/sci/ - Science & Math

Problem 81 is a large-ish table, and partial solution, which extends the basic idea of the table in 80. In fact, the first part of the problem is a simple verbatim repetition of that table. Chace's version of the statement is needed now.

"P.81: Another reckoning. Express fractions of a hekat as 'Horus eye' fractions and in terms of the hinu."

Basically, Ahmose lists not quite 30 combinations (additions) of the six Horus eye fractions

[math]

\displaystyle \frac{1}{2} \;\;\;\;\; \frac{1}{4} \;\;\;\;\; \frac{1}{8} \;\;\;\;\; \frac{1}{16} \;\;\;\;\; \frac{1}{32} \;\;\;\;\; \frac{1}{64}

[/math]

, and also gives their equivalents in hinu (and sometimes also in ro), a tedium.

What this problem suggests to me by way of failed generalization, is that either Ahmose or his source were trying to exhaustively list all combinations of the above six fractions, falling short by over 50%, not making the leap, to another anon's point about the frustration over failure to generalize. Consider the expression I just wrote, above. Ahmose partially considers situations where each term is either /present/, or /absent/. this of course gives 2^6 = 64 possibilities, in general, but he doesn't seem to register that possibilities are missing. In fact, any and all combinations of the above are strictly less than 1, staying in the neighborhood of investigation. One cannot help but think of Zeno's paradox, and the associated convergent series.

I'm going to drill into the table now and see if I can find a pattern in the information, specifically the information which is missing.