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

Authored by Robert on July 15, 2007

### 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.
• � 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 � 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 � circle is a 90 degree angle; it is also a 100 grad angle (the grad being a unit based an the � circle and being a precedent for the D�ni use of such a system.)
• If a � 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 � circle.

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

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