Last week I gave you this rather beautiful mystery object from my old place of work, the Horniman Museum:

It’s the only example I’ve seen of this species that’s been prepared to show it from this perspective – and it’s pretty special. There were plenty of answers, with most people on the button with the what it’s from.

Goatlips was the first to jump in with the broader identification, but palfreyman1414 was first to get the the species. The highly reflective, pearly surface (comprised of mother-of-pearl or nacre) provides a bit of a clue. This is a transverse section of a Pearly or Chambered Nautilius Nautilus pompilius Linnaeus, 1758.

Normally when people take sections through a Nautilus they take a sagittal section, to show the near perfect logarithmic spiral formed by the shell as it grows, so the transverse section offers a perspective that’s much less familiar:

Since the transverse section is so unusal it’s quite difficult to find good references for identification. However, with a good imagination you can work out what’s going on with the relative sizes of the chambers and how much they overlap, to get a sense of the shape in the coronal plane (that’s the line through the body that gives us a transverse section).

That said, it’s easy to recognise that this shell is from the genus Nautilus rather than Allonautilus thanks to this image from Jereb and Roper, 2005:

There is also a paper by Ward and Sanders, 1997 with the same sections shown, plus an additional illustration of N. macromphalus which lacks the thick side walls seen in N. pompilius. From what I’ve seen I’m reasonably happy that the specimen is a Pearly Nautilus, but the taxonomy of this ancient group of cephalopods is still quite poorly known, so I’ll hang on to a shred of doubt for a while.

Goatlips– Golden ratio and Fibonacci are, indeed, “the same thing,” in the sense that as you go further and further along in the Fibonacci series, the rate between one number and the next approaches the Golden Ratio as a limit. (The approach is fast enough that you can see it easily by calculating the ratios between the first half dozen or so Fibonacci numbers.) “Phi” is the conventional name for the Golden ratio, which is an irrational number (=non-repeating decimal), 1.618 to the first four digits.

Indeed. But his point is that, unless you squeeze it in (as per his second link), it doesn’t really relate to the growth rate of the Nautilus shell.

You could probably (and in some ways with greater justification), relate it to the basic logarithmic spiral, based on e (or Euler’s number) which is not just irrational, but transcendental, approximating to 2.718.

While you can “solve” for phi, as the solution of a quadratic equation (in spreadsheet terms =((power(5,0.5)+1)/2) ) for e you need to use a limit: = lim n>infinity (1+(1/n))^n .

A less celebrated number than pi or phi, but deserving of equal respect.

Gees – Even with the answer I can’t visualize how this shell is the one in the photo! Even with the beautifully carved drawing that Goatlips provided in a link. I just don’t get it. Does someone have another view of this?

LOL – ROBBED!

I found the FMO I.D. answer here: https://www.nhm.ac.uk/galleries/galleries-home/treasures/specimens/nautilus-shell

BTW, that article says the spirals are the Fibonacci 1.618 phi golden ratio (not sure they’re all the same thing, but I’m not going down that rabbit hole), but Dr. Clement Falbo’s research said they’re actually 1.33 on average:

https://www.goldennumber.net/nautilus-spiral-golden-ratio/

So, is that black piece man-made and holding it together?

Sorry, I see this was answered last week and that the black bit is natural.

Sneaky!

Good one, I really had no idea!

Goatlips– Golden ratio and Fibonacci are, indeed, “the same thing,” in the sense that as you go further and further along in the Fibonacci series, the rate between one number and the next approaches the Golden Ratio as a limit. (The approach is fast enough that you can see it easily by calculating the ratios between the first half dozen or so Fibonacci numbers.) “Phi” is the conventional name for the Golden ratio, which is an irrational number (=non-repeating decimal), 1.618 to the first four digits.

Indeed. But his point is that, unless you squeeze it in (as per his second link), it doesn’t really relate to the growth rate of the Nautilus shell.

You could probably (and in some ways with greater justification), relate it to the basic logarithmic spiral, based on e (or Euler’s number) which is not just irrational, but transcendental, approximating to 2.718.

While you can “solve” for phi, as the solution of a quadratic equation (in spreadsheet terms =((power(5,0.5)+1)/2) ) for e you need to use a limit: = lim n>infinity (1+(1/n))^n .

A less celebrated number than pi or phi, but deserving of equal respect.

Gees – Even with the answer I can’t visualize how this shell is the one in the photo! Even with the beautifully carved drawing that Goatlips provided in a link. I just don’t get it. Does someone have another view of this?