard.

The buoyant conversation to and from the market is nearly as enjoyable as the experience itself. Although, having a royal guard at your side did draw its attentions. But the drawbacks aren’t nearly as bad as the niceness of having to not carry all the produce alone.

It’s a pleasant rhythm: wake up, clean, perhaps talk to Mrs. Dolie or Adonis, read, sleep. Even my dreams fall into a lovely, blank pattern.

Until they don’t. I blame the book for it really, knights and their damn passionate love and carnal tales.

It’s innocent enough to start. I’m back on the turret, Peter with me, but instead of just brushing my cheek with his hand, his mouth catches mine.

I bolt upright in my bed, and I can’t even muster an apology in reply to the annoyed whine from the bunk beside mine. I row my mind back and forth through the dream, and can only settle myself back down when I know it lacked that abnormal quality that meant I shared it.

My cleaning in the morning is vigorous and over-focused, but, thankfully, no one says anything, not even Mrs. Dolie, despite her aware gaze.

That night, I forego the book, hoping it helps.

Instead, I have the same dream, except this time, my hands are in his hair, and his hands are on my back, tracing and burning. The sensation of his tongue meeting my lip finally shoots me toward consciousness.

I’m unable to fall back asleep, even after assuring myself this one too was my dream alone.

I tripped three times the next day, and got caught staring off into space five times.

I do read my book the following night, with no intention of going to sleep. But I must at some point fade off, because the dream visits even in face of my efforts.

I’m not in the tower this time, but I’m in what I recognize as the High King’s chambers. I don’t clean it, but I have been in to fill a vase once or take the curtains to wash, I’m not sure which, but it’s enough to identify where I am. I’m wearing my sleep shift, white and borderline transparent, and I haven’t even time to fluster at my own indecency before looking up to find Peter only in loose sleep breeches.

I look everywhere but his exposed chest, finally descending my line of sight to the design of the duvet behind him. I can feel his eyes on me, and despite the simmer it holds, it doesn’t feel profane. My curiosity gets the better of me, and I search his face for meaning, but I can’t label any of the micro-expressions dancing across his features.

Handsome features, my useless mind offers.

Then, before my mind can offer anything else, I’m stepping towards him, wrapping my arms around his neck, and kissing him without restraint. He hums something incomprehensible against my mouth and then he’s lifting me by the back of my legs, which I wrap around his waist the first moment I can. I’m dazed and giddy and something much much worse, but whatever the later is, it has momentum, and I’m not even trying to stop it as I move my hips down against his waist.

I feel before I see his eyes snap open, and I blink as that awful sensation of becoming aware during a dream rushes over me.

What in the…

The sinking in my stomach advances as I hear him ask, tentatively, “____ are you actually here?”

I just stare as he lowers me down, places a finger under my chin, tilting my eyes up as he searches them for something.

And it hits me.

Aslan help me…I am sharing this dream.

********

I’ve never been so thankful for kitchen duty. Mrs. Dolie’s conversation is just about the sole thing that can get my mind off a night like that.

If she can tell I’m distracted, she keeps it to herself.

I’m chopping celery while she adds a plethora of spices to a large pot without measuring them, not even looking at her own hands as she tells me how one of the other maids burnt a pie yesterday.

She’s smiling, even though she is obviously still quite grieved over her charred pie. I feel the beginnings of my own smile when the screech of iron startles the knife down, and I slice one of my knuckles.

The clammerings beside me tell Mrs. Dolie isn’t much better off. I’m sucking my knuckle between my lips before the second it takes me to turn around.

Mrs. Dolie and I exchange confused glances as we recognize at the same moment the sound came from the panty.

I’m reaching back behind me with my unhurt hand for the knife when the pantry door is pushed open and a cloud of white is unleashed.

I don’t even have to wait for the white dust to settle before I recognize the stature of the man before us.

“Peter?” I ask toward the cloud, knife still in hand.

There’s coughing, and when I can finally see him, he’s dusting a hand through his hair, knocking another smaller cloud into being. His clothes are coated in white powder too.

“I think,” he covers his mouth for another cough, “that perhaps the passage entrance to the pantry hasn’t been in use for some time.”

Mrs. Dolie has dropped into a curtsey, and I debate on if I’m to curtsey as well, and I keep going back and forth on it, so I just end up in an awkward ankle cross with my finger back in my mouth.

Oh, gods, I am not ready to see him, not after last night. And he’s here, and so very real and it’s far too much.

“Your Majesty,” Mrs. Dolie half rises from her curtsey, “It hasn’t been used in years indeed, to which point I’m afraid we’ve placed shelving around it. It’s where we keep the flour nowadays.”

She’s honoring, but her tone of voice is the same as ever, even in the presence of one of our sovereigns, and I can’t help but respect her more for it.

Peter’s chuckle forces my attention back to him, “Yes, I’ve certainly found the flour.”

He looks at me for a second past a comfortable glance, then back to Mrs. Dolie, “I apologize for the mess, if you’ll point me in the direction of your broom…”

She makes a noise somewhere between disbelief and disgust. “If it pleases your majesty, the maids are quite capable…”

“It’s my mess really,” he interrupts, moving towards us.

I finally set my knife down. He notices the movement, and the side of his lip quirks up, then it’s gone.

“Really, your majesty, while your offer is appreciated, I actually have the perfect maid for the job. I have a charred pie that demands revenge.”

He looks baffled, and turns to me for reasoning. I just shake my head, smiling.

“To what do we owe the pleasure of your company this afternoon?” I ask, wiping my hands on my apron.

“I was…” he starts, then concern twists his face as his eyes follow my hands. I look down to see my apron splotched with red. “Are you bleeding, ____?”

“Heavens! Yes she is!” Mrs. Dolie exclaims, grabbing a dish towel from the nearest table, wrapping my entire hand.

I laugh and hiss at the pain in the same moment, creating a strange, twisted noise. “It’s just the finger, you know, not my whole hand.”

“I’m relieved your tongue is unaffected,” she bites back, looking up at me only briefly before starting to look for something.

“Just about everything is unaffected,” I snort. “It’s just a …”

I’m silenced by the hand on my elbow. I tense at first, but then relax at the cautious eyes of the hand’s owner.

“Is this okay?” he asks quietly. I nod, even as my useless mind silently adds, “more than.”

“Can I see it?” I must be still gathering my wits from my stupid, stupid mental running column because he adds, “your hand?”

I raise it, and he takes it, unwrapping the clumsily tied dish cloth, sending another bit of flour into a cloud as his sleeve contacts my wrist.

He addresses Mrs. Dolie over my shoulder after a glance at it, “You were correct in the need for it being covered, but not before it’s washed. May I use your wash bowl?”

“Of course, your majesty.” She indicates over to the corner. She’s addressing him, but she’s looking at me. To my face, then to where Peter carefully grasps my hand and leads me over to the wash bowl, then back at my face pointedly, looking herself as smug as anyone ever has.

I roll my eyes.

“You know, I really am fi..”

I swallow a yelp as Peter pours a pitcher of water over my knuckle.

“I know you are, but it still needs cleaning, and it honestly might need a stitch or two.”

“You have a habit of being overprotective, sire.”

He smiles as he runs his hand over mine, squeezing slightly. I sharply inhale at the pain, then almost make a similar sound at his hand’s comforting stroke. His shoulder bumps mine.

“And you have a habit of being hurt, milady.” I turn my face to him, and he’s close, so close at my side. I can feel his exhale on my neck, and he’s positively magnetic, and I’m so pathetically caught in his pull…

Mrs. Dolie clears her throat, “I’d clear out, but, alas, the soup is still on the fire.”

Peter laughs, although somewhat tight, still authentic, as he turns to address her. “My apologies, I need to get her to the healer anyway.”

“The healer! Honestly, Peter!” I exclaim in exasperation.

He pivots back to me. “Yes, the healer. Stitches and soup aren’t best made in the same room.”

“I have to agree with his majesty on this one, deary,” Mrs. Dolie pipes up.

“But…” I start to protest, but Mrs. Dolie starts literally pushing me toward the door to the passageway in the pantry.

Peter gives his thanks and farewell, and then we’re off into the tunnel. It’s dark, except for some torches up the way.

The tunnels aren’t foreign to us maids. They’re not only for protection in case of an attack, they also make for fantastic shortcuts and dubious visibility at the height of hosting guests.

Since this entrance has remained unused, there’s no torchlight given nearby. Even still, it’s not pitch black at least, and the ground is flat in these parts.

So my grip on his forearm is superfluous. Ridiculous.

I don’t let go.

His voice pierces the dark as we walk. “I tried my hand at subtlety, using the passage and whatnot. Flour it seems, had plotted to thwart me.”

“Ah, yes. If only it weren’t for the nefarious flour, then subtlety would be yours to obtain,” I say, trying to chase the playfulness of my voice with fabricated solemnity, failing mostly. “Although I might suggest that if subtlety is truly close to being possessed, then the use of passage tunnels needn’t be necessary.”

He endeavors to clear his throat of a laugh, which escapes anyway in the end. “Redhanded, milady.”

“I appreciate the attempt nonetheless. Which brings me to… why were you trying to find me?”

We’ve gotten to where the torches are lit, and I can see his face much better now. I really could let go of his arm. Really should.

“Well, I know I’ve been occupied all week, and I mentioned perhaps trying sparring last...” he trails off, and I glance up at him, only catching glimpses of his demeanor as we kept passing torches. He seems to be considering something. Then decided upon it.

“We’ve been nothing except forthright toward each other, and I have no intent of stopping now. Or ever. I honestly just wanted to see you. How you were doing. And perhaps a question, which I can leave ‘till later.”

I’m momentarily lost over what to say, my heartbeat drowning out any coherent thought from forming. First, that he wants to see me, and second, what that question will likely be about. Hopefully not. I keep hoping I’m wrong about that dream not being mine alone.

Forthright. I can do that, at least. “I’m glad you did.” I hope he can see the sincerity in my eyes in spite of the dim light. “And I’m actually a little relieved you haven’t brought up the whole sparring thing. I…” I lick my bottom lip and the rest of my thought down as I consider for a moment, what level of vulnerability I want to reveal.

I catch another frame of his face, but it’s just enough. There’s a genuineness his presence radiates, and it inspires the same from me.

“I’m not ready yet, I think. Touching people and people touching me,” I inhale, conjuring courage to finish. “It’s formidable at best in most cases. But I’m learning. I just need smaller steps than that, I think.”

“I should say that’s more than understandable. Plus, I only mentioned it in hopes to increase your comfort, not fret you more than you already have been.”

“Thank you,” I say, quietly.

He nods, and we walk in silence for a few moments. We reach a door, and he opens it, indicating for me to go ahead.

I’ve barely a second to take in the room, stocked floor to ceiling on more than one wall with numerous jars full of colorful substances. There’s a table in the middle, and many places of storage everywhere. A fireplace in the corner, a daybed near the window.

He speaks again. “Please, if I ever do anything that makes you nervous, don’t hesitate to say.”

“Thank you,” I say again. I look away, over at some sort of plant hanging from the ceiling. As if my nerves will ever be in order around him. “You’ve been beyond respectful, and I’m grateful.”

His mouth purses. “I don’t feel I need gratitude for what equates to plain decency.”

“My gratitude still stands, even so.”

“Just please promise me, ___, that you’ll tell me?” He’s adamant in a way that I know needs assurance.

“I will. Touch with you is… different.” The moment I realize what just came out of my mouth, I look down at my feet again, opening my mouth to find something, anything, to say that will mitigate what I just stupidly said aloud.

When I gather the grit to look him in the eye again, he looks struck. Not as much in that he’s hurt as much surprised at the impact.

His throat bobs. “I….I want to say I’m honored, but it’s not even close to the right word.”

I can’t think of anything else to say, meer words feeling empty in comparison to the momentousness of what I’d actually just admitted.

I trust you.

And he heard it.

A bird’s chirp from outside the window calls me back to why I’m actually here.

“So, when is the healer joining us?”

His appearance turns sheepish. “Well, she should be making her rounds in one of the villages today. I’m set to meet with her tomorrow, as usual, but I’m confident I’ve done stitches enough to do it without her instruction.”

He turns and starts opening a cabinet, gathering supplies, then plucks some type of dried plant off the string from which it hangs.

I try to put the situation together in my mind. “She teaches you?”

He half turns back to me, hands still busy with some type of thread. “Yes, because I asked her to. Medicine has always held an interest for me.”

Huh. I hadn’t foreseen that coming.

He seems to have gathered everything he needs, because he approaches me again. “I would wait for her, if I knew she would be back before dark, and this truly requires attention now,” he waves in the direction of my hand.

“It’s alright. Between you and me, I prefer it to be you anyway.” I smile, hoping it reassures him. I don’t doubt his capacity the way he seems to think I might. I wouldn’t have done anything to the cut, so anything is an improvement on nothing.

He smiles back briefly before crushing the dried plant with a shaped stone. He combines it with some type of liquid until it forms a paste.

When he holds out his hand, obviously meaning for me to give him mine, I do without thought. But when the fingers on his other hand caress around my wrist before applying the paste, it brings to my attention just how intimate the setup is. And how much more he’s going to need to touch me before this is over.

My thoughts flicker back to the moment at the sink, just mere minutes ago. How he leaned in, how I did too…

And I’m a selfish girl in some respects, not content just to be touched, apparently, because even as the one hand is wounded, the other itches to reach up and touch his hair, remembering the soft texture of it from the staff courtyard.

He’s almost done smearing the paste when my hand twitches.

“Did it sting? This salve shouldn’t.”

“No, it’s… not that.”

“What is it, then?” He hasn’t been entirely looking at me, half submerged in his task, but now he does, broad shoulders squared to me, both hands holding my injured one.

I blush, and an expression that’s half boyish cockiness and half curiosity is sent my way in return.

I sigh, impatient with myself. “Just... “ I just go for it, reaching my other hand up, fingers close to the shorter hair above his ear. “May I?” I ask, making sure this frivolous indulgence of mine is fine by him.

He nods. “Whatever you want.”

I comb my hand through his hair, and he hums, deep in his throat as he leans into my hand. “I’m at your mercy, milady. Do as you please.”

It’s a heady, heady thing. The power he gives me.

What an interesting commodity he makes of power. What I’ve known of power is the abuse thereof. It becomes a completely different substance when it lays itself down willingly.

His eyes close when I reach the nape of his neck, dragging my fingernails. A thought plants in my mind, and my brazzenness hasn’t wavered, so I press my lips to his jaw, even as my hand shakes at his neck. I feel the muscle under my lip clench before he pulls back a little.

I’m worried I’ve misread things before he explains with a scratchy voice, “If I’m going to have enough concentration to stitch your hand, I can’t have you continuing that now.”

He pets at my cheek, swiping his thumb across my bottom lip. “And maybe then you’ll grant me permission to reciprocate?”

I can’t tell if the swoop in my stomach is fear or anticipation. Or both. “Please,” I answer still, meaning it with every bone in my body.

“Then let me finish my task, milady.” His smile is teasing, even as his hands busy themselves again after we’re both seated at the table.

The paste he made must have some type of numbing quality, as the poking of the needle isn’t nearly as bad as I brace myself for it to be. Still, the stitch in the middle of the cut bites, and I gasp a little. He looks up to me briefly, muttering an apology, stroking my hand again in a soothing motion. “Nearly finished.”

He’s completely in a zone, and I distract myself with watching his fingers as they work.

Finally, he bandages the area. He seems a little lost in thought, still.

When he addresses me, he looks a little… guilty?

“____, I need to ask you something before anything else.”

“Yes?”

“I…” he looks down, dropping his head and running a hand over his face. “Did we share a dream last night?” When he looks back up at me, his cheeks are a little red.

Oh. I had almost forgotten about that. I’m sure my cheeks matched his too, now. How would he feel, knowing I dreamed of him that way?

I answer slowly. “I believe so.”

“I believe I owe you an apology, then. Forgive me, I…”

“Pardon?” I cut him short.

“I’m trying to say I’m sorry, it was inappropriate, and you shouldn’t be subjected to my mind running and setting you in situations like that. Especially in light of everything you’ve been though, and I can’t in good conscience...”

“But it was my dream? You shouldn’t be sorry.”

It takes him a second to realize my words. “Really?”

“At least I thought it was. It makes sense, all the other dreams this week were similar.” I realize what I just admitted, and I laugh even as my whole face burns.

He just stares for a second, looking like he’s still trying to comprehend what I just said.

“Perhaps it’s me who should be apologizing to you for my mind’s lack of chastity, then, sire.” I continue.

Some disbelieving sound leaves him before he protests. “But I’ve had similar dreams all week as well.”

I should, perhaps, be scandalized. I should, maybe, be offended, even. I am, in fact, completely flattered instead.

“Huh,” is all I can say, stupidly.

We meet each other’s eyes at the same moment, then laugh a little at ourselves and the situation as a whole.

Peter speaks again. “I just hope that anything you did today wasn’t a reflection of what you think I wanted because of that dream.”

Aslan, how was this man even real?

“Everything I did today was because I wanted to.” My voice isn’t loud, but what I say seems to ring in the small space between us, creating a potential that demanded some type of action.

“Do I still have your permission then?” His leg bounces a little, like he’s channeling energy there in order to stay still.

I nod, and it’s all it takes. He scoots off his chair and offers a hand to pull me up.

The next moment, the warmth of his lips are against my temple. I lace our fingers where our hands are still clasped, my breaths coming uneven.

How is this even real?

I can feel him lick his lips before kissing down the side of my neck. When his tongue darts out a little, my hand clutches onto his arm haphazardly, ending in an awkward grab of his elbow.

His hand finds my waist, and he pulls back enough to see my gauge my reaction. “Is this still okay?”

His hair is still messy from when I touched it, and it makes me want to grab it again.

“Like I said, touch with you is different, Peter.” I close the gap between us, pressing our lips together. The reaction is gentle to begin: The hand on my waist clutches a little tighter, and I indulge the itch to play with his hair again.

Then he deepens the kiss, tilting his head a little and breaking our clasped hands to cup my face. He darts his tongue out once, and I feel the impact all the way down my spine. I hear myself make some noise I’ll care to be embarrassed about later, but when a similar noise echoes from his throat, I know I’m not alone.

Kissing Peter feels like the last moment of a fall and the following moment of catching yourself. There’s the exhilaration and fear of the uncontrollable sensation of tumbling toward something, and then there’s the swoop in your stomach as it all catches up, landing after it all on something solid and unshakable.

I pull back, breathless and unsure where to go next. He follows, slowing his breath as well, hands not leaving their place.

Then, without even thinking, he rests his forehead on mine.

And it happens.

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mathematicianadda · 4 years

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The Big Lock-Down Math-Off, Match 26

Welcome to the twenty-sixth and final match in this year’s Big Math-Off. Take a look at the two interesting bits of maths below, and vote for your favourite.

Here are today’s two pitches.

Colin Beveridge – The Miracle Sudoku

Colin blogs at flyingcoloursmaths.co.uk and tweets at @icecolbeveridge.

You’ve seen the Miracle Sudoku video, right? If not, watch the Miracle Sudoku video. I was skeptical, but it was absolutely worth 25 minutes of my time.

youtube

If you can’t be bothered to watch, the puzzle in question is a sudoku with three additional rules:

No two cells separated by a chess king’s move may contain the same digit

No two cells separated by a knight’s move may contain the same digit

No two vertically/horizontally adjacent cells may contain consecutive digits.

(Try it yourself here!)

At the risk of minor spoilers, the solver in the video is skeptical that the puzzle presented can be solved; it has only two clues, and he suspects he is being trolled. Yet the puzzle can indeed be solved! Which, of course made me wonder: how many such puzzles are there?

I’ve put my only-really-meant-for-me code here.

As @realityminus3 has pointed out at least once, counting is hard, so I made a computer do it. It turns out, there are only 72 possible ‘miracle’ grids.

But wait, there’s more!

(Not more grids. More analysis.)

Is there some way of generating miracle grids? . When I looked closely at the 72 possibilities, some things looked… awfully familiar. Repetitive, even.

For example, every sudoku (not just the miracle flavour) has one column that starts with a 9 and one column that ends in a 9; the same is true for rows – and for any digit: I just happened to pick 9. Let’s call those the 9-strings.

In all of the miracle grids, the four 9-strings (in some order) are

936|471|825,

948|372|615,

951|627|384 and

963|528|174

… and the middle two of those cracked it open!

How? Look at the alternate digits: in the second one, you’ll see 9-8|-7-|6-5 and -4-|3-2|-1-; in the third, it’s 9-1|-2-|3-4 and -5-|6-7|-8-: you just count up or down, skipping a space each time.

Looking more closely at each grid, either the rows or the columns do the skip-counting, and all in the same direction. This is how we build it!

Pick a digit to go in the top-left corner. (Say 1. It doesn’t really matter.) Using the skip-counting, fill in the top row as 162|738|495.

Now, where’s the first place the 1 can go in the second row? It can’t go in the first three spaces because there would be two 1s in the first box, so the first place it can go is in the fourth column. Putting the 1 there means filling out the second row as 495|162|738 (the first row moved on by three spaces).

Similarly, the first place the 1 of the third row can go is in column seven, and the third row is again a simple twist of the first: 738|495|162.

The same logic continues down the grid: the first place a 1 can go in row four is column 2 (516|273|849), and the first place in row 5 is position 5 (849|516|273).

You can probably complete the grid by yourself from there:

There are eight ways to reflect and/or rotate the grid (the 1 you started with could go in any of the four corners, and the 162 could go vertically or horizontally), and nine digits you could start from in the top left – accounting for all 72 possible grids!

Easter Eggs and Open Questions

Pick a position in a 3-by-3 box – say the top middle. Write out the digits in that position for each box to form a 3-by-3-square. This box, when reflected across the minor diagonal, is in the grid. It’s in the position reflected across the minor diagonal from the position you picked (top-middle reflects to middle-right):

In any row of 3-by-3 boxes, look at the diagonals moving up and to the right, wrapping around the top of the box and either end of the row. The offset is 1 each time.

The box with a 5 as its middle number? That’s a magic square. In fact, any digit 5 is at the centre of a magic square if you wrap the same way as in the previous bullet.

Some questions that are open (at least for me):

Under what circumstances do two digits uniquely determine the whole grid? (My code says there are 87408 = 72×2×607 clue pairs that give unique solutions.)

Under which of those circumstances would @crypticcracking be able to solve it?

CreativeCrocheter – Three Geometries in Crochet

CreativeCrocheter is the pseudonym of a person who blogs about crochet and maths.

As part of a math symposium at my undergraduate alma mater, I set up “learning stations” with my crocheted items that demonstrated various mathematical concepts. You’ve already seen the first station’s challenge if you voted in Match 5. The second station contained three crocheted objects – yes, the school team colors are purple and gold.

I invited the attendees (who included a number of local weavers!) to consider the following:

There are 3 objects, that will be referred to as follows:

Object A is the solid purple object

Object B is the purple and gold object

Object C is the purple and white object

These objects share the following characteristics:

All three were crocheted with the same hook and the same diameter yarns

All three started with the same number of stitches in the first round

All three were worked in continuous spirals of stitches

All three have 16 rounds of stitching

Name the type of geometry exemplified by each object

Hypothesize how to determine the curvature of each object

What other items in nature share the characteristics of Object B?

What type of spiral appears on Object C? Alternatively, what search terms would you enter in an an Internet search engine to find the name of the spiral?

Bonus for fiber folk: Why did the purple and white object take on a hexagonal shape?

Once everyone had a chance to look and consider, we discussed their answers and also considered the following:

How might you use objects such as these to engage non-mathematicians in exploring various geometries?

What would you do to demonstrate the parallel axiom in each geometry using these objects? This would be a good student topic for a future talk.

Ready for some answers?

Object A: Euclidean plane – the two colors form an Archimedean spiral, where each spiral arm remains the same width, created by increasing the number of stitches in each round by the same number as we started with.

Object B: hyperbolic plane (also called saddle or Lobachevskian geometry) – its geometry is shared by lettuce leaves, the saddleback on a mountain, and the crotch of your slacks, to name just a few, and is created by increasing in each round by more stitches than we started with.

Object C: ideal sphere (spherical geometry, also called elliptic or Riemannian) – there are fewer increases in each round for the first half, then corresponding numbers of decreases in the second half to close the sphere.

For more, do explore some of the sources and inspirations for this exercise!

Susan Lombardo

Woolly Thoughts

Daina Taimiņa

Margaret Wertheim

Ms Premise-Conclusion (ideal sphere pattern and other geekery)

Bridges

Oh, that bonus question? A crocheted spiral forms a regular polygon when the increases (two stitches placed into the same stitch) align – in this case by always increasing in the second stitch of the increase done in the previous round. The resulting polygon has the same number of sides as the number of increases per round. So starting with 6 stitches, as I did for each of these shapes, gives a hexagon.

As noted in some previous matches, the supposed dichotomy between logical thinkers and creative thinkers simply doesn’t hold up when it comes to exploring math concepts with fiber!

So, which bit of maths made you say “Aha!” the loudest? Vote:

Note: There is a poll embedded within this post, please visit the site to participate in this post's poll.

The poll closes at 9am BST on Wednesday the 3rd. I think this is the last match of this year’s math-off. Thanks for reading, and thanks for playing!

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robertkstone · 6 years

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Best Cars of the 2019 Detroit Auto Show: MotorTrend Favorites

As the first major event of the year, the Detroit auto show has historically marked the start of the auto show season. But in 2020, the show will move to June, which likely means 2019 is the last year the Motor City gets to kick things off for the auto industry. It’s the end of an era for the North American International Auto Show, and it went out with a bang by hosting big debuts like the Ford Mustang Shelby GT500, sixth-generation Ford Explorer, and the highly anticipated return of the Toyota Supra. Keep reading to see which cars MotorTrend editors liked most from this year’s Detroit show.

2020 Ford Explorer

Yes, the Mustang Shelby GT500 is hundreds of horsepower sexier, but the importance of a new Explorer cannot be understated. It’s one of those bread-and-butter vehicles. The 2020 looks better inside and out, feels much roomier inside with a wheelbase that grew 6.3 inches, and adds two key new models: an ST and the first new Ford hybrid in six years. But the main reason we want to drive it is because it has moved to Ford’s new rear-wheel-drive platform with available all-wheel drive. And with the 3.0-liter twin-turbo V-6 in the ST tweaked to get 400 hp and 415 lb-ft of torque, Ford promises it will be the fastest SUV under $60,000. –Alisa Priddle

2020 Toyota Supra

Toyota’s fifth-generation Supra is my car of the show for two simple reasons. First and foremost, it led all 2019 NAIAS coverage for MotorTrend, likely for reason two: It sparked some huge debates on social media. Purists, it seems, are not impressed with the BMW partnership, specifically that the flagship sports car has the I-6 heart from BMW. I addressed this in my column, but was not prepared for the depth of purist rage. Some feel Toyota, with its deep pockets and huge resources, should have invested in a new inline-six, or wackier, used the 5.0-liter V-8 from Lexus or even the Yamaha-built V-10 from the Lexus LFA supercar. This is not as ludicrous as it sounds when you probe these true believers; that Supra apparently is not set up to deliver world-beating performance on the order of what the Nissan GT-R did back in 2007 is galling to these super fans. This wasn’t a perspective I had considered, but it’s interesting and, in many ways, understandable. –Ed Loh

Infiniti QX Inspiration Concept

Infiniti’s electric crossover concept was damaged in transit and could not drive onto the stage for its big moment in the spotlight. I’m OK with that because it speaks to the fact that it is a true concept, not a production-ready car gussied up for a show. Real concepts are becoming a rare breed. This baby FX is the design direction for the brand’s future crossovers while playing with ideas like a suede flat tile floor that looks like tile, a lattice glass roof, a marble center console that extends to the second row, Orient Express–type gold table lamps, and a shark nose with no grille up front. –Alisa Priddle

2020 Ford Mustang Shelby GT500

As one of MotorTrend’s chief numerologists, I’m going with the big-number intros. OK, “700-plus” horsepower may not earn absolute segment bragging rights in the crazy/wonderful world we’re living in, but after my tech deep dive with the new Shelby GT500’s chief program engineer Carl Widmann, I’m willing to guess that the Ford’s savvier tire, brake, and chassis tuning will more than compensate for any deficiencies it suffers in outright brute strength relative to the ultracharged Mopar rivals for overall track dominance. Its aero tweaks and giant grille also seem better integrated than those on previous “road kings” from Shelby. –Frank Markus

2019 Ram HD

The other big number on everyone’s lips in Detroit was 1,000—as in the peak twist, in lb-ft, that Ram’s reimagined Cummins 6.7-liter cranks out in pursuit of its other crazy numerical statistics—35,100 pounds of towing (which the adaptive cruise control will brake to a stop and restart for you when traffic clears) and 6,910 pounds of payload (which actually jumps to 7,680 if you choose the gas V-8). We’re also pretty geeked about the number 12.0, which is the diagonal dimension of the Tesla-esque touchscreen handed up from our reigning Truck of the Year, the Ram 1500. Make mine a Power Wagon, please. –Frank Markus

Lincoln Continental 80th Anniversary Coach Door Edition

Just a few short years ago, the industry was talking about Lincoln’s product line struggles, which was heavy on uninspiring, mustachioed sedans. The Germans and Asian luxury brands were eating their lunch, and Cadillac looked to be miles ahead. But now, after a strong Navigator launch, a shockingly sweet follow-up in the Aviator, Lincoln is back. Adding coach doors to the flagship Continental sedan is another neat, super-smart party trick. It automatically moves the brand upmarket (a real consideration for the chauffeured set) thanks to the massive rear cabin created by stretching the wheelbase 6 inches. The world needs more coach doors. –Ed Loh

The Entire GAC Lineup

This isn’t a best-in-show nomination, but it is an honorable-mention round of applause. The GAC GA4/GA6/GA8 sedans, GS3/GS4/GS7/GS8 crossovers, and GM8 minivan are potent commodity entries in every potential U.S. market segment. Unlike past almost-comedic displays by Chinese automakers, across the board the styling may be anonymous, but it is sufficiently attractive. The interiors are laid-out well with intuitive, not-too-plasticky controls and sharp details like the Judas Priest–esque leather-stitched floormats. The doors close with a reassuring “thunk.” Important packaging elements—legroom, foot room, shoulder room—tick all the boxes. There are no glaring errors. We still have no idea how well the GAC vehicles drive (or crash), but if you peeled off the labels and put them next to a fleet of top-end Kias or Chevrolets, on initial impression you might not be able to tell them apart. If GAC arrives in the dawn of a recession with a strong value play on price, they could do some damage. —Mark Rechtin

2020 Cadillac XT6

I really don’t know how well Cadillac’s new three-row crossover will sell, but it’s 100 percent a car you have to see in person. In photos, it looks pretty boring. In person, it actually has some real presence. –Collin Woodard

Lexus LC Convertible Concept

I am absolutely not a convertible guy, so for me to call out the LC Convertible concept is significant. Just look at it; it’s an absolute stunner. Mystifying to me is why it’s a concept. Build it, Lexus. Right now! –Ed Loh

Mahindra Roxor

How can you not love this silly little side-by-side? Sure, there’s that legal issue with Jeep, but come on. It’s super cool! How can I convince someone to let me do an off-road adventure in this thing? –Collin Woodard

2020 Kia Telluride

Holy moly, what an interior! And the exterior ain’t bad, either. Kia continues to make huge strides, and many in the industry have taken notice. We heard murmurs from other car brands, a few from luxury marques, who were suitably impressed. –Ed Loh

The post Best Cars of the 2019 Detroit Auto Show: MotorTrend Favorites appeared first on Motortrend.

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