This post is one of those posts where you really do have to have read the preceding post first. (So look below if you haven’t.) I wanted to show you what my “Vulgar Fractions Slide Rule” looked like. Each part of it consisted of a graph, as each fraction was represented by a line with a length representing the weight. You might recall that I had decided to weight the fractions with a factor equal to the reciprocal of the product of the fraction’s numerator and denominator. The reason for this was that whole number fractions where the whole numbers are small were considered much more significant than when the numbers were large.

It was tricky to get a graph to show you, as the style where each point is represented by a vertical line is not one of the styles readily available on the software I tried. I could get a graph on my screen, though, so what I have here is a photo of my computer screen.

I created this for you by taking the logarithm of the fraction value so that the abscissa  would have a log scale. Unfortunately this has not been properly achieved here, as this graph shows the data being equi-spaced on the abscissa, and we know that they are not. Regard the pictures on this post as indicative only. We do not have numbers on the abscissa, but you can easily see the fractions 1/1 with its weight of 1, and 2/1 with its weight of 0.5, 3/1 with a weight of 1/3 etc. The slide rule consisted of two pictures like this: the bottom one being a mirror image.

My crude graphics do not provide us with a abscissa scale, but you get the picture. Here we see the slide rule set for w/h = 1.226. The second and third red lines represent two possible room proportions that would meet the criterion:
First:      l/w = 1.37,  l/h = 1.68
Second: l/w = 1.78,  l/h = 2.18
I do not want to get too distracted by this, but might come back to it, if I find a really easy way to show you a more accurate graph.