**HypoTinuës**

The first thing to remember is that Atur is the Capitol of the Aturan Empire. Not just a big city, this is the administrative centre and temple of church and state. All power stems from here through the hands of the Emperor and the Pontifex. It’s symbol is the six-spoked Iron Wheel of the Tehlin Church like the one we witness in Trebon. Chronicler also wears an iron wheel around his neck.

Its position on our maps puts it pretty much at the centre. The map we need to view first is that of The Eternal Aturan Empire which shows the extent of it’s range of conquest from it’s origins. Outward growth has been in all directions and near total at the height of the Empire’s power with only a few unconquored lands remaining ‘free’, notably…

The forest of The Eld which has also been claimed by Modeg as it’s royal border.

The Shalda Mountains in which the Cealdish nomads have made their home.

and the last few bits of Yll which haven’t been stamped on by the Aturan Empire’s boot yet.

The Adem have been antagonised off the edge of the map onto poor land the empire doesn’t want.

Modern day Vintas has been completely absorbed by the empire along withThe Small Kingdoms, internal strife led to revolution and eventually the Empire’s borders were pushed back to their current limits enabling the rise of the Commonwealth.

The Great Imperial Road ignores borders as it does trees and ploughs straight through everything.

It wasn’t built by the Aturans, it is older than them, but the Empire has expanded around it adopted and renamed it and assumed complete control over its length. Our original edition map show Atur’s border today, the dotted lines depict all the current borders in the land. Whist far reduced in size, it’s centre remains strong and the most central part of the Great Stone Road, as it is now being called, still rolls across their land obliviously. Various place names are shown on the maps. They show government seats and notable cities, one or two for each country dotted seemingly at random.

But getting clever with rulers and pencils will reveal some wonderous things on our Third map.

Make
a photocopy of the New 10^{th}
anniversary Four Corners of Civilization map and draw the following
instructions on it.

- A line fom Junpai to Khershaen.
- A line from Khershaen to Keretes.
- A line from Keretes to Junpai.

This will give you an equilateral triangle between these diverse cities, the exact centre of which is the Capitol at Atur. We can prove this by drawing further lines from each of these cities towards Atur which then continue to bisect our triangles edges. All roads lead to Atur.

Extending these imaginary lines beyond our triangle gives us some rather exact destinations.Whilst the Junpai line goes nowhere significant, it does follow exactly a true North/South bearing.The extension line fron Keretes leads us unerringly through the eld until it smacks straight into Renere. The Khershaen line also crosses the world before it ,too, manages to pinpoint a distant city at Iskur.

We now have something resembling a giant crop circle, all geometrically worked out before us.

But we aren’t done yet, Our line heading Westwards leads to Iskur, about as far as you can go. So…

- Draw a line from Iskur to Fehn Illiel
- Then a line from Fehn Illiel to Carcen
- and last from Carcen back to Iskur.

This triangle is not equilateral.

Brandeur is the man we need here, Master Mathematician at the University.

He knows all about triangles. At first admissions he asks Kvothe…

‘You have a triangle. One side is Seven feet, one side is Three feet.

(the side between them) is sixty degrees.

What is the length of the remaining side?’

In a right angled triangle, which our newly mapped triangle does appear to be,

The square on the Hypotinuë is equal to the sum of the squares on the remaining two sides.

If this were a right angled triangle the correct angles would be the 30, 60, and 90 degrees.

Kvothe’s answer is ‘close enough’. The correct answer would be the square root of 40. or 6′ 3”

but he gives *two* answers, depending on which edition you read.

Changes have been made to the 10^{th} anniversary edition,
which is where we get these beautiful maps from. Thank you Farrowton
Sisters Cartographers.

But elsewhere, some small things have been altered in the text itself, every one of them a clue.

These changes were deliberate. They are an admission of falliability. Homer sometimes nods.

In the originals, Kvothe offers ‘Six feet six inches. Dead even.’
This gets a surprised *Hmmpht *noise. But in the new version it
is ‘Six feet and an inch.’ ‘Well, almost an inch.’

Both answers are declared ‘Good enough.’

But they can’t both be right. In fact they are both wrong. Root40 is Six feet and 3 inches. Or 6 ¼ ft.

Calculating square roots is bloody hard, yet a rather generous master Brandeur seemed surprised Kvothe was not closer given his previous accurate answers. He did approach his last question more seriously than the others. It’s also lovely to see an Image of the scene, with Kvothe standing in the shadow of the noonday sun…shining through a wheel shaped window! Great stuff Nate.

But why alter the new copy with a wrong answer? This is not a correction, it is an Alteration.

That is why I spotted it, because I was looking which comes before seeing which is E’lir level.

But what has that got to do with O*ur* triangle, we don’t know
the lengths of the edges.

Measuring the book page itself gives gives us a HypoTinuës of 3 ½ ” and a short edge of 1 ½.”

and if you double them both we get Seven and Three which we are told are both lucky numbers.

Lucky for me because they prove that Master Brandeur was describing
an exact scale model of the triangle which we have uncovered in our
map, a triangle who’s answer underlines The University. *Littera
Scripta Manet.*

Very pretty this all is too, but to flesh it out a bit more, to give it some motion, we need a pair of builders compasses.

- Draw a circle, centre Atur, radius Junpai.
- Draw a circle centre Atur, radius Renere.
- Behold! The Great Iron Wheel of The Aturan Empire.
- Pretty neat, huh?

really amazing. More evidence that the sword is shaped by story. I think my idea of Tinue being the unfolding land isn’t as much of a stretch given this finding. But given its not nearly as mathematically ast his, it still likely my own wishful thinking.

I couldn’t quite find the wheel though. Here is my drawing with me attempting to make the 3 missing spokes in pink just by drawing them and not following your instructions. The second tringle is just in the bottom. What is a builders compass?

https://docs.google.com/drawings/d/1rXh-Ge3wH9BY00kvD4QWdjR0pgwZ_GYnU5BjwrHEqMM/edit?usp=sharing