As some of you may know ,I am a metal sculptor who often uses Sacred Geometry in my art and constructions.
I have tackled the challenge of making a (large) NAUTILUS SHELL in stainless steel. I started from the premise that it represented the PHI or Fibonacci spiral. I plotted the spiral on a large piece of paper to make a pattern for the cutting of the metal sheet to make up the two sides of the creatures shell. I have a small sliced REAL nautilus shell,and I placed it on the pattern and simply couldn't find where it mated up...This was rather vexing I can tell you. I'd heard pretty much since I began my studies in Sacred Geometry through the popular literature that the nautilus shell was the QUINTESSENTIAL example of the Fibonacci spiral,but when it came time to accomplish this construction the spiral DID NOT MATCH THE PHI SPIRAL.
Here's a link to a short paper published by the British mathematician John Sharp explaining why...
It turns out the Chambered Nautilus shell DOES NOT represent the Fibonacci Spiral but rather a logarithmic spiral based on 3. In the article above there is a comparison of the two spirals showing clearly that they are NOT congruent.
I think the fact that there is so much popular literature stating that the Nautilus represents the Fibonacci spiral or the Golden Spiral is simply a case of so many people accepting what is written without actually questioning it. And if there is a certain number of people who accept it as truth,it no longer bears the scrutiny of inquisitive minds. Had I not built an actual sculpture of this fantastic and wonderful form,I never would have questioned it myself. But when I completed the first Nautilus(based on the Fibonacci Spiral),it was so obviously distorted I knew something was wrong...So this one you see here is my second attempt and actually conforms to the REAL spiral evident in the Chambered Nautilus shell.
As with the first one, I made a paper pattern(this time off a real nautilus shell),overlaid it on two pre-formed bowl shapes in stainless steel.
after cutting the mirror image spirals with my plasma cutter,I formed a tapering strip that connects the two sides and is welded all the way round the form,ground and polished. The stand is made from mild steel and I turned OFF the shielding gas on my wire feed welder in order to encrust and carbeurize the surface.Turning off the shielding gas allows oxygen to combine in the weldment. the steel literally burns and the weldment becomes quite porous. I then used a spray bottle of copper sulfate in solution,spraying it on the work as I heated areas with the torch and sort of burned it in. I was trying to get an effect as if it had been beneath the sea for a very long time and had only recently been retrieved...
I would like to stress at this point that the fact that the Nautilus Pompilius does not conform to the Fibonacci Spiral does not in any way reduce our fascination or admiration with such an exquisite form. To my eye nearly ALL logarithmic spirals are gorgeous,remind one of Nature ,and as such are Sacred.
Sacred Geometry is about a PATTERN in the known Universe of structure and proportion. It is NOT about obsessive adherence to arcane laws that counter critical OBSERVATION and REASON.