Yes! Absolutely! Below is a photo of another nautilus shell. pomatia). Guest. It looks like if it was a golden spiral, it would be a 90 degree one. For the former the sinistral is again specific in contrary to Perhaps The Designer of our universe and our world, more correctly, Logic would dictate, (His Universe His World) Perhaps He designed it with Absolute Mathematical Precision. The snail produces new shell material, like the soft material of its protoconch, that expands its shell and then hardens. Life, however, is very different by its very nature. I foundmine at 67.97. So, if we have followed the described mathematics, it is clear that any plant that employs a 137.5 degree rotation in the dispersion of its leaves or branches is using a Phi value intrinsically in its very form. There is, however, more than one way to create spirals with golden ratio proportions of 1.618 in their dimensions. Partula snail, but Macro, closeup. The longer pair on top contain eyes and are used for seeing. I recently found out that if leaves spiral based on a Golden Spiral, they get optimal sunlight absorption (they don’t get in each other’s shade.) several factors. molluscs. The snail has two pairs of tentacles on its head. Which now compels us if not Obligates us to ask a question of more consequence than our first…….. WHY has He done so? This is a compound curve build from arc sections. Some say yes, but offer no proof at all. Your Spiral Snail Shells stock images are ready. Using Markowsky’s ±2% allowance forto be as small as 1.59, we see that 1.33 is quite far from this expanded value of phi. 1.1 The equiangular spiral As far as the animal that lives in a shell grows it needs the shell to grow in the same proportion, in order to continue to live inside it. In contrary, the four-toothed bulin, Jaminia answer #2. The golden ratio proportions are indicated by the red and blue golden ratio grid lines provided by PhiMatrix software. dividing successive terms) until one gets closer and closer to the Golden number; but if one looks at it differently one can see a definite relationship exists from the get go.. Multiplying the Golden Ratio by itself repeatedly gives the Fibonacci sequence. What a perfect symbolic example in nature for spiritual and emotional development. A point that you have overlooked with regard to the Golden Spiral and, Since you are using the Fibonacci sequence to draw your golden spiral You must remember that “The golden ratio is the limit of the ratios of successive terms of the Fibonacci sequence” (wikipedia: http://en.wikipedia.org/wiki/Golden_ratio#Relationship_to_Fibonacci_sequence). As the snail grows, its shell gets larger. They were using compasses and the resulting volute -although aethetically pleasant – was drawn as a compound curve with distinct circular sections joined together at the ends and with matching start/end tangents. that rule, there is the genus Alopia mainly occurring in Rumania, that is, with geometrical mirror plane to divide the shell in two equal halves, which is why a snail's shell may not be reflected horizontally in When shells grow they keep always the same shape. The shell of Helicodonta obvoluta seems to look the same from above and below, as flat and round like a loaf of cheese, which is why the species is also called cheese snail.However, upper and lower side of the shell are clearly different, the upper side showing the spire … But, like humans, a nautilus spiral itself are never have a perfect “Phi” spiral in nautilus spiral shell. Freiburg). This Golden Spiral based on a 180 degree rotation is a much better fit to the Nautilus Spiral. Your point is valid that a Fibonacci spiral approximate the Golden Spiral as the numbers grow. I have been making an effort in my old age to let G-d out of the box. des Conchylienreichs, An Insight Into Collecting Sinistral Shells. characteristic towering shell, there is the large At the end of the last whorl is the aperture, or opening. coiled to the left or to the right at about even rates. can be found in natural history museums, that often enough evolved from those To the naked eye, without a protractor of course, the Nautilus shell does seem to have the golden ratio rule. species is sinistral (e.g. way into naturalists' collections as "conchylia sinistralia" and so What is Phi? The question is how a simple animal makes a decision as it goes in building each next layer of shell. Maybe, as some believe, we are participating in some project of the universe developing self-awareness through us, along with our mathematics, our philosophies and our technology. (The Basics of the Golden Ratio). SHELL SCULPTURE: One of the main shell features is the sculpture, a character that is important for distinguishing species. To be sure, the Nautilus shell is a spiral, and it is moderately close to spiraling by a constant angle, but that angle is not the Golden Ratio. However, since Phi is irrational, the stem and leaves could keep on growing to infinity and one leaf’s tip would never fall on top of another’s. snail families are definite in this matter, such as the Helicidae, to Thanks for the thoughtful discussion, Tim. The shoreline was the logical result of the process of the ocean acting upon the land over time. In fact, the curve drawn in the first two illustrations (by joining subsequent quarter arcs) cannot be named “spiral”. Just as with the human form, nautilus shells have variations and imperfections in their shapes and the conformity of their dimensions an ideal spiral using either of the two methods shown here. to the genus' name: So, for example, Amphidromus butoti from Java is However, the snail itself remains asymmetric, the genital opening, for example, is on the right side of the body. Those then are colloquially referred to as So there is no connection. snail species, that it may be used for identification purposes. The Multiplier to reach the next chamber was about 1.0852 [best fit] which comes to near 3.14 for the full turn of 14 chambers which looks much closer to pi than phi to me. This is not exactly a golden ratio, but then it’s not hard to see why it would appear to be one. There’s a video explaining more about it here.”, The Golden Ratio—A Contrary Viewpoint by Dr. Clement Falbo (page 127) – “The nautilus is deﬁnitely not in the shape of the golden ratio. Let’s continue to explore that fit of a slightly different variation on a golden spiral. Is it defined by species? species, however, is that some species show the so-called amphidromy, which led Only 30 samples are required for statistical validity. have got a spindle-shaped shell which makes it easy for them to hide from What is the Fibonacci Sequence (aka Fibonacci Series)? You’re measuring the growth rate from the width of each chamber to the next as you go around one 360 degree cycle of the spiral. These shells protect snails from birds and snakes by sealing the snails away from predators. If anyone finds a shell with the growth ratio that equals Phi, this will be pure coincidence only. I’m assuming he has in mind the florets of a sunflower, which are arranged at every 137.5 degrees. That the shell has the same proportion in every point you get. 3 G + 2 = G^4 = 1.618033988749^4, 3 + 5(1 + √ 5)/2 i.e. It is evident in pinecones, pineapples, many different shells, fireweed, and other flowers and seeds. What you found was a sample of the way in which the majority spiral. More liquid is released over time, and the shells get larger. 5 G + 3 = G^5 = 1.618033988749^5, 5 + 8 (1 + √ 5)/2 i.e. Rather than seeking a golden ratio from the spiral’s center point, let’s try measuring the dimensions and expansion rate formed by these three points: As illustrated in the Nautilus shell below, the distance from Point 1 to Point 2 divided by the distance from Point 2 to Point 3 is quite close to a golden ratio for the complete rotation of the Nautilus spiral shown below. The spire can be high or low, broad or slender, according to the way the coils of the shell are arranged, and the apical angle of the shell varies accordingly. This is what a nautilus shell would look like if it were based on a golden spiral. For some obscure reason, all scholars tend to draw the golden spiral using the growth rate P = 2.618033988 = Phi^2 = Phi+1. a picture. By the same token, self-conscious beings though we are, it may be too much to assume that we are capable of conceiving accurately the true nature of that which is behind all creation. The width of the spiral from the center is now 2.618, which is the golden ratio (phi) squared. to such objects. isolated insular populations there are quite many species. Of course, one can create different spirals depending on your reference angle – whether it be full turn, half turn, third turn, quarter turn, fifth turn; or 1 radian or 2 radian, etc So there is a range of possibilities of making a match. Spirals are a common example of this; these manifest as snail shells, sunflower seed arraignments, even DNA strands themselves. A volute IS a spiral. Sorry, I am not up on Fibonacci numbers, but the “idealised” snail shell is a logarithmic spiral: i.e. other Amphidromus species. I truly love this Golden Ratio in nature and in mathematics but am not cognitively chained to its concise conceptual constellation. “There is a peristent misconception about the character (and naming) of this curve. There is a fair amount of confusion, misinformation and controversy though over whether the graceful spiral curve of the nautilus shell is based on this golden proportion. It does, however, very closely follows a spiral that expands by the golden ratio every 180 degrees. Wouldn’t we be a reflection of it, created in its image, just as a painting or invention would be a reflection of the artist or inventor? The Nautilus shell if often associated with the golden ratio. Indonesia) and only some exceptions are dextral (e.g. Feelers Hello, thank you for this detailed explanation! Plants are actually a kind of computer and they solve a particular packing problem very simple - the answer involving the golden section number Phi. 21 G + 13 = G^8 = 1.618033988749^8. They’re not. Amphidromus floresianus from Flores, “The Golden Ratio” book – Author interview with Gary B. Meisner on New Books in Architecture, “The Golden Ratio” book – Author interview with Gary B. Meisner on The Authors Show, Point 1 – The outside point of any spiral of the nautilus shell, Point 2 – The first inside spiral at one full rotation (360 degrees) from Point 1. This averages to 1.587, a 1.9% variance from 1.618. Does this explain its association with the golden ratio? So what do you think? tis, the height of one of the spikes of the pentagram is sin 72 degrees .951056516. This process may or may not have any self awareness of itself. pomatia. I told him that setting up a 1:1.618 relationship along a single (in this case lateral) dimension seemed useless if the goal is to develop harmonious, two-dimensional compositions. I think such a thing exists, but the limits we place on our imaginings, the way we anthropomorphize creation simply cannot due justice to such a “thing”. Using this approach, the actual spiral expansion rates for the above Nautilus shell, taken every 30 degrees of rotation were: 1.572, 1.589, 1.607, 1.621, 1.627, 1.622, 1.616, 1.573, 1.551, 1.545, 1.550 and 1.573. This had led many to say that the Nautilus shell has nothing to do with the golden ratio. Amphidromus are distributed from East India A biological basis (nautilus shell, human body and face, etc) are never fit perfecly with the geometrical basis (pentagon, decagon, etc) because a geometrical basis are a perfection of line, shape and pattern of nature and a mathematical equation. These shapes are called logarithmic spirals, and Nautilus shells are just one example.

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