Talk:Conchoid of Dürer

Other equations

Just to note that the German version of this article has the equation

$(y^{2}+xy+ay-b^{2})^{2}=(b^{2}-y^{2})(y-x+a)^{2}$

which I have just checked is indeed compatible with the equation here, which follows Lawrence, with (a,b,x,y) → (b/2,a,x-b/2,-y). Richard Pinch (talk) 16:10, 23 August 2008 (UTC)

A little confused

Let Q and R be points moving on a pair of perpendicular lines which intersect at O in such a way that OQ + OR is constant.

First try:

Let Q and R be points [] which intersect at O [in such a way that OQ + OR is constant].

I don't think points can intersect in this sense.

Second try:

[] a pair of perpendicular lines which intersect at O [in such a way that OQ + OR is constant].

I have a picture in my mind of perpendicular lines intersecting at O, and they all look like rotations of the Cartesian axes. So what does this constraining subclause contribute here?

If "intersecting" binds to neither the points nor the lines in a variable way, I don't get this definition whatsoever.

Is this for some reason not the singular origin O? Is OQ + OR supposed to be vector addition? Or something else? What aspect of this geometrical shorthand am I not grasping? (And if I'm not grasping it, how many other non-geometers with no mathematical training are even deeper into the weeds?) — MaxEnt 21:00, 22 October 2018 (UTC)

It serves to name the intersection point O. But I will rephrase for clarity. --JBL (talk) 00:03, 23 October 2018 (UTC)

Another good question is, "What is the geometric meaning of the constants a and b that appear in the equations?" --JBL (talk) 00:07, 23 October 2018 (UTC)

The length OQ + OR = b and the distance from Q to P (and P', the points on the curve) is a. This is described in the Lawrence reference and I'll give this article another look when I get a chance. These definitions really should be part of the article.--Bill Cherowitzo (talk) 03:37, 23 October 2018 (UTC)