POV: HELENA IVYRA.
I spread my notebooks and notes across the table and took a deep breath.
The silence in my room had always been comforting, just like the sacred quiet time I used to rest and practice a little.
My routine was turning into a habit: staying after lunch, while the hallways emptied out, to take advantage of the free time until the special class with Professor Miguel.
It was a good time to study and solve group exercises with Renata.
Even then, it couldn't compare to my room and my own study schedule. Having a moment to myself was wonderful and necessary every now and then.
I feel more at peace when I'm alone, as if silence is a companion and not an enemy.
And, honestly, without Renata poking me every five minutes to make some random comment.
I managed to concentrate better on today's goal… the accursed axioms.
I opened my notebook to a page scattered with symbols, lines, and geometric figures.
The title was written in big letters: Axiomatic Tessellation – Review of the Fundamentals.
Just looking at it already made me feel the weight of responsibility.
My literary mark, engraved on my wrist, glowed softly.
This always happened when I dove deep into this kind of study: it was as if it called me to work, pulsing like a natural reminder: Oh, Helena, go study!
Ever since I awakened this enchantment, I always knew it wasn't just about memorizing formulas.
The idea had something more... I'd have to learn to manipulate invisible concepts, to mold them in the air as if they were luminous threads ready to be woven into a magical tapestry.
The weaving process was very similar to sewing, except I didn't use thread. I used theorems and axioms.
Those types of basic concepts you only believe in because… It's just like that and there's nothing we can do.
I closed my eyes and let the energy flow through my fingers.
My enchantment worked pretty much like an arsenal of magical crochet, because I needed to understand how to connect the constructs and build them one by one.
After that was done, the next step was to memorize those equations in order and repeat their execution in my mind, so that when it was time to channel energy into the mark, the construct would be executed.
With every breath, I felt the gentle warmth of QPs running through my mind. I remembered the first time I awakened this enchantment, almost two years ago, when I was starting to get interested in more technical math books.
Today, after two years of training, the constructs felt as natural as writing a sentence.
Of course, instead of letters, words, and sentences, I used logical operators, theorems, and proofs.
'Mathematics is a language on its own… Like it or not'
I looked at my notebook and decided to quickly review the first axioms...
Between two distinct points, a straight line can be drawn.
Simple and straightforward, but it was the foundation of everything. It lets me connect points and lines to form objects.
I opened my right hand and imagined two floating points of light before me.
They appeared, small, bluish, and vibrating like stars.
A moment later, I connected them with a straight line. It shone steady and unchanging, like a rope stretched between two worlds.
"The shortest path... is always the safest."
The second axiom came right after:
A straight line segment can be extended indefinitely in a straight line.
That part always made me a little uncomfortable. There's something about the concept of infinity that messes with my head.
In math, we regard some concepts as true without really knowing if they are, for example.
With this second concept... any line could be extended infinitely depending on the points I used to define it.
Still, I took a deep breath and extended the line as far as I could with my arms outstretched. With my arms in that position, I channeled energy to the mark.
"Axiomatic Tessellation."
Using the vocal invocation, my enchantment became independent of the continuous energy flow.
That way, the line stayed firm, vibrating in silence. I could almost see it hovering over my hands, as if reality itself were forced to recognize that line.
"Okay, this is just the foundation. Let's see if I can go further," I said, smiling slightly.
I quickly turned the page and saw the second-degree axioms, the ones requiring more delicacy.
It was like embroidery in the air, needing total concentration so as not to unravel the drawing.
With any center and radius, a circle can be drawn.
I put two fingers out, choosing the center point with a finger in the air. The energy responded at once, swirling around my hand.
A perfect circle appeared, clear as glass and solid as steel. It spun slowly, emitting little waves of energy that made the hair on my arms stand up.
I knew how useful that circle was. It could become a shield, a gear, or even the base for more complex structures.
I was satisfied, remembering how often I'd failed to keep the shape stable.
Now, it seemed almost natural.
And with it, the fourth axiom came too:
All right angles are equal to one another.
I drew four lines and closed them in a shining square. The sides were perfect, each angle exactly like the others, solid as a brick.
The precision filled me with pride and also a cold thrill.
It was odd to think that, with enough training, I could turn a square like that into a whole wall.
'If the Chinese had had this centuries ago... The history of the great wall would have been very different…'
I opened my eyes and contemplated the set: the long line, the perfect circle, the rigid square.
The three forms floated before me, connected like the gears of an ancient clock. Each one pulsed to its own rhythm, but together they vibrated in harmony.
I could feel how each axiom behaved alone, and also how they gained strength together.
The lines provided the foundation, the circles reinforced it, the angles gave resistance.
It was like assembling an invisible puzzle, with each piece supporting the next.
"So that's it... I don't just need to repeat the shapes. I can combine them."
I let the long line cross the circle, and the result was a structure that resembled a compass. The intersections gleamed with more intensity.
Then I brought the square closer, fitting it inside the circle. The contrast between the rigid and the curved made the energy tremble, but it didn't fall apart.
It still wasn't perfect. The energy vibrated unstably, almost slipping from my fingers. I undid the construction before it collapsed on its own.
The blue sparks scattered in the air, vanishing like shooting stars.
I leaned back in the chair and took a deep breath. Sweat trickled down my forehead, even though the effort was more mental than physical.
Working with the axioms was always like that: each session drained a bit of my energy, as if I'd just run kilometers.
I grabbed my notebook and quickly wrote:
Combining lines, circles, and squares leads to instability. Needs external support points.
I looked at the phrase and laughed to myself. Support points... just like in life, huh?
No structure lasts on its own for long.
My thoughts wandered for a moment. I remembered Renata, who always said I overthought things. Maybe she was right.
But deep down, I knew these moments of reflection were as important as the practice. It wasn't just about raising barriers or building shining forms.
It was about understanding what they meant.
I raised my hand again. The lines still vibrated within me, begging to come out. I decided to try something new.
I created two points, joined them with a line, then extended it a bit less than before. Then, I drew two circles, one at each end of the line.
The result looked like a balanced scale floating in space. I tried reinforcing the structure by adding squares at the intersection points.
The glow flickered but held longer than I expected.
"Ha!" I exclaimed, almost laughing. "It works!"
It didn't last long, true, but it was enough to confirm I was on the right track.
I wrote again: Composite structures can hold if distributed symmetrically.
With every attempt, the feeling grew inside me: I was learning new tricks, and each of them could be useful when the time came.
I closed my notebook for a moment and stared at the ceiling. The house was quiet, except for the distant buzzing of some random motorcycle outside.
I wonder what it would be like to face a real battle using all the new information.
Circles as shields, squares as barricades, lines as spears... maybe even more complex combinations that I hadn't even discovered yet.
I already had some complex constructs in my arsenal: gauntlets I used often, simple protective hexagons, simple platforms with rectangles or squares.
All these formulations were useful in battle, but they were always fragile and usually single-use. Which made long-lasting battles in training complicated, or even in...
"Library..."
Best to focus my mind elsewhere. I plan to start investigating that incident soon, just waiting until the first tests are over.
"One day, these figures will be more than practice," I said softly, as if making a promise to myself. "They'll be my weapons."
I let the pen drop onto my notebook and closed my eyes for a few seconds to rest my mind. The training had drained me, but left me with a strange euphoria.
It was as if every line I traced was also a stroke for my own future.
And, in a way, it really was.