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Base 6 grouping & fractions
This public article was written by [Deactivated User], and last updated on 15 Aug 2019, 15:29.
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1. Grammar & syntax
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2. Nouns and pronouns
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Counting in Hapeze is done in base 6. Hand-counting is particularly noteworthy, as each fist represents one digit in base 6 (which can range 0 to 5 risen fingers). As a result, the word for 36 is derived from the word for "hand", and 1296 (6^4) comes from "body". Now, on to the actual system:To produce a number between 7 and 35, concatenate the digits with no special joining words. 23 (12 + 3) = bico (2-3), 50 = dolak (5-0), 11 = kiki/kihi (the word for one, hi, becomes ki in the sixes place, and sometimes leaks onto the ones place in the word for 7)
To produce a number between 36 and 215 (3 digits), state the multiple of 36 (the hands place, akin to hundreds) followed by "zig" (shortened version of the more proper word zwiga), followed by the other two digits as normal. 543 = dozig cico, 123 = zwiga bico (for the special case of 100 (36), the full zwiga is used)
To produce a number between 216 and 1295 (4 digits), read the first two digits, "zig", and then the last two. 1234 = kibizig(a) coci
To produce a fraction (P divided by Q) read it as "Q heqwa P" (of Q parts, P many)
To produce a mixed fraction, read the whole portion first, then the word "ki" (meaning and/add/plus), then the fractional part.
To produce decimals (or rather, seximals) use "kilak" to join the normal left side, and the paired up right side. More literally, it translates to "and nothing/ and 0", as if preparing for dividing by 0, but most accurately it translates to "and (with an arbitrary denominator)". 1234.54321 = (12)zig (34) kilak (54) (32) (10), 1.0002 = hi kilak lak bi, 1.002 = hi kilak lak bilak, 1.02 = hi kilak bi, and finally 1.2 = hi kilak bilak. The important note is the distinction between 0.01 and 0.10: lak kilak hi, lak kilak kilak. In the event of odd-many decimals, always attach a dummy zero, otherwise it will appear as though the final digit is in the wrong place.
To produce numbers greater than 1295, use ta()dxi for this language's equivalent to the -illions series in english. ta()dxi numerically represents 1296^x, where x can be any number, even another 1296^x (which amounts to well over 10^4000). for the special case of 1296 itself, use tapudxi (meaning body).
Numbers will generally look like:
[... (xx zig xx) tabidxi (xx zig xx) tapudxi (xx zig xx) kilak xx xx ...] ki (qq zig qq) hequa (pp zig pp)
In practice, including both kilak and ki - hequa would be considered improper, but a proper number is everything before the ki, and a mixed fraction is simple A+P/Q, where all three are proper numbers.
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