We’ve already seen that while the angled lines do map to a quadratic they do not simplify down to having no ‘c’ term. I wanted to have a look at one of H. Rudd’s lines using methods I was using. The line below is (p=273 x=8 c=7) This would be the first vertical line on his images.
They have a pattern but it is significantly different than the ones I was looking at. Here the first term is going up by one while the second term is going up by four. This means that the gap between the two term is growing. With the angled lines both terms go up by two and stay the same distance apart. So again there are more differences. With my lines distance between the two factors grows by four for each new line. So for the 3 lines that we looked at earlier (21,273,1333) the distance between the two factors is (4,8,12). I have checked this out for a couple of more lines. The next question is is there such a pattern to H.Rudd’s lines.