One of the curious features of the pentagram embedded in the Weissenstein wheel shown in Johann Bessler’s Das Triumphans book, (and at the top of my blog) is that it is slightly tilted. Given that he provides a strong indication that the pentagram is deliberate by including two of Euclid’s pentagram construction steps within the illustration, how come it ended up tilted?
In the illustration below I’ve shown the Weissenstein wheel with Euclid’s 11th proposition, next to it which ran thus::-
“To inscribe an equilateral and equiangular pentagon in a given circle….”
Below I refer to the padlock line (blue) which follows the diameter of the wheel. I also use the rope line (red) which shows the path of the rope which actually passes behind the wheel.
By including the padlock line (blue) which clearly bisects the angle of 36 degrees formed by CAD at the point where the rope line (in red) meets the padlock line, implies that the result was deliberate and therefore for him to produce a tilted pentagram, either he introduced a deliberate error, or he deliberately included it as another clue towards an eventual solution. He emphasised the precision of the pentagram by drawing attention to the base of the triangle where it overlies a succession of hatching lines which are perfectly aligned with it.
Of course he might just have drawn the rope line in the wrong place or at the wrong angle, that could create a tilted pentagram; but given his skills in drawing, measuring etc, that is too unlikely to consider.
Knowing Bessler and his habit of including more than one solution to each clue, I’m sure that he tilted the pentagram for a reason. The rope line should form an angle of 54 degrees with the central pillar upright, 54 being an multiple of 18 degrees like every angle in the pentagram, but it is hard to be sure if it hits that angle. I considered that he might have altered the angle to 55 degrees but such a small difference would be easily missed missed and I concluded that he didn’t.
I tried many times over the years to make the pentagram sit straight with the upper chord exactly horizontal, but failed and it wasn’t until I discovered a second clue which explained how and why the pentagram had a tilt. I’ll explain why it’s tilted in my next blog, next week.
I’m away up north with my granddaughter Amy until the next week. She’s just hit 3.5 million followers, amy pohl on TikTok.