E.g.,In[162]:= triangs[144, 135, 31] Out[162]= {ArcCos[475/486], ArcCos[-(5/27)], ArcCos[7/18]} In[144]:= Rationalize[#, 99^-9] & /@ Ratios[%] Out[144]= {3400276089/412519223, 2/3} I.e., two of the angles of a 31:135:144 triangle are in ratio 2:3 . --rwg ---------- Forwarded message ---------- From: Mike Hirschhorn <m.hirschhorn@unsw.edu.au> Date: Sun, Sep 28, 2014 at 7:10 PM Subject: RE: gluing a 3-3-3 triangle onto a 3-5-7 To: "billgosper@gmail.com" <billgosper@gmail.com> Dear Bill, I wrote something related to this some years ago. Please see gosper.org/paper166.pdf. It appeared in the (British) Mathematical Gazette). Best wishes, Mike H.