### Radian

**Location: Mechanus / the Geometric Centre**

Radian is a burg where mathematics reigns supreme, and geometry is the lifeblood that flows through every cog, every street, and every thought. If youâ€™re a basher who thinks theyâ€™ve got the measure of **Mechanus**, think again. Radian is a place where even the angles have right-angles, and a squared mind is the only way to thrive. The chant goes that the high-ups have done the maths and claim Radian is located at the dead-centre of Mechanusâ€”but of course the locals would say that, wouldnâ€™t they?

Itâ€™s this burg where the sect called the **Mathematicians** does their finest number-crunching and calculating. There’s an entrance to the Labyrinthine Portal here, and apart from the modrons, there cutters are the best-qualified to operate the barmy thing. The more adventurous members of the sect chase the results of their calculations and explore the distant parts of Mechanus in search of… well, whatever it is these basher seek.

#### The Perfect Precision of Radian

Radian is a place of perfect order, where even the cobblestones are laid out according to precise mathematical principles. The city is a flawless circle, its radius extending from the central hub known as the **Set Square** (ironically a circle)â€”a vast, open space where the moignos (those peculiar beings of pure mathematical thought) gather. The cityâ€™s sectors radiate outward from the Set Square like the spokes of a wheel, each sector dedicated to a different branch of mathematical study. Its radius is precisely defined by the ancient calculations of the mathematical architects who first raised (to the nth power) its gleaming walls. The streets radiate outward like spokes from a central hub, dividing the city into sectors that are as logical as they are beautiful.

The Set Square is where the cityâ€™s most important discussions take place. The plaza has seating arranged in concentric circles, designed to amplify sound so that even the quietest voice can be heard at the outer edges. Here, the cityâ€™s Mathematicians gather to debate the nature of reality, exploring concepts like the golden ratio, Fibonacci sequences, and the grand theory of Everythingâ€”all of which are represented in the precise patterns that adorn the plazaâ€™s floor.

Here, the concept of symmetry is more than aesthetic; itâ€™s a way of life. Every structure, from the smallest hovel to the grandest hall, adheres to strict geometric principles. The buildings themselves are crafted from polished steel, and cast shadows in perfect alignment with the cityâ€™s grid.

Radianâ€™s government is a model of efficiency, putting any **Guvner**-run town to shame. Everything occurs on the exact second that it is supposed to, and the massive water-clock in the centre of town dictates the time of day to all.

Across the street from the water-clock is the Mathematicianâ€™s most prized building: the **Library of Numbers**. This gargantuan building of stone and iron houses all of the Mathematicians research. Everything every Mathematician has discovered, devised, calculated, formulated and thought up is written down and stored in the Library, which is guarded by the most expensive mercenaries money can buy, as well as potent magical traps.

#### The Mindset of Radian: Where Equations Rule

The cutters of Radian are folk who breathe numbers and dream in equations. The air here hums with calculations, and youâ€™ll often find the locals muttering to themselves as they walk the streets, solving complex theorems or debating the finer points of non-Euclidean geometry.

In Radian, a problem isnâ€™t a problem unless itâ€™s expressed in mathematical terms. The inhabitants have little patience for those who canâ€™t see the world through the lens of logic and precision. If youâ€™re the sort who prefers a bit of creative chaos, youâ€™ll find yourself out of sorts in Radian, where every law is determined by the strictures of mathematical logic.

The cityâ€™s mathematicophilosophersâ€”known as **Ordinals**â€”are revered figures, their solutions treated as gospel by the locals. Take for instance **Quotidia** *(planar tiefling wizard [she/her] / Mathematicians / LN)*, a thoughtful and demure tiefling. Her mind is constantly at work, pondering the mysteries of the multiverse through the lens of mathematics, seeking to uncover the hidden equations that govern all things.

Radianâ€™s landmarks are, unsurprisingly, a study in geometric perfection. One of the first places a basher ought to visit is the **Axle of Pi**, a towering obelisk that rises from the centre of the city. The axleâ€™s height has been precisely calculated by an army of moigno and apparently represents the infinite nature of pi. Its surface is etched with the digits of that transcendental number stretching upward in spirals. Legend has it that the axleâ€™s apex touches the very limits of Mechanus, where order begins to break down. No cutter has ever been able to travel up it far enough to learn if thatâ€™s true, mind

**The Mathematicians**

Unlike most sects, the leader of the Mathematicians is not called the â€œsectols”. They are referred to as the “Prime Digit”, or often just the “Digit”. The Digit of the Mathematicians is selected by the previous Digit. Thus, before Rikard died, he calculated that one of his most intelligent pupils to take his place, and then that one chose their favourite, and so on. The current Prime Digit of the Mathematicians is **Laretua Quinton** *(planar human diviner [she/her] / Prime Digit of the Mathematicians / LN)*. Laretuous has been the Digit for about eight years now, and she’s the youngest Digit to date, aged only thirty-one years.

The three principal sectors (the equivalent to factors of the factions) of the Mathematicians in Radian are brother and sister pair of tiefling bashers named Sine and Cosine and a rogue modron called Tangent. These names are the traditional ones adopted by Mathematician sectors; the real names of the cutters are kept a secret by the sect until they are replaced. Nobody really knows why, but the Mathematicians are a very traditional lot, prone to following the well-established patterns of dogma.

**The Negatives of Radianâ€™s Precision**

But donâ€™t go thinking Radian is all perfect squares and no flaws. For some, the cityâ€™s obsession with perfection can be stifling. The constant need for order, for everything to fit neatly into a preordained structure leaves, for planewalking visitors especially, little room for spontaneity or creativity. Visitors often find the cityâ€™s rigid mindset a bit much, and even the locals can occasionally crack under the pressure of living up to the cityâ€™s nigh-impossible standards.

So while Radian is a haven for those who live and breathe numbers, itâ€™s less forgiving to those who donâ€™t quite measure up. The cityâ€™s laws are as unyielding as its geometry, and thereâ€™s little room for mistakes. A single miscalculation can land you in hot water with the **Auditors**, the cityâ€™s enforcers, who ensure that everything and everyone adds up, and there are no rounding errors (the local lingo for a crime). Get caught, and the chant goes say thereâ€™s no punishment worse than being forced to spend to years hard labour trying solve a mathematical paradoxâ€”a task that can drive even the most logical mind to madness.

Since the Mathematicians are generally not a very physically-inclined bunch of bloods theyâ€™ll often hire out groups of adventurers and mercenaries to guard the town for them. These kinds of cutter arenâ€™t generally as scrupulously lawful as the burgâ€™s rulers might like though, which can result in the bizarre situation where itâ€™s the security hired to defend the town that actually cause more crime than the residents.

**A Life of Calculation**

For those who choose to settle in Radian, life is a constant calculation. Every aspect of existence is measured, weighed, and calculated according to the cityâ€™s rigid principles. The markets operate on a bartering system based on the value of pi, with goods exchanged in carefully measured portions. Even time is measured differently here, broken down into units that align with the cityâ€™s mathematical calendar, which shifts and adjusts according to the cycles of Mechanus.

Social interactions in Radian are equally precise. Relationships are governed by the principles of compatibility and balance, with marriage contracts often drawn up as complex equations to ensure a harmonious union. Children are raised with an emphasis on mathematical education from the moment they can count, and itâ€™s not uncommon for a Radian nipperâ€™s first words to be numbers rather than letters.

Despiteâ€”or perhaps because ofâ€”its precision, Radian is a place of deep intellectual satisfaction for those who thrive on logic and order. Thereâ€™s a sense of peace that comes from knowing that everything has its place, that every problem has a solution, and that the world operates according to principles that can be measured, understood and mastered.

**The Moignos**

At the heart of Radian, in the Set Square, youâ€™ll find the **moignos**â€”creatures formed from pure mathematical thought, embodying the concepts of rationality and irrationality in ways that defy easy understanding, or indeed explanation to anyone without advanced degrees in mathmology. The **rational** moignos are straightforward, predictable even, their actions governed by clear and understandable principles. The **irrational** moignos, on the other hand, are a different story altogether. They move in ways that seem random, their patterns impossible to predict or comprehend. Yet, within their chaos lies a deeper orderâ€”one that only the most enlightened Mathematicians can begin to grasp. Watching them is like trying to follow a fractal pattern; the closer you look, the more complex it becomes.

The moignos are both a blessing and a challenge to the Mathematicians. On one hand, they offer insights into the deepest mysteries of the multiverse. On the other, they represent the limits of even the most advanced mathematical understanding. Itâ€™s a rare sight to see a Mathematician openly admit defeat, but the moignos have been known to humble even the most confident scholars.

**The Labyrinthine Portal**

Radian is also home to a terminus of the Labyrinthine Portal, a Mechanus-spanning planar pathway thatâ€™s as much a puzzle as it is a passageway. This portal doesnâ€™t lead to just one place; instead, its destination shifts according to complex equations that only a mathematical genius can decipher. Some say the portal is a testâ€”a way for the universe to challenge the minds of those who dare to use it. Others reckon itâ€™s set up that way so only true scholars of Mechanus can take full advantage of it.

Navigating the Labyrinthine Portal isnâ€™t for the faint of heart. Youâ€™ve got to understand the numbers, the geometry, and the logic that governs its twists and turns. Even then, thereâ€™s no guarantee youâ€™ll end up where you intended. But for those with the wits to match its complexity, the Portal offers a way to explore the furthest reaches of Mechanusâ€”and beyond.

#### Radian: Summed Up

Radian is more than a burgâ€”itâ€™s a living, breathing temple of equations. For those with a mind for numbers and a passion for precision, itâ€™s a place of endless fascination, where every day brings a deeper understanding of the mathematical principles that govern all things. But if youâ€™re visiting just remember, cutter: in this burg, the equations calculate *you*.

**Canonwatch:** *The Mathematicians were first introduced in Planes of Law: Mechanus. This entry expands upon that lore.*

**Source: ***Brant Casavant and Jon Winter-Holt*