V. good. Thank you. I last thought about this problem in 1st year college, many decades ago. At that time a fellow freshman Norman (who went on to get a Ph.D. at MIT) argued, for x%y, that there must be a 1 and then did the construction for x%y using 1. I recall he said "there must be a 1" in the sense of "it has to exist" rather than in the sense that "you have to use a 1 in the construction" or "you can not construct x%y without using 1". I don't remember what we did with x*y; there was some doubt in my mind earlier today that we _were_ able to construct x*y without using 1 all those years ago.
On Thu, Jul 14, 2016 at 10:46 AM, Raul Miller <[email protected]> wrote: > Proof that x*y requires reference length: > > if x is reference length then x*y is y > > if y is reference length then x*y is x > > If we do not know the reference length and if x and y are different > then we do not know if x*y is x or y but we know that it could be > either of those. > > -- > Raul > > > On Thu, Jul 14, 2016 at 1:19 PM, Roger Hui <[email protected]> > wrote: > > Given line segments x and y, construct (using compass and straight edge) > > line segments having the following values: > > > > x+y > > x-y > > x*y > > x%y > > > > The first two are immediate. I have proven that x%y is impossible if you > > are not given a reference length 1 (or some other reference length from > > which to construct 1). > > > > The problem is, prove or disprove that you construct x*y without using 1. > > (Constructing x*y and x%y _with_ 1 are pretty easy.) > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
