22. All That Geometry Gibberish
All That Geometry Gibberish
Standing in front of the king was more frightening than I had anticipated. He looked…
“I’m waiting.”
…impatient.
The resigned look in his eyes told me he was just tolerating this as a formality, but he had already decided my fate.
“Well, I wanted to—oh,” I stopped myself and bowed low.
Right. Manners, Wren. Probably should have led with that.
As I rose, I noticed the look of sheer intolerance now seeped through every pore on his face.
I glanced at Mali’s stony stare as she lounged on the cushion next to the King and knew I would get no help from her.
Better get on with it.
“I wanted to speak with you because I believe I can offer you something in exchange for Griffon’s life.” I paused, but the king said nothing, so I continued, “I can tell you where the headpiece of the Staff of Helios is hidden.”
King Faisal’s eyebrows rose. “And how might you be able to do that?”
“By using the coordinates on the tapestry behind me.”
“The greatest minds of my kingdom have failed at trying to decipher that weaving. What makes you think you can?”
Oh, I don't know. Hubris? Desperation? A frankly alarming lack of self-preservation? “Because it takes a combination of the understanding of the Sideri religion and scientific principles related to projective geometry. In this case, I am well-versed in both.”
The king glanced at Mali. They did that eye thing that couples do when they’re communicating without speaking. “So, where is the headpiece located?”
“I want to see Griffon first.”
“No. You have given me nothing to warrant such a concession.”
“Okay,” I nodded, considering my options. Which were, let’s be honest, depressingly limited. “If I give you one part of the solution, to prove to you I indeed have the knowledge I claim, you allow me to see him. If he is unharmed, I will gladly calculate the rest in exchange for his life.”
He studied me with cold calculation. “You think I will actually spare the man who killed my brother on the word of a foreign girl who arrived here in rags? And arrogantly assumes she can do what no one before her has done?”
Well, when he puts it like that… “I’m asking you to verify my calc—”
“And I will,” he interrupted me. “Once you calculate the correct coordinates and the relic is found, only then will I honor the rest of that agreement. But understand this: unless it is in my hand by dawn on the morning of the festival, you will both burn.”
My mouth went dry. Just thirty-six hours. And yet that was so much time for so many things to go wrong.
Well, I just hoped the coordinates were correct and the relic was still there. And that I haven't just spectacularly bet both our lives on medieval cartography and my ability to do math under pressure.
“You have a deal.”
“So what is the first part of this ‘solution’, as you call it?”
I swallowed the lump in my throat. “The cardinal points, as indicated by the orientation of the tapestry, are ninety degrees off.”
His brow furrowed in confusion.
“The tapestry is hung sideways,” I clarified.
“And how is that possible?”
“It’s the stars,” I explained. “The white star represents the star Castor, and the black star represents Pollux. They are the twin stars of the double quasar Gemini in the Sideri religion. It is theologically incorrect to orient Castor above Pollux.”
The king steepled his fingers. “But one is good, and the other is evil.”
“The Sideri religion values balance, not good versus evil. One is not superior to or even valued more than the other. The tapestry needs to be rotated ninety degrees to the left. Castor flies toward the north, but he is not the north itself. And the opposite is true for Pollux.”
Unfortunately, he still didn’t look convinced.
“Think of them less like moral absolutes and more like…cosmic dance partners who take turns leading.”
The king cocked an eyebrow at me. But then he sat back against the throne and studied the tapestry.
What felt like minutes crept by. The only thing that broke the silence was the sound of guards occasionally shuffling their feet as they stood against the walls.
I couldn’t help being aware of the many eyes on me as the sweet, heavy scent of incense drifted down from the ornate brass burners hanging near the vaulted ceiling.
The guards, advisors, and servants all waited to see if I'd just made the worst miscalculation of my very short life.
“Okay,” he finally stated.
I let out a breath I didn’t realize I was holding. “I want to see Griffon now.”
“Guards, bring the prisoner.”
While we waited, the servants removed the tapestry from the wall and laid it on the floor in front of the dais. In the correct orientation now, of course.
“I will need a map of the lower half of the continent that is to scale,” I said, “a meter stick with measurements to the millimeter, parchment, and something to write with.”
Flanked by two guards, Griffon entered the hall in chains.
He looked tired, but surprisingly, he also looked good.
Even clean. The dark circles under his eyes, which stood out so prominently on his pale face the last time I saw him, were faded, almost gone.
He wore a plain gray tunic with the sleeves rolled to his elbows and black linen pants.
A small, white bandage stood out starkly against the tan skin of his arm, indicating that they must have cleaned it up and stitched the wound.
I guess they didn’t want their prisoners to die before they had the chance to execute them. How thoughtful.
His eyes met mine. There was a question there, but obvious displeasure as well. Such the martyr. How could he expect me not to—at least try to—free him? The guards halted him five meters from where I stood. Apparently, they took the words ‘see him’ literally.
“And now the rest of what you promised, Wren.”
It was the first time the king had said my name. It sounded strange on his tongue, as if a name coming out of his mouth should have been grander, more noble. Like Anastasia. Or Isabella.
A tall man in a white robe with a wide gold sash entered the hall with the servant carrying the items I requested in tow. His long, thin face had such deep lines around his scowl that I assumed he never smiled. Or laughed. Or experienced joy of any kind. Probably kicked puppies in his spare time.
He stopped near the dais, folded his arms across his chest and tucked his hands into the opposite sleeves. And then just stood there like a cranky man in a bathrobe radiating disapproval.
I knelt down to measure the distance between the points.
“This is an azimuthal conformal projection. You see, the world isn’t flat, it’s a sphere,” I explained, “When you take a sphere and flatten it into a two-dimensional map, all of those coordinates are distorted because you are not taking our curved surface into account.”
I glanced up to see blank looks on multiple faces. Right. Maybe I should've opened with 'the world is round' and built from there.
“To keep it simple,” I continued pointing at the tapestry, “this black dot with the N stitched next to it is the pole, the black dot with the slanted line, here, denotes the intersection of a line from the pole to the x-axis and then the red dot,” I tapped the tapestry with my quill, “is your projection. And that is where the headpiece is located.”
The king huffed a short laugh. “Yes, yes, that was a much simpler explanation.”
I stopped. “Oh, ah…” Was that sarcasm? That felt like sarcasm. Did I just get roasted by a king?
“Continue, continue,” he said, motioning with his hand.
Heat rose in my cheeks as I got back to work.
The thin man in the robe peered over my shoulder at the calculations I scribbled on the paper. I suppressed the urge to give him a side-eye. Personal space clearly wasn't covered at whatever monastery trained this guy.
Ignoring him, and the fact that I could feel his breath on my neck, I cleared my throat and went on.
“So if you have these three variables, you just need two more pieces of information. First, you need to know the radius of the sphere, and in this case, that’s easy because we’re referring to Earth’s radius. ”
King Faisal leaned forward on his throne, his elbows coming to rest on his knees. Mali's smirk suggested she was enjoying watching me perform like a trained monkey for the court—so I just ignored her.
I stopped calculating and looked at the king.
“The second piece of information seems obvious, but it isn’t to everyone.
These projections typically use the coordinates of the north pole, in the northern hemisphere at least, as the reference point.
But Hermes wouldn’t have used the north pole,” I reasoned.
“It would have made the distance too great to be accurate. As a former Empyrean monk, he would have used the center point in his world, the epicenter of the alignment, the Stella Noctus Citadel.”
I finished calculating the last formula. “Okay, so these are the coordinates,” I went on as I pulled the map closer. “And the headpiece,” I paused, measuring and marking the coordinates onto the parchment, “should be right here.” I drew a small X on the map.
The thin man then pulled the map out from under my quill. Rude.
“It’s just southwest of here, Your Majesty, along the base of the mountain range,” he offered, stepping closer to show the king.
“Hmm. I’m not familiar with that area.” The king studied the map and rubbed his chin.
“Neither am I. There are no trade routes in that direction.”
“So what do you think of all of this, Malik?” The king asked the thin man, motioning toward the tapestry and the page filled with my formulas and calculations.
Oh good, Judgy McBathrobe has a name.