Talk:Apotome (mathematics)

This cannot be right

The definition and the example (an irrational number) seem to contradict each other. Abtract (talk) 08:12, 10 December 2009 (UTC)

I have removed the example and added a referenced definition. Abtract (talk) 19:02, 10 December 2009 (UTC)

modern terms

I'm guessing this means an apotome is a number of the form

$a-b\,$

where for some positive integer n,

$\left({\frac {a}{b}}\right)^{n}$

is rational. Is that right? Whether it is or not, it should be explained in language that people not accustomed to reading translations of Euclid will understand. Michael Hardy (talk) 23:49, 4 December 2013 (UTC)

From the Knorr reference I added, it seems to be more specifically n=2 rather than just any positive integer. Also, Euclid would have defined it in terms of commensurability of two line segments rather than by somehow breaking the symmetry by choosing one of them to have rational length. —David Eppstein (talk) 07:36, 9 January 2014 (UTC)