### Minkata Navigation & D’ni Distances (p2)

### Measure of Angle and the Compass Rose

- The D’ni divided a circle into 62500 angular units called torans. (about 174 torans per degree)
- 625 x 100 = 62500
- 625 is a power of 5, 100 is not.
- 625 can be written as 01-00-00 in base 25 notation; this is rather elegant.
- 100 can be written as 04-00 in base 25 notation; this is much less elegant.
- 62500 can be written as 04-00-00-00 in base 25 notation with about the same level of elegance as 100.
- But, 25 can be written as 01-00 in base 25 notation and 25 times 4 is 100.
- ¼ circle is 15625 torans and can be written as 01-00-00-00 in base 25 notation; this shows a return to the simple elegance of the number 625.
- Are the D’ni basing their unit of angle on a quarter circle instead of a full circle?
- The compass rose in Minkata and the compass roses in the book of clues have 20 divisions around the perimeter.
- 20 / 4 = 5
- There are 5 divisions to each ¼ circle.
- The 625 x 25 torans (01-00-00-00) in each quarter circle can be broken down into 625 x 5 torans (05-00-00) for each compass point.
- 5 is the fundamental number in the D’ni base 25 number system.
- The ¼ circle is a 90 degree angle; it is also a 100 grad angle (the grad being a unit based an the ¼ circle and being a precedent for the D’ni use of such a system.)
- If a ¼ circle is used as the base of all angular measure, then the D’ni units that make it up (in all known subdivisions) are all factors of 5.
- D’ni buildings commonly used vertical walls if they did not utilize existing rock formations (or other material such as giant mushrooms) in their construction, so the D’ni had to understand the concept of a right angle and hence the ¼ circle.

All of the above leads me to believe that the toran system is based on units of a ¼ circle rather than a full circle