… All music intervals are the products of three numbers 2, 1.5, and 1.25,….<. Shell-coiling is important because a snail’s sexual organs are usually twisted and it is difficult for snails of opposite handedness to reproduce. species is sinistral (e.g. If you doubt this, take a look at the video I created at https://www.youtube.com/watch?v=AcGw21Wbcgk. Following are comments by three Ph.D.s in mathematicians who say that the Nautilus has no relationship to the golden ratio. For some obscure reason, all scholars tend to draw the golden spiral using the growth rate P = 2.618033988 = Phi^2 = Phi+1. Rates over 3 were observed in other shells. Some say yes, but offer no proof at all. In these shells, the spire does not have a raised point, but instead is sunken. Edit: forgot to mention that an interesting feature of snail shells specifically, in contrast to most other molluscs, is that they are asymmetrical in the left-right axis. We call it the Asynsis forms synergised by Constructal flows; since Form follows Flow. https://quran.com/67/3 [And] who created seven heavens in layers. Amphidromus kruehni If finally a snail's shell is coiled to the right or to the left, is based on Carl Ruscoe (British Shell Collectors https://quran.com/55 … So which of the favors of your Lord would you deny?…. But then humans have also shown their ability to assume a simple solution when in fact more complexity does exist. over South-east Asia as far as Northern Australia. And even then one will have to contend with the standard deviation. This process is repeated to arrive at a center point, as shown below: The golden spiral is then constructed by creating an arc that touches the points at which each of these golden rectangles are divided into a square and a smaller golden rectangle. Trevor Belmont And Sypha, Nyu Np Program Acceptance Rate, Duke Library Covid, Nexgrill 720-0925p Cover, Barbeque Misal Sahakar Nagar, Restaurants That Have Released Recipes, Change Font Size Chrome, "/>
Contunico © ZDF Enterprises GmbH, Mainz See all videos for this article The typical snail has a calcareous shell coiled in a spiral pattern around a central axis called the columella. units). Or R/a = e^(b.θ) For 1 full turn: θ = 2.π radians and, from my measurements, the average R/a = 3.221 for the Nautilus shell spiral. The coiling direction of the shell is basically as specific for a certain http://www.stefanides.gr/Html/Nautilus.html, http://www.stefanides.gr/Html/why_logarithm.html. Carwow, best-looking beautiful cars and the golden ratio. Shells are mainly calcium carbonate but are covered in an organic layer called the periostracum. 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. As the Golden Ratio and PHI show, since we all emerge out of the same creative matrix that has produced oceans and shorelines and nautilus shells and sunflowers, this mathematical property must have some universal significance on many levels because it appears everywhere from the microscopic to the galactic. I am fascinated by the fact, How many natural things have golden ratio concepts integrated with them. Is the Nautilus spiral related to the golden ratio or not? Let the past go, look within yourself for all the answers and evolve into the next phase of life to become the best, inner-aligned version of yourself possible. Wishing you all and your families a happy, 2018 holiday season where ever you are! This spiral is often seen in nature, other than the nautilus shell. It does, however, very closely follows a spiral that expands by the golden ratio every 180 degrees. However, the snail itself remains asymmetric, the genital opening, for example, is on the right side of the body. With each generation, the rotation of leaves about the stem would close in on 1/phi^2/360 degrees. It’s close, albeit not entirely accurate, it’s close to the golden ratio. Or better still, the ocean and the land and the climate are all co-creators of the shoreline. 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. Your article proves the obvious. OR, perhaps it is some combination of the two. This universal aspect makes us think “somebody or some “thing” must have “designed” this. (The Basics of the Golden Ratio). the coiling direction of a snail shell, Von 13 G + 8 = G^7 = 1.618033988749^7. 1 decade ago. For example, the ocean can be thought of as the designer of the shoreline, but the ocean did not make a conscious decision to create a shoreline. Good to see the Nautilus and Phi revisited from several new perspectives that reveal a closer fit than the usual method derived from the golden rectangles, “whirling squares” path. I truly love this Golden Ratio in nature and in mathematics but am not cognitively chained to its concise conceptual constellation. Snails can also show ‘handedness’ — some individuals have shells that spiral in a right-handed direction, others have left-handed shells. Since you are examining the nautilus shell to compare to the Golden Spiral, you should realize that the difference growth rates between the two is proof of the rule rather than the exception. Personally, I think that some specimens can be exact, but, it’s rarer than usual. Handedness — asymmetrical anatomy or behaviour — is a fundamental feature of many animals, but how it occurs remains a mystery. Plants are actually a kind of computer and they solve a particular packing problem very simple - the answer involving the golden section number Phi. In universal terms, we really should be surprised not to see the golden ratio in growth and morphogenesis, because it reveals nature’s most finitely simple, yet infinitely varied heursitic for generating complexity, evolutionary potential and fitness. 3 G + 2 = G^4 = 1.618033988749^4, 3 + 5(1 + √ 5)/2 i.e. The special thing about Amphidromus The Evidence certainly lends creditability to this Theory. species on the Balkan peninsula and in Greece, but are also spread of the rest I’ll add a few thoughts in response: There’s one significant challenge in thinking of the “Designer” as merely a “process.” It’s easy to create a natural process that shifts a shoreline, because a random result from a random process is a viable result. This has the property (again, ideally) of meaning that growth occurs without any change of shape. I built it in halves on a raft, then glued the halves together. In nature there are numerous examples for the rule that right is rarely the Amphidromus are distributed from East India * http://www.stefanides.gr/Html/Nautilus.htm, * http://www.stefanides.gr/Html/why_logarithm.htm, * http://www.stefanides.gr/Html/logarithm.htm. “There is a peristent misconception about the character (and naming) of this curve. Amphidromus: An article in the English edition of Wikipedia. Wherein the next chamber of growth can only be resided in when the former chamber is closed off. This is indicated by the golden ratio ruler below, which has a golden ratio point at the division between the blue and white sections. Guest. Nautilus shell spirals may have phi proportions, but not as you may have heard. Which now compels us if not Obligates us to ask a question of more consequence than our first…….. WHY has He done so? Many believe that the golden spiral is in de nautilus. The Big Deer is a symbolism and gear review blog where we talk about anything and everything related to symbolism, hunting, gears and equipment. I was wondering if a nerites shell spiral is a golden spiral as well. reply #3. In Darwin’s day, they incorrectly assumed that microscope life was little more than a simple gel or plasma. some exceptions, dextral, as are some species of the Greek genus group Albinaria Reply:They don't. So there is no connection. Hello, thank you for this detailed explanation! Snail has a triangle shaped shell with a spiral pattern. At the end of the last whorl is the aperture, or opening. The Nautilus shell if often associated with the golden ratio. Of course sinistral specimens of dextral snail species not only may be found The illustrations shown however use a true Golden Spiral, which is based on successive golden rectangles whose sides are already in the ratio of 1.618… to 1. It looks like if it was a golden spiral, it would be a 90 degree one. they are larger than those (between 25 and 75 mm) and they belong to another ”. Life, however, is very different by its very nature. I have recently analysed a Nautilus spiral that I obtained from the Qingdao Shell Museum. Eye stalks. How to 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. This is slightly less than 2.618, Phi squared, as in the idealized golden spiral above. 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. the other rare sinistral specimen. If we were to multiply the value of 1 over Phi to the second power (0.3819659…) times the total number of degrees in a circle (360), we obtain for a product nothing other than 137.50… degrees. A web designer friend of mine was showing me how he uses the phi ratio to set up the relative widths of two text columns. Normally the whorls are circular or elliptical in section. 21 G + 13 = G^8 = 1.618033988749^8. 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”. such as the plaited door snail (Cochlodina laminata) or the can be found in natural history museums, that often enough evolved from those a loaf of cheese, which is why the species is also called cheese snail. 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. isolated insular populations there are quite many species. Each spiral adds up to 8, or 13 , or 21 segments. now I see how consistent this law of growth is expressed in the nautilus shell. 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. Those small snails living on rocks and trees However, it is believed that the majority of all plants make use of either the 137.5 degree rotation or a rotation very close to it as the core number in their leaf or branch dispersion, sending out each and every leaf or branch after rotating 137.5 degrees around the stem relative to the prior branch. characteristic towering shell, there is the large I hear all the time that the Fibonacci sequence of numbers oscillates about the Golden Ratio (i.e. The reason spirals are so common is because the "code" is easy. If you think that this “thing” (i.e., God) has to be far beyond our meager faculties, then how is it consistent to assume that it “may not have any self awareness of itself?” If it’s greater than us, then wouldn’t it be greater than us in every way, have all of our capabilities and then much more? (Bear with me for a while) In an overwhelming number of plants, a given branch or leaf will grow out of the stem approximately 137.5 degrees around the stem relative to the prior branch. Perhaps also by His Design He allowed His Creation to be subjected to corruption in which case the Perfection would be marred though still evident. 1 G + 1 = G^2 = 1.618033988749^2, 1 + 2 (1 + √ 5)/2 i.e. which belong the largest land snail in Central and Western Europe, Helix Gastropod shells. Just as tree growth rings can be read to identify particular years, why not nautilus shell growth and other inert carbon forms? There are venomous snails, which kill their prey using a harpoon tooth, and others which besiege a mussel, until it opens its shell. So return [your] vision [to the sky]; do you see any breaks? If you equate the 360 degrees to Pi and calculate the constant growth rate for 14 chambers, mathematically this is Pi ^ (1/14), which is 1.085202299. “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. molluscs. But things like the Golden Ratio and PHI do seem to support interconnections between all things on multiple levels. So, we see that not every nautilus spiral is created equal, nor is it created with complete perfection. Correct. : pomatia. the family rule. Golden Ratio, Phi, 1.618, and Fibonacci in Math, Nature, Art, Design, Beauty and the Face. They occur in an especially rich number of Think about it this way: if you construct a circle and then go 1/phi^2/360=~137.50… degrees around the circle, and repeat the process into infinity, no rotations will land on the same point. This article does NOT use the Fibonacci sequence to draw the golden spiral. Sorry, I am not up on Fibonacci numbers, but the “idealised” snail shell is a logarithmic spiral: i.e. 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. I have measured several Nautilus shells, using avilable photographs. https://en.wikipedia.org/wiki/Neritidae. This very special spiral (called the logarithmic spiral) is exactly that of the nautilus shell and of certain snails (the planorbe or flat snail). To this day, no one has explained this discrepancy. You are asking about the geometry of the Ammonite shells. Those then are colloquially referred to as This ratio, being fundamental as it is, will naturally generate expressions of itself everywhere in creation. Developing from the very middle and only slowly growing and emerging from one closed chamber of existence and development to the next. This is thought to aid in reducing competition between high and low-spired species in a habitat. In fact, the curve drawn in the first two illustrations (by joining subsequent quarter arcs) cannot be named “spiral”. A snail’s slimy organs and parts follow suit, developing with a twist that echoes the asymmetrical shell — a fact that inspired a team of researchers to identify that trait’s source. 2 years ago. 0 0. 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 longer pair on top contain eyes and are used for seeing. Notify me of follow-up comments by email. shell's conspicuous navel, also called an umbilicus. He disagrees with me. All the while aspiring to grow into the Golden Ratio Perfection as a goal! 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. The snail’s shell is a safe hiding place. The Man of Numbers – In search of Leonardo Fibonacci by Dr. Keith Devlin (page 64) – “Unfortunately, the belief that the Nautilus shell has the form of the Golden Spiral is another of those false beliefs about Euclid’s number. snail (Macrogastra ventricosa), both of them sinistral. Because of the high amount of So what do you think? dryness in cracks and behind bark. shells snails. The linear growth ratio of the Nautilus shells measured varies from P = 2.76246446 to P = 3.01421291 per turn. It appears the best description of the golden ration is not ‘static’, but a ‘growth’ ratio. Your physical measurements are confirming that result, and of course when you take your result raised to the 14th power you get right back to Pi. 8 + 13 (1 + √ 5) /2 i.e. coiled to the left or to the right at about even rates. There are also door snails in Central and Western Europe, They are both euclidean volutes, constructible with compasses and straightedge. Rotation of the planet? 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. But, like humans, a nautilus spiral itself are never have a perfect “Phi” spiral in nautilus spiral shell. However, rather than consider the “Designer” as a being, think of it as more of a process. I wonder if these golden spirals may relate to my speculations on Phi in the Solar system my web site is at http://john-shanahan-berlin.jimdo.com/blog/. Is there a pattern to the arrangement of leaves on a stem or seeds on a flwoerhead? Whenever we encounter such precision and beauty in nature, it is not unusual to suspect a “Designer” at work. This Golden Spiral based on a 180 degree rotation is a much better fit to the Nautilus Spiral. Image of design, collection, coral - 156293291 Ropes are dead, they do not grow. That the shell has the same proportion in every point you get. Quite far from Phi. Snails with high spires tend to prefer vertical surfaces while those with low spires prefer horizontal surfaces. The ancient Aztecs saw the snail as a sacred being because its shell represented the cycle of life. If, however, the common ancestor of all plants with vascular systems such that they could spiral had DNA that encoded that many degrees of separation, and managed to pass it down to most plants, that could explain the prevalence. special addition to a shell collection, sometimes even a basis for specialisation. Several university math professors say no, but they only compared the nautilus spiral to the spiral created from a golden rectangle. It goes to show skepticism can lead you to make false assumptions. The traditional golden spiral (aka Fibonacci spiral) expands the width of each section by the golden ratio with every quarter (90 degree) turn. Thanks for the thoughtful discussion, Tim. to such objects. The spiral structure is formed due to stars inside the protogalaxy developing at different intervals. The shell of Helicodonta “The Kingdom of God is found within”. Yes! They’re not. These shells protect snails from birds and snakes by sealing the snails away from predators. answer #2. The rectangle is then divided to create a square and a smaller golden rectangle. The spiral shells of snails are often used as a textbook example of biological structures that possess chirality. The Nautilus shell if often associated with the golden ratio. Snails can go over water - well, at least they can crawl hanging from its surface. Let’s continue to explore that fit of a slightly different variation on a golden spiral. Below, however, is another golden spiral that expands with golden ratio proportions with every full 180 degree rotation. The ratio being discussed in this article is not based on a cycle of the chambers, but rather is looking at the dimension from any given spiral to the center of the spirals as compared to the dimension of the spiral that is on the opposite side of the center to the center point. Rotate a small angle, then build up a little bit more. See also https://www.goldennumber.net/solar-system/ and http://www.solargeometry.com/. The whorls som… How is that done? each later whorl expands as the same proportion of the previous one. The shell begins with the larval shell, the (usually) minute embryonic whorls known as the protoconch, which is often quite distinct from the rest of the shell and has no growth lines. This can be constructed by starting with a golden rectangle with a height to width ratio of 1.618. The shoreline was the logical result of the process of the ocean acting upon the land over time. of whorls, though without a clearly visible apex. The point of the article is that a Nautilus spiral does NOT conform to the classic Golden Spiral that expands by the golden ratio every 90 degrees. collections. The center/vortex of the above spiral increases to a width of 1 at point A. 8 G + 5 = G^6 = 1.618033988749^6, 8 + 13 (1 + √ 5) i.e. Long setae on the shell which… They are strong without it. The heights of the two columns varied according to the writer’s “word count” for each given column, and these height dimensions were completely independent of the column widths. Let’s explore a little further. same as left. 1 G + 0 = G^1 = 1.618033988749^1, 1 + 1 (1 + √ 5)/2 i.e. 2 G + 1 = G^3 = 1.618033988749^3, 2 + 3 (1 + √ 5)/2 i.e. If the leaves fell every 90 degrees about the stem, only the top four would get full sun. The pineapple spirals round in three different ways. Consider also seasonal and environmental changes and influences – such as summer and winter, or rainy and dry periods which might vary significantly in nourishment, etc.. Years from now, we might all have a good laugh as we look back on our simple friend, the nautilus, as a key partner in the advancement and evolution of liquid math…. The same difference applies to ELLIPSES and OVALS: ellipse is a parametrically defined curve with smoothly changing curvature. The other thing I would like to point out is whenever one is comparing theory to practice; one needs a hell of a big sample size. bulin snails For example in As the snail grows, its shell gets larger. a picture. 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. Partula snail, but Club). 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.) It is a hallmark trait of humans to see complexity instead of the simpler solution. Compared to a Nautilus's symmetrical shell, This had led many to say that the Nautilus shell has nothing to do with the golden ratio. Is it defined by species? A posting by Peter Ryall in the Petsnails forum (http://petsnails.proboards.com). Anyone want to volunteer? So rather than some kind of genie, or Lord, or Father figure, or Grandmother, I think there is some eternal emergent process at work throughout the universe, (or multiverses). Part of this is that Phi is irrational. As you can see, the fit is fairly good for the first three full rotations from the center point. An eye for this stability and the use of it may have evolved over time, like how hexagonal nest building probably evolved over time in honeybees. Spirals are a common example of this; these manifest as snail shells, sunflower seed arraignments, even DNA strands themselves. The 1:1.618 for every 90 degree turn seems like it’s the only useful format for 2D design applications. Some are spiral shaped, and others are cone shaped. There is a fair amount of confusion, misinformation and controversy though over whether the graceful spiral curve of the nautilus shell … You do not see in the creation of the Most Merciful any inconsistency. Photo about Spiral snail shells. While the golden ratio is often illustrated with the familiar 2 dimensional golden spiral, it can be applied just as successfully in design aesthetics in a single dimension or line. For such a “thing” to exist that has the capabilities we attribute to it, such a “thing” has to be far beyond our meager faculties. February 8, 2014 by Gary Meisner 63 Comments. snail's shell special, is the fact, that it is asymmetrically coiled to one Nature give close approximations to our “perfect” straight line measurements. Continue another half turn of 180 degrees to point C to complete the full rotation of 360 degrees. Honeybees are not building hexagons they are stacking circles and filling in the gaps. See the Spirals page for more information on spirals in nature. The Chambered Nautilus form is not a Golden Spiral. Wikipedia: When the blue section has a length of 1, the white section has a length of 1.618, for a total length of 2.618. It is evident in pinecones, pineapples, many different shells, fireweed, and other flowers and seeds. As such, the shell is nothing special for a mollusc. Note: A special thanks go to Oliver Brady for his astute analysis of this article, which led to improvements in its clarity and accuracy. Anyone with access to such a shell can see immediately that the ratio is somewhere round 4 to 3. The illustrations shown however use a true Golden Spiral, which is based on successive golden rectangles whose sides are already in the ratio of 1.618… to 1.” There is a peristent misconception about the character (and naming) of this curve. 44.41. The 180-turn golden spiral mentioned is this one, if anyone is interested click HERE. Amphidromus floresianus from Flores, The snail has two pairs of tentacles on its head. The width of the spiral from the center is now 2.618, which is the golden ratio (phi) squared. For instance, how might we account for depth, water pressure, current, temperature, etc.. The appropriate name would be VOLUTE (yes, we could name this special case “golden volute”). Feelers And I suppose that every organism with a spiral shell has a distinct growth rate, with variations between individuals of the same species. 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. from the Indonesian island of Sumba): Another species was even named 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 way of drawing volute of this type is similar to the method used by ancient Greek architects to draw volutes before ioic column head was carved from stone block. Log spirals are growing spirals, so that is why they are used by nature. des Conchylienreichs, An Insight Into Collecting Sinistral Shells. Note how it expands much more gradually. I have a "left handed" whelk (conch) shell I found on the beach in VA. One finds it also in the horns of certain goats (markhor, girgentana), in the shape of certain spider's webs, handed) and dextral (right handed) specimens occur at even rates. Zur Systematik This is a compound curve build from arc sections. Whatever is ultimately behind creation does not have to be a conscious entity to produce things of beauty that also exhibit signs of intelligent handiwork. “I Like It”. So while many inaccurate claims have been made regarding both its existence and non-existence, we see that the Nautilus spiral can exhibit dimensions whose proportions come close to phi. All that to say that there’s absolutely no way a plant could make this calculation on its own. Your Spiral Snail Shells stock images are ready. 5 G + 3 = G^5 = 1.618033988749^5, 5 + 8 (1 + √ 5)/2 i.e. Darwin had no understanding of the very sophisticated technology within our DNA that encodes the instructions for life. SHELL SCULPTURE: One of the main shell features is the sculpture, a character that is important for distinguishing species. There is, however, more than one way to create spirals with golden ratio proportions of 1.618 in their dimensions. obvoluta seems to look the same from above and below, as flat and round like Even the simplest of bacteria have hundreds of thousands of base pairs in their DNA that are required to define all their life functions. I have been making an effort in my old age to let G-d out of the box. Nature is not only a beautiful rendering of the Divinity in all things but in its inspiring physicality, this nautilus shell clearly supports us in our own evolutionary spiritual paths of the never ending cycle of life. Then this creature can expertly mange its mobility by navigating through the ocean depths by maintaining its balance and buoyancy which these empty chambers offer from within. Zebrina To the naked eye, without a protractor of course, the Nautilus shell does seem to have the golden ratio rule. It grows in a spiral pattern and is always big enough for the snail to hide its whole body inside. Thanks for this insightful, inspiring contribution,Johan. 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 shoreline emerges as the result of the processes set in motion by the ocean, land and climate. Plants use a constant amount of rotation in this way, although not all plants use 137.5 degrees. 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. In contrary, the four-toothed bulin, Jaminia The shell on the garden snail is used when the snail is not eating or when it feels it is in danger, although it still protects the snail even when the snail isn’t inside of it. I just found that there is a close relationship between the nautilus shell and Fibonacci sequence which is more or less related to the golden ratio, and decoding the relationship of these two, correlates the relationship of nautilus spirals and golden ratio. 0 + 1 ( 1 + √5 ) /2 i.e. 13 G + 8 = G^7 = 1.618033988749^7, 13 + 21(1 + √ 5) /2 i.e. Very interesting link [http://www.john-shanahan-berlin.de/], >… All music intervals are the products of three numbers 2, 1.5, and 1.25,….<. Shell-coiling is important because a snail’s sexual organs are usually twisted and it is difficult for snails of opposite handedness to reproduce. species is sinistral (e.g. If you doubt this, take a look at the video I created at https://www.youtube.com/watch?v=AcGw21Wbcgk. Following are comments by three Ph.D.s in mathematicians who say that the Nautilus has no relationship to the golden ratio. For some obscure reason, all scholars tend to draw the golden spiral using the growth rate P = 2.618033988 = Phi^2 = Phi+1. Rates over 3 were observed in other shells. Some say yes, but offer no proof at all. In these shells, the spire does not have a raised point, but instead is sunken. Edit: forgot to mention that an interesting feature of snail shells specifically, in contrast to most other molluscs, is that they are asymmetrical in the left-right axis. We call it the Asynsis forms synergised by Constructal flows; since Form follows Flow. https://quran.com/67/3 [And] who created seven heavens in layers. Amphidromus kruehni If finally a snail's shell is coiled to the right or to the left, is based on Carl Ruscoe (British Shell Collectors https://quran.com/55 … So which of the favors of your Lord would you deny?…. But then humans have also shown their ability to assume a simple solution when in fact more complexity does exist. over South-east Asia as far as Northern Australia. And even then one will have to contend with the standard deviation. This process is repeated to arrive at a center point, as shown below: The golden spiral is then constructed by creating an arc that touches the points at which each of these golden rectangles are divided into a square and a smaller golden rectangle.