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== Translator's notes == This document contains a lot of mathematical notation and seems to provide a lot of insight as to how the D'ni wrote and thought about mathematics. This might be a veritable Rosetta Stone of information. I have put all of the things I believe to be mathematical terms in quotes in the main body of the letter. I will now go through them and explain how I came to discern their meaning and translation. –tobyas "Square side"—This appears to be the D'ni form of the square root. Not surprisingly, the D'ni seem to have kept their tie between geometry/design/engineering and the abstract mathematical concept of numbers by permanently paying homage to the relation between the radical and the side of the square. "Cube side"—Unsurprisingly, the D'ni have extended the square root to the cube root the same way we do. Unfortunately this document makes no mention of the existence of a forth or higher root. I highly doubt they would use a term like "hyper cube side." This is something to look out for in future documents. "Dividing line" or the alternate translation "Separating line"—used in this context it appears to directly refer to the diameter of a circle. However, I might speculate that these terms may refer to any line of symmetry in a geometric figure. "Horizon"—This appears to be a trigonometric function as the author makes numerous references to using it on an angle at the center of a circle to determine the distance between two points on the circle. With the approximate values given the horizon of an angle looks to be 2 * sine(angle / 2). Technically with this we could create an additional trigonometric function "cohorizon", but it is unclear if the D'ni used anything like this. An additional note about this is in regards to the name. The name appears to come from the idea that a surveyor’s view of a new age seems to be a circle. Then, the distance between two points on the horizon can be calculated knowing the angle between the two items and the visibility of the day. The number that would be calculated using Koh'shee's method is pi/2. This is an interesting curiosity about D'ni mathematics as this seems to be another aspect which seems based off of a quarter of a circle. On the surface, we use a measure of angles called radians. Pi/2 happens to correspond to a quarter of a circle. "Multiplication"—I have used the symbol * in place of the D'ni symbol of multiplication. After a little bit of research the D'ni symbol for multiplication is the letters of the word for "with" or "by" (''t''' in English letters) written on top of each other inside of a box. "Division"—Just like with multiplication, division is denoted by two letters on top of each other drawn inside of a box. The letters are ''te'' which corresponds to "of" as in "a member of." This is hardly surprising considering the words that Cahy'leh used in the first letter of this series. As for the equation itself, the D'ni numerical system is rather unique in that all the numbers have boxes around them. As a result when writing a number with multiple digits the whole number is written inside of a long rectangle. This has been seen in many places all around D'ni and their ages. Here it seems that D'ni extended this to their equations. The same long rectangles are written around whole expressions seeming to indicate, truthfully, that an expression is actually just a different way to write a number. Incidentally, this may explain why we have never see equations anywhere as the D'ni simply treated them as numbers and found little use for the equations themselves in formal letters. Additionally the D'ni have a unique way of writing an equation. The advantage of their system is that it allows us to write expressions without the use of order of operations or parenthesis. So, an expression like 2 * (3 + 4) would be written ''2 34 + *'' all in a large rectangle with double lines separating the different numbers. At the very least, this particular D'ni man had this habit. As we discussed, it is possible that not all of D'ni shared this notation. —tobyas
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