“How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?”
Albert Einstein

I have always been pretty sure that mathematics and science are the best languages to explain the natural phenomena. While for many mathematics is too abstract, for me, it is the beautiful language of the universe.

There is no upper limit to the numerical abilities of humans. First, we discovered fire, to get warm. Then, we needed light, so we invented electricity. When we needed to talk to someone 10,000 miles away, we invented the internet. Behind all these inventions, was mathematics.

Of course, the universe cannot speak or think. However, we, the people, can read the universe. There are many scientifically and mathematically inclined people who can read the universe and find answers and then describe them. We, the normal people, can also use our imagination as an apparatus to read the universe and nature. If we can read, hence, something is written. In order to write, a language is always needed. So, the universe should have a language. The letters are circles, triangles, hexagons, etc.

Everything in life has mathematical patterns. Think of the wild animals with stripes or patterns for the purposes of camouflage. But why does a leopard or cheetah or tiger have a particular design?

The Enigma codebreaker, Alan Turing, had a mathematical theory about leopard’s spots. Turing suggested in his paper “The Chemical Basis of Morphogenesis” (published in 1952) “a mathematical schema for the formation of the patterns found in animals and plants.” This was 60 years ago [1].

Stars have patterns. Astrologists have been looking at the outer space searching for patterns to better understand life. Whatever it may be that they find, it is always about mathematics.

Seasons have patterns. They come and go. And they influence nature: the climate changes, animals migrate north or south, rain comes, snow melts, the earth changes color, etc.… Of course, seasons cannot make these miracles. They can only have mathematical patterns.

Einstein had pondered for years on how mathematics works so perfectly. He knew that mathematics is the bridge or the language that connects humans with the universe. And being a connection between us and the universe makes mathematics the greatest achievement of mankind.

If you take a closer look at the patterns of our world, you will witness the language of mathematics. Let me give you some specific examples.

Fibonacci, the golden ratio, spiral, cabbage…

Our universe is filled with spiral designs. Spirals can be found in the shapes of the DNA double helix, flowers, elephant tusks, sunflowers, hurricanes, draining water, animal horns, a nautilus shell, a snail shell, a pinecone, a cabbage, a fingerprint, algae, galaxies… the list goes on and on. Tons of lifeless and living things have spiral designs. And they are not random spirals. They have something in common: the golden ratio! And surprisingly, “there is a strong case that this so-called ‘Golden Ratio’ (1.61803…) can be related not only to aspects of mathematics but also to physics, chemistry, biology and the topology of space-time” [2].

All these spirals in nature tell us there are numbers all around us. Let’s observe the numbers of petals on some flowers. When you count the number of petals of the flowers in your garden, you will get the numbers 3, 5, 8, 13, 21, 34, or 55. These numbers are not random numbers. These are very unique numbers; they are part of a sequence developed by Fibonacci, a 13th century mathematician, by adding up the last two numbers starting from 1:

1+1= 2, 1+2= 3, 2+3= 5, 3+5=8 …

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …

F_n= F_n-1+F_n-2, F₁=1, F₂=1

But, why are those Fibonacci numbers so important? The key is, the relationship between the progression of growth and the proportion. There is a harmonic proportion hidden in the Fibonacci sequence.

A fact: If you divide one number in the sequence by the previous number, the answers result in or come closer to phi:

For example: 5/3 = 1.6666;

13/8 = 1.6250; 377/233 = 1.61802575; 317811/196418 = 1.618033399

Definition: In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities [3].

These numbers can be demonstrated with the spiral of the florets in a sunflower. The florets in a sunflower head also form two spirals. If you count the clockwise and counterclockwise spirals that reach the outer edge, you’ll usually find a pair of numbers from the sequence: 34 and 55. If it is a very large sunflower, you will get 89 and 144 [4].

These spirals are not only in sunflowers. You can see them if you look at a pine cone or a daisy. If you mark the spirals and count them, you will always get a number from the Fibonacci sequence. And if you count in the other direction, this time you will find an adjacent Fibonacci number.

The nautilus shell, the golden mean

What makes the nautilus shell so special for mathematicians? Having the Golden Mean. But how do we know that the nautilus shell has the Golden Mean?

First of all, we will start with drawing a small, one unit square. Then we will draw another square which is larger than the previous one. We need to add in a counterclockwise direction. The length of each square has a value from the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 … Then we can draw spirals, starting with the smallest one, outward through the largest one. Then the Golden Mean will appear.

Flowers, plants, or objects have no idea about mathematics, yet they manifest the best of mathematical patterns. This marvelous mathematical art has been placed in their nature for us not to be fascinated only but also to explore the mysteries behind it.

Note

1. https://www.bbcearth.com/blog/?article=the-maths-behind-a-leopards-spots
2. https://www.sajs.co.za/article/view/4033
3. http://mathworld.wolfram.com/GoldenRatio.html
4. http://www.sciencemag.org/news/2016/05/sunflowers-show-complex-fibonacci-sequences

A new Artificial Intelligence (AI) approach to translate brain waves into speech

Akbari et al. Towards reconstructing intelligible speech from the human auditory cortex. Scientific Reports January, 2019.

In a recent study, researchers demonstrated that brain signals from the human auditory cortex can be reconstructed into intelligible speech with a high rate of success. In the study, the brain signals from the auditory cortexes of five participants (suffering from epilepsy) were recorded while they were listening to stories and numbers being read. Researchers specifically chose epilepsy patients as they were already undergoing a clinical procedure involving the placement of electrodes into the temporal lobe of their brains. This procedure is called invasive electrocorticography. The researchers then spoke 10 numbers into the ears of the test subjects: zero to nine. Each number produced a unique response in the brain. The sound produced by the vocoder in response to those brain signals was analyzed and cleaned up by neural networks, a type of artificial intelligence that mimics the structure of neurons in the biological brain. Remarkably, the robotic translations were successfully understood by 75% of people enlisted to test the technology. These results suggest a hopeful future for the Brain-Computer Interface. In particular, this new technology has great potential at giving a voice to people who are paralyzed or severely injured. Despite the potential, the path for a practical device is still long. To go beyond simple numbers and access the thoughts that go with speaking, the researchers will have to probe a different part of the brain known as the Broca area. It is found in the frontal lobe and linked to speech production and language processing.

Milky Way is warped and twisted, not flat

Chen, et al. An intuitive 3D map of the Galactic warp’s precession traced by classical Cepheids. Nature Astronomy February, 2019.

Astronomers have been studying the Earth’s home galaxy, the Milky Way, for centuries in efforts to get a better understanding of its size, structure, and place in the universe. While modern instruments have provided invaluable details about our galaxy and others, a truly accurate model of our galaxy has been missing. Researchers have recently built, for the first time, an accurate 3D map of the Milky Way. We often think of spiral galaxies as a flat thin disk of stars that orbit around a central region, where billions of stars provide the massive gravitational force to hold everything together. However, a new study showed that the Milky Way’s gas disk is no longer confined to a thin plane, but is instead organized in an S-like, warped appearance. The researchers determined the Milky Way’s exact shape at high accuracy by measuring the distances to so-called Cepheid variable stars. Cepheids are young stars that can be up to 20 times as massive and 100,000 times as bright as our Sun. These high stellar masses live fast and die young, sometimes after only a few million years. They also show day-to month-long pulsations, which are observed as changes in their brightness. Combined with a Cepheid’s observed brightness, its pulsation period can be used to obtain highly reliable distances.  By using the data of 1,339 Cepheid stars as benchmarks, researchers were able to map out accurate distances between objects in the Milky Way. Interestingly, in the Milky Way’s outer regions, they found that the S-like stellar disk is warped in a progressively twisted spiral pattern. Researchers suggested that the Milky Way’s warped spiral pattern is most likely caused as a result of rotational forcing or “torques” by the massive inner disk. The further stars are from the center of the galaxy, the weaker their gravitational pull is. This new morphology is expected to provide a crucial updated map of our galaxy’s stellar motions and the origins of the Milky Way’s galaxy.

Smart fabric self-cools or self-insulates depending on conditions

Zhang et al. Dynamic gating of infrared radiation in a textile. Science, February 2019

Decades of innovation in fabrics have yielded high-tech materials that react to hot and cold conditions, allowing them to keep marathon runners cool or alpine hikers warm. However, there was never a material that could change the insulating properties of fabric in response to the environment. A recently developed fabric is the first to automatically warm wearers up or cool them down as needed. Infrared radiation is the primary way the body releases heat and is the focus of this new technology. When the condition is warm or moist, like when a body sweats, the fabric allows the infrared radiations to pass through. Conversely, in cool and dry conditions, the fabric traps the surrounding heat that escapes. The fibers are made of two different synthetic materials coated in carbon nanotubes – one absorbs water, and the other repels it. When the material gets hot and wet during sweating, the strands twist and warp. This distortion brings the strands of yarn closer together, which opens the pores in the fabric to allow heat to escape. When a wearer is too cool, this mechanism is blocked, trapping heat close to the skin. The reaction takes place almost instantly. The garment cools people down before they realize that they are getting hot. Athletes perhaps will be the first people to wear clothes made from the material, but it could be useful for infants, people with disabilities, and the elderly. Researchers say it could be in production within months as the base material is easily available and the carbon coating can be effortlessly added during the standard dying process.

By the time you finish reading this sentence, you will have been carried over the earth, passed the sun, and moved through actual space of 1000 kms! In the time it takes you to ponder upon this, you will have moved another 1000 km through real space. Fast isn’t it? This is the speed at which one arm of our galaxy moves through space every second, and we don’t even feel a thing!

The motion of stars in their dedicated orbits, black holes, nebulas, and infinite number of other phenomena in the outer space display spectacular and equally thoughtful exhibitions thanks to Hubble and other new technologies. An increasing number of studies are thus devoted to stars, supernovas and interstellar space in recent years. Our contemplation of the universe deepens as we accrue more knowledge about it. Just as a cell is the functional building unit of the body, the main building blocks of the universe are galaxies. Just like every other living thing, galaxies will not be around for eternity; they form, develop, and cease within the cosmic laws that are put in place by their Creator.

According latest findings, it is estimated that around 100 billion galaxies exist in the observable universe and that there are galaxies 100,000 light years in size. A year has 31,536,000 seconds. Light travels 300,000 kilometers per second, therefore one light year equals to 946,080,000,000,000,000 (quadrillion) kilometers. Apart from the dispersal of stars, intergalactic distances of galaxies are not much bigger than their own galactic size. For example, the big Andromeda galaxy (the galaxy which is the closest to us) appear from the earth as wide as the sun or moon in the sky and can even be noticed with the naked eye. Latest research in astrophysics revealed that stars are not dispersed equally but rather found together in galaxies as an open system that exchanges energy and matter with its surroundings. A big portion of the galactic space is filled with gas and dust clouds which enable such exchanges to take place. This interstellar stage in which stars are born and die bears vital importance in sustaining and maintaining a galactic presence.

Some amazing characteristics of galaxies

Stars with different masses exist in a galaxy. Smallest one can be one tenth of the Sun’s mass whereas the biggest can be 100 times bigger than the sun. The most important feature of a star in a galaxy is its mass. Brightness of stars increase with their mass and this relation is three dimensional (cubic mass). Therefore if a star is twice as big, it is eight times brighter. Another feature is the relation between the age and mass of a star. The bigger the star, the shorter its life. These big stars live shorter compared to smaller ones despite their giant fuel reserves because they consume it very fast. Similar relations can be observed in the human body, which is an index of the universe, such that overweight people who consume more calories than people with less calorie intake eventually consumes more energy and become subject to deterioration in health and faster aging. The lifespan of a star is inversely proportional with its square mass (1/m2). For example, if a star is twice as massive, it lives only for one fourth of the time. Calculations show that our sun has a lifespan of 10 billion years. Compared to this, if a star is 30 times bigger than sun, it will only live for 10 million years.

The timescale of events that are occurring in galaxies can vary from thousands of years up to millions of years. Time required for the creation of a star is perhaps like a day in a galactic scale. This long time frame is considered short when compared with the age of galaxies. Furthermore, verses in the Qur’an (Al-Ma’arij 70:4) open new horizons in this matter and point out to the fact that time can change depending on different ratios and scales; so a day can indeed vary in length from being 1000 years or 50,000 years.

The movement and behavior of galaxies are quite complicated. Such that even if the galaxy formation process is completed, the creation and expiration process of stars within the galaxy still continues. It takes tens of thousands of years for a gas cloud to collapse inwards under its own gravitational force and become a star under normal conditions. Even five-ten billion years after the creation of a galaxy, it amazes scientists that there is still plenty of gas to remain in the interstellar stage, enough for a star to be born. On the other hand there are galaxies in which star formation is much faster than our Milky Way galaxy. These galaxies are called “starburst” galaxies and new stars are created in variable speeds over a long period of time. The uniqueness that is observed in the specific characterization of animal and plant species can also be witnessed in the creation of stars at different speeds, making spiral galaxies even more mysterious. This is because while a steady and balanced speed in the creation of stars is maintained in spiral galaxies, all the gas and dust available is consumed for the formation of stars in other galaxies. In a galaxy where stars continue to be created, the regions where large stars are created can be observed better compared to other regions in the night sky.

Spiral galaxies

Galaxies are generally divided into three groups: irregular shaped, elliptical, and spiral. Irregular shaped galaxies are composed of many young stars, gas and dust clouds without a definite shape. Elliptical galaxies are made up of old stars and limited number of gas and dust clouds. They are created in different shapes such as round, flat or like a baseball. Spiral galaxies are in the shape of a disc composed of spiral arms extending out of the center as they rotate. Solar system is located inside such a spiral-like galaxy. In these types of galaxies, stars contain spiral signatures. Bright spiral arms found in many images taken of galaxies generally show star forming regions and not the locations of the stars themselves. That is why the exceptional quality of spiral galaxies is hidden in the continual formation and expiration process of stars. Spiral displays which show star creation regions do not revolve along other stars in the galaxy. However spiral galaxies do exhibit a special rotation. Observations point out that spiral signature within the galaxy deteriorates gradually and reshapes in a slower fashion than the galaxy rotation speed. With these new findings, it is possible to say that it is more appropriate to understand galaxies as dynamic systems which change in time instead of being static under the constant and instantaneous intervention and control of the infinite power and wisdom of the Almighty.

One of the most impressive features of spiral galaxies is that the regions where stars are created in the main spiral contain new sublevel spiral patterns. Just like clouds, it is possible for different spiral forms to be created. Sometimes very symmetric spiral arms or rectangular stick-like formations via extensions of spiral arms along with regular spiral looking shapes are generated. Despite this spiral variety, when observed from outside, stars are seen to be surrounding a flat disc and forming together as a giant globular halo. This halo was generated billions of years ago from short and longer aged stars. It is the dimmer region of the galaxy yet this halo is considered to contain most of the galactic material. Stars are located in a fashion that resembles a disc in this halo of dust and gas. The layer of dust slowly rotates around an axis that passes through the center of the halo. This rotation is not coincidental; it is controlled in such a way that the speed of stars nearby do not differ in the rotation speed of the whole disc any more than 10%. In other words, the disc does not have a constant speed. It exhibits flexibility and variations from within. Stars and gas clouds are made to revolve in similar average speeds no matter how far they are away from the center. These notions are confirmed with the use of motion laws that Newton discovered and named after himself.

Numerous types of stars from different age and mass groups exist in the disc section of a galaxy. The age of stars is determined by analyses of the light spectrum that they emit. According to the results from these analyses, the creation speed of stars has been found nearly constant around the disc section in a spiral galaxy. In many galaxies, disc material has been discovered to be around 10% gas and dust cloud and that 80-90% of the rest remains outside the disc in an invisible form, unlike stars and gasses. This is because it absorbs the majority of the light to be reflected. This kind of material is called “dark matter.” It is thought to be a very old black hole, with expired stars or an extremely cold dust cloud or a combination of these. Aside from this, it has been discussed that they are created from neutrinos or undiscovered particles. According to common notion, dark matter as generated by expired stars in the galaxy does not have any relation to the movement of spiral galaxies and their kinetic behavior, it only has gravitational effects.

Gas cloud in the disc is not dispersed proportionately; instead, it is collected in a thin layer. Furthermore, it is understood that these clouds are composed mainly of carbon, silicon, iron and many other elements, and these particles get ripped from surfaces and flown around via star winds or thrown towards interstellar space. Surprisingly, the interstellar space is a scarcely populated place. Even in areas that are considered to be empty, one atom exists in 1,000 cm3, and it can vary from one million atoms to a couple hundred per cm3 in denser regions. The density of interstellar spaces from the highest to the lowest can vary within a factor of a billion. This ratio is much greater than the density difference between air and a piece of rock.

Systems established without thermal equilibrium

Interstellar space is not in a state of thermodynamic balance. Very sizable molecular clouds are constantly shaped and get scattered into the medium. This way material exchange is carried out in between different phases on a smaller scale. Maintenance of a system where different components are preserved in a stable state with no equilibrium is a mystery to all. This elusive phenomenon has been studied by both physicists and chemists for the last 40-50 years. Data obtained so far recommends that two processes are particularly used to establish and maintain stable compounds away from an equilibrium state. The first is that such systems should include material recycling mechanisms between different components. Second is the regulation of processing speed with feedback. These two events should be executed with a balanced fashion so that the amount of material in each composition does not change. Thus, these two phenomena are executed in the most finely calibrated manner in spiral galaxies that can never be possible out of coincidence.

Plasma, one of the phases of matter, is about a couple million degrees Celsius. However, it is a much diluted phase; only one atom exists in a volume of 1,000 cm3. Temperatures rising to these levels are made possible by the energy provided from supernovas. A supernova explosion releases such energy into the space that it forms a hot gas cloud and this starts to expand. This gas cloud releases its electrons into its surroundings as it dissipates. A phase of diluted hot plasma in a bumpy shape is generated as gas cloud expands throughout the matter. One of the reasons that interstellar space took so long to be discovered is because we are still located in a hot bubble. This bubble has a magnitude of 300 light years. Studies so far have mapped this bubble and discovered it to have an irregular shape.

Aside from this, recently a new neutron star was discovered and this star is thought to be remnant of a supernova explosion that created this bubble. It should not be surprising that we are located in such a hot bubble because this only occupies 70% of our galactic disc volume. A supernova is created once every 30 or 40 years in our galaxy. Supernovas have the task of supplying the energy needed to keep the entire interstellar space under a constant pressure. It is an incredible phenomenon to ponder that a habitable planet exists in the depths of a cold space.

Interstellar spaces resemble an ecosystem from a standpoint of events that are taking place inside it. Each galaxy could be viewed as a dynamic system where stars are constantly born and extinguished in the presence of a determined cycle of energy and matter. Events that are executed with Divine wisdom in these heavenly systems (galaxies, stars, interstellar spaces) testify in their own languages to their Creator who fashioned them in the form of an art with wisdom and generously. Galaxies behave as if they are living organisms; they are born like humans and they die like humans. Continual composition and decomposition of galaxies with their contents stand as major proof to the cosmos of present and absent worlds. The heavens and the earth, the stars and galaxies all make up the Divine canvas painted and repainted on the easel of God’s command: “Be and it is.”

References

• Smolin, Lee. 1997. The Life of The Cosmos, Oxford University Press, New York.
• Syed, Ibrahim B. 2003. “Understanding String Theory,” The Fountain, Issue 41, January-March 2003.

Galaxy and the Sun

The 21 cm long radio wave radiation emitted from the hydrogen gas within the dense dust and gas clouds of the arms of the galaxy enables us to know about the structure of the galaxy. This information led us to conclude that our galaxy is indeed not a solid object and displays a circular motion of 250 km per second. The Solar system is estimated to complete one revolution around the galaxy in approximately 200 million years. At this point the critical question that comes to mind is how a solar system orbit is maintained and protected during these journeys where the solar system bypasses the gravitation and effects of strong heavenly bodies without causing disruption and collisions. The Earth just won’t become a habitable place only by considering planetary solutions. We may have to consider measures regarding our solar system and other galaxies, since the solar system has a very sensitive relation with the other heavenly systems in our galaxy.

The Sun’s position in the Milky Way

Trillions of comets in the Milky Way galaxy fill the outer space and encompass the solar system in a globular fashion. One of the comet groups orbiting the solar system is called Oort or Opic-Oort cloud. A hundred billion comets is estimated to exist in the Oort cloud.

These comets follow the designated orbits until they deorbit with gravity of another strong heavenly body other that the sun. Stars and masses of the Milky Way constitute a globular center with spiral arms where these arms extend out of the center in the same galactic plane. There are a limited number of systems located in the space between these spiral galactic arms. In fact, this is where our solar system exists. In other words, it deserves attention that the sun does not reside in the dense centric part of the galactic arm Orion (Hunter) but exists in the nearby sparsely populated galactic mid space. The solar system that has been placed in the most appropriate position within the Milky Way also needs to be protected from possible dangers it may encounter (like crossing paths with dense spiral arms) during its journey around center of the Milky Way.

Scientist who study the place of our solar system in galactic maps particularly point out that we are far away and safe from the devastating effects of cosmic storms.

If the solar system did exist in the arm where stars are densely populated and near each other, gravitational forces could result in changes in planetary orbits. For instance, in the spiral arms of the galaxy, comets would easily deorbit and bombard the earth momentarily under the strong gravitational force of these arms. Yet remarkable measures have been taken to protect against this as well! One of them is the velocity value of the Sun. For example, in order to provide an effective communication, a satellite positioned in the earth orbit is given a speed equal to the one earth has for rotating around its axis. Our sun is given a suitable velocity to move with almost the same speed of galactic arms without intercepting each other, thus providing a safe passage. However this is not the case in 95% of the stars and the spiral arms in our galaxy unlike the one determined for our solar system. This is something to reflect and think about. Another measure that prevents the sun from intersecting with the spiral arms is that it has a circular orbit rather than in the form of an ellipse like stars of the same age. Also in this regard, we observe that our sun is given a special movement allowing Earth to become a habitable place for life. The All-Wise and All-Mighty Creator works the galaxies just like a giant machinery wheel with his established laws.

The stars in the spiral arms may in time get sucked into the inner parts of the structure, not being able to hold on to their position for a long period of time. This is also applicable for the sun. Divine measures also intervene here and leave the sun in the protective zone. The sun is located in the “galactic common rotational radius” where strong spiral arm effects do not exist. Furthermore, when Supernova explosions take place, giant star debris can reach a couple thousand light years away, enabling the sun not to be negatively affected from these explosions since it exists in the outer regions of the arms.

Cosmic dangers in the galactic center

The solar system is 28,000 light years away from galaxy center. If our galaxy is considered to be 200 thousand light years wide, one can say that we are relatively close to the center.

This location in the galaxy is distant enough to be protected from the negative effects that could arise from the galaxy center. What would happen if the solar system was closer?

In this case we would constantly be exposed to dangerous gamma, X-ray, and cosmic radiations, therefore no life on Earth! Not to mention the black hole in the galaxy center which has a mass 3 million times as much as the sun. If the sun were to exist near the black hole, life on earth would again be negatively affected from the strong gravity of it. The extraordinary measures that have been taken for our solar system, the sensitive adjustments that are put in place, and the maintenance of such balance and complexity all displays a perfect science and a Divine power in the background. All these events demonstrate clearly that no single event of randomness and chaos exists in the universe. The most complicated and sensitive tasks are resolved in the best possible way, therefore revealing a perfect organization. We see this perfect organization between the Milky Way, the solar system and the earth!

Reference

Mishurov, Y.N. and L.A. Zenina. 1999. Yes, The Sun is Located Near the Corotation Circle. Astronomy & Astrophsica 341: s. 81–85.

One category of galaxies is the spiral; this is dependent on the galaxies’ appearance. The magnetic field of the Sun is also a spiral. Among many things that have a spiral form are the cochlea inside our ears, our navel cord, our fingerprints, the teeth of mammoths, elephant trunks, some spider webs, the horns of some goats, cluster of sunflowers, thousands of types of mollusks, the pattern in which subatomic particles move, plus many more examples. Grapevine shoots, ivy, some microorganisms, and the positioning of some leaves around their branches are in the form of a helix. Nature displays brilliant examples of spiral and helix forms over a wide spectrum, ranging from fossils to galaxies. Below we will discuss some of them:

The Archimedean spiral

Named after its discoverer, this spiral is the geometrical location of a point which moves across a line turning around a fixed point at the speed of q and with a straight angle (Figure 1). The equation for the polar coordinates is p=aq. The distances between the curves are equal. A good example of this type of spiral is the spider web constructed with equal distances from the center.

The Equiangular (Logarithmic) spiral

This spiral type was defined by Descartes in 1638. In an equiangular spiral, any line that crosses the center cuts through all coils of the curve (Figure 2). The equation for polar coordinates is Inr=a.q or r=ea.q. Sea shells and the shells of snails are formed with this spiral.

Fibonacci Numbers and the Golden Ratio

The following numbers, the sequence of which is made by adding the last two numbers together, are known as Fibonacci numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, … In other words, each number is the sum of the preceding two numbers. Let us divide each number with the preceding one and write down the quotients:

1/1=1; 2/1=2; 3/2=1.5; 5/3=1.666…; 8/5=1.6; 13/8=1.625; 21/13=1.615…; 34/21=1.619…; 55/34=1.6176…; 89/55=1.618…

If we continue to divide in this way, we will reach a mathematical constant, i.e., 1,618034, which is known as the golden ratio (φ).

Let us now draw a new geometrical shape with the Fibonacci numbers. Next to a 1-unit side square put another square that has equal dimensions. Then add another square, this time equaling the sum of the sides of the previous two (2 units). As we continue to add new squares with double the units of the previous two we get what is called the Fibonacci or golden rectangle. When we draw an arc from one corner of this rectangle to an opposite corner and continue drawing through neighboring squares, as in Figure 3, we will get a spiral. A good example of this is the nautilus shell. The golden rectangle and the spiral is frequently used in fine arts, architecture, and technology.

The Helix

The space curves that coil around a cylinder and cut through its main axis at a right angle is called a cylindrical helix (Figure 4). An ivy plant climbs a tree in a helix, and a helix is the shortest distance to a certain height. The Selimiye Mosque, Edirne, Turkey, features one of the best examples of helices in architecture. The architect Sinan designed the minarets of this mosque with three balconies, which are reached via different stairs that have no connections between them.

The 3D Archimedean spiral and the Logarithmic spiral (Helico spirals)

Conical helices are the space curves that coil around a right cone and cut through its main axis at a right angle. Sea snails, or limpets, have this spiral shape (Figure 5).

Galaxies and hurricanes

Galaxies and hurricanes are also spiral in shape and they have some similar features. Sharing the Stamp of Unity, the law of which governs the entire universe, both galaxies and hurricanes are affected by major forces, like the force of gravity, angular momentum or rotation.

Spiral galaxies are divided into two categories: elliptical and barred spiral galaxies. Barred spiral galaxies have arms that extend away from the main core (Figure 6).

(As evidence for a people open to belief) We have assuredly set in the heaven great constellations, and We have made it (the heaven) beautiful for those beholding. (Hijr 15:16)

The Nautilus: A wonder of creation

The hard shell of the nautilus has a beautiful logarithmic spiral shape. Each coil is at a distance from the next at an increasing proportional distance, each coil is multiplied by a constant. The chambers in the shell are similar, but they widen in a geometric sequence. It is amazing that calcium carbonate, the material that makes up the shell, can accumulate in such a way so as to comply with this geometrical pattern. In this pattern, the nautilus occupies the least space that is possible, thus losing as little heat as possible. Architects have been inspired by the nautilus to produce designs to use the smallest possible space to contain the most possible room.

The Cochlea

The cochlea in our ears is like a double-ramp tunnel coiled upon itself. Etymologically, the word cochlea comes from a Greek word that means snail. The spiral shape of the cochlea reminds one of sea shells.

Horns

Horns of the sheep and goats have the shape logarithmic spiral; they grow in the form of helicoids, as if coiling around a cone.

The Rose

The leaves of a rose are lined up and shoot out in a spiral shape.

Spirals open for us gateways to thought in our efforts to explore the wisdom and beauty that have been set in motion in the universe and are constantly maintained. Spirals, like other living or non-living objects or beings around us, are exquisite works of art that point to the fact that nothing exists from coincidence. Looking through a telescope to a marvelous galaxy in outer space or examining a sea shell on the beach or holding a rose in the spring may become a rewarding act if we contemplate on their Fashioner, for such “contemplation for an hour is worth voluntary prayer for a year.”