It was finally the weekend! After my long mathematics presentation, I came home to watch my favorite tv show, Person of Interest, to de-stress. Surprisingly, the episode was about the most famous mathematical constant, pi (π) which is equal to the ratio of a circle’s circumference to its diameter, commonly approximated as 3.14159. Mr. Finch (the main character) was acting as a substitute teacher and wrote on the chalkboard 3.1415926535. Then he asked the students, “What does this mean?” I answered the question in my mind, thinking, “If I have a bicycle tire with a diameter of 1, then one full revolution of the bicycle tire would travel the distance pi.” However, in the show, nobody answered. Then Mr. Finch answered the question himself, saying:

Person of Interest, Season 2 Episode 11 “2 Pi R”

“Pi, the ratio of the circumference of a circle to its diameter — 3.1415926535 — is just the beginning. It keeps going forever without ever repeating, which means that contained within this string of decimals is every other number; your birth date, the combination to your locker, your social security number, etc. It’s all in there somewhere. And if you convert these decimals into letters you would have every word that ever existed in every possible combination; the first syllable you spoke as a baby, the name of your latest crush, your entire life story from beginning to end, and everything we ever say or do. All of the world’s infinite possibilities rest within this one simple circle. Now what will you do with that information; what it’s good for? Well, that would be up to you…”

Although that scene was actually inaccurate, I loved it. This scene is beautiful because most teachers in the world struggle to be as good and as interesting of a teacher as Mr. Finch is here. His knowledge about the subject expands the discussion beyond the textbooks and keeps the students focused throughout the lecture.

Wikipedia, gif, “Pi Unrolled”

We have all been taught that pi is the ratio of a circle’s circumference to its diameter.

Unfortunately, this is wrong because mathematicians have not proved that pi has the characteristic of “normality” yet. In other words, mathematicians are not sure if pi contains all the finitely long permutations of digits from 0 to 9. They are not sure if every digit continues to be used after a certain amount of time or an unlimited number of times in pi’s decimal representation. Nobody knows what we will find in the digits of pi if we keep going. For instance, when we check the first billion digits of pi, we see that the digit 7 occurs almost 100 million times. This makes pi a nice random number generator. However, after some points, pi may not contain the digit 7 and might instead have a non-repeating number with just two or three digits such as 010203112233000111222333…

For instance, after the first 761 digits of pi, there is a famous mathematical coincidence where six nines occur in a row which is called the Feynman point.

Twitter, Feynman’s Library, “Feynman Point in Pi”

But we are sure that the digits of pi keep going on forever and in a random order. This makes pi interesting because the value of pi is finite; however, its decimal value is infinitely long. This is not a contradiction. Pi is a constant number because it is the ratio of the circumference of a circle and its diameter, which are finite values. Still, we need an approximate value for pi.

In 1768, Johann Lambert proved that the value of pi is an irrational number and it cannot be written as a rational simple fraction. 22/7 is a commonly used approximation but does not contain all of the digits of pi. This is because irrational numbers cannot be written as a ratio of two numbers, such as , because they continue on to infinity and do not follow a pattern. In 1882, Ferdinand Lindemann proved that pi is a transcendental number because it is not algebraic; it is not a non-constant polynomial equation with rational coefficients (“Transcendental number”, Wikipedia).

We can safely say that pi is transcendental because the mathematician Yasumasa Kanada found that the first trillion digits of pi appear to be statistically random. If you check the table below, you see that the event of each digit occurring is independent, and the probability of it is one-tenth of the time (“Kanada Laboratory,” Super Computing)

After many years, Emma Haruko Iwao found 34.1 trillion digits of pi in 2019. It took 121 days for Haruko and his computer, because calculating pi requires a lot of power, even for a computer. You can picture it in your mind like this; if you were to print a billion decimal values of Pi in normal sized, ordinary font, it would stretch from New York to Kansas.

However, 34.1 trillion digits is still not enough to prove whether pi is normal or not (“Pi in the Sky, Google Cloud Blog). Supercomputers are still crunching the numbers. If you check the graph below, you will see the number of known digits of pi, by year, since 250 B.C.

FiveThirtyEight, Graph, “Even After 31 Trillion Digits, We’re Still No Closer To The End Of Pi”

Going back to Mr. Finch, we see that he is not 100% wrong. We can find our birthdays in pi easily. If you go to mypiday.com and type your birthday, it will give you the decimal place in pi. For example, my birthday occurs at the 675,097th decimal place.

If pi is a normal number, then we can say that our whole destiny is encoded in pi. The pictures we are going to take in the future, will be in pi because there are binary numbers behind images. All digital products are in pi. Even this article has been in pi for thousands of years. Furthermore, the DNA of every creature is in pi. Mr. Finch was actually right.

There is an interesting and artistic way to show the randomness of pi. Some scientists might be happy with their tedious scatter plots, but there are some artists who use colors for data visualization to communicate with the public. Martin Krzywinski is one such artist, who found beauty and artistry in the randomness of Pi. He took the digits of pi and gave each digit a different color. For instance, he gave 3 the color orange, 1 as red, 4 as yellow, and so on. Then he made a beautiful poster. And if you look at it carefully, you do not see any particular pattern to the colors.

Science Art by Martin Krzywinski

Should we stop working on pi? Or should we continue looking for a better approximation? Is assuming pi as equal to 3.14 good enough? Or is it enough to use 40 digits of pi to find the circumference of the Milky Way galaxy to an error less than the size of a proton (JPL NASA)? Are the first 152 digits enough to find the circumference of the observable universe at 93 billion light-years (WIRED)? There are hundreds of mathematicians who have been trying to figure out more digits of pi for years. It is like trying to get to the moon and then to the next planet, and so on…

But why? Why do mathematicians bother calculating any more digits? Why aren’t 34.1 trillion digits of pi enough? Is it because pi lurks in every circle?

The logical reason seems cryptic: is it because pi is a beautiful source to generate random numbers? Or is it that countries can show off their technology to other countries, because calculating trillions of digits of pi requires a very powerful computer? For instance, in the Star Trek episode “Wolf in the Fold,” Spock foils the evil computer by commanding it to “compute to last digit of the value of pi.” So asking a computer to compute pi is called “a stress test” and may make it crash.

On the other hand, we humans are just weird. Staying at home and drinking tea is a beautiful activity, but when we get bored, we try to climb the highest of mountains, befriend a tiger, or try to memorize the digits of pi, like Chao Lu, who correctly memorized the first 67,890 digits of pi. We will keep doing these things because we like to understand the world around us.

We are inevitably connected to the past, and pi is a thread that’s gone through all of human history. That’s why we can say that as long as there are people, there’s always going to be somebody who wonders what’s next. And I assure you that somewhere in the world there is a mathematician or scientist using pi for something important, because pi is still the mysterious constant of nature.

Finding Pi

The previous statement is utterly true: there has always been someone who works on pi. Math is as old as civilization. Pi has been studied by the human race for almost 4000 years. When the last mammoths were going extinct, people were studying Pi. As far as we know, Archimedes was one of the first humans who calculated pi. He was most likely helping wheel makers. But how did he estimate the value of pi?

Firstly, he saw that all polygons are a circle. According to Archimedes, if you keep increasing the number of the sides of a polygon, you get closer to the perfect circle. In other words, a pentagon is more circle than a square, but a hexagon is more circle than a pentagon, and so on… Thus, more than two thousand years ago, he defined a circle as a regular polygon with an extremely large number of sides.

His definition is useful because measuring a curved surface was hard to do accurately. He found a way to find the circumference of a circle. First, he drew a square with its corners touching the perimeter of a circle and found the perimeter of the inscribed square. Secondly, he drew another square with its sides also touching the perimeter of the circle and found the perimeter of the circumscribed square. He came to the conclusion that the circumference of the circle had to lie somewhere between the value of those two perimeters of squares.

Using this method, however, the difference between those two values was pretty big. So, he drew pentagons to see the upper and lower bounds of the circumference of the circle. This gave him a smaller range of bounds. He kept increasing the number of faces of the polygon that he was drawing inside and outside the circle. Each time he did this, his estimation was getting more accurate. Archimedes got up to a 96 sided regular polygon [called an enneacontahexagon] until he grew exhausted. The lower and upper bound that he found were 3.1408 and 3.1429. Thus, he calculated π to two decimal places.

Archimedes’ method needed improvement because his life span was not going to be long enough to find the other digits of pi by hand. Mathematicians needed to discover more efficient formulas and new techniques.

Before they could do this, they needed to discover algebra. Its discovery by the great mathematicians inspired a whole new way of looking at the world.

The next great jump in calculating pi was the invention of calculus. After that, mathematicians started working on infinite series. An infinite series is an expression with numbers added together until infinity; sometimes these infinite series converge to a particular value.

There are many methods available now to calculate pi. Gottfried Leibniz found pi in infinity. James Gregory was working on one of the astonishing infinite series for the inverse tangent function below. He added infinitely many small numbers together and found pi.

He put x = 1 into the inverse-tangent series. He showed us the further we go, the closer to the estimation of pi we get. However, in order to get 10 digits of pi, we need to write about 5 billion fractions.

After that, another great mathematician, Leonhard Euler – who officially adopted the Greek letter “π” as a symbol to represent the value – found a more efficient equation for pi, when he was only 28. The symbol became iconic. Euler’s Pi equation calculates an infinite sum. The Basel Problem was named after him.

Euler also used pi to write another beautiful equation, Euler’s Identity.

Thanks to the Indian mathematician Ramanujan’s obsession with pi, we have many new formulas to find pi. When he arrived at Cambridge from India, he brought with him a notebook in which there were 400 pages of formulas to find pi.

After the invention of mechanical computers, mathematicians used Leibniz’s, Euler’s, and Ramanujan’s infinite series to calculate a trillion decimal digits of pi (Stanford Cryptography Group). Without a supercomputer, finding this many digits of pi would be difficult. For example, the mathematician William Shanks managed to calculate the first 707 digits of pi by hand but unfortunately, he had made a mistake after the 527th place.

Pi is everywhere

Children start learning about pi when they are in 7th grade and use it until they graduate from college. Even after that, most people use pi again when their children go to school. Pi appears everywhere in the universe. It is literally woven into our universe: the orbits of planets, electromagnetic waves, rivers, the colors of auroras, the structure of DNA, the Great Pyramid of Giza… If a scientist wants to describe the structure of the universe or find the relationship between planets, he/she definitely needs to use pi: anything involving a circle or a sphere is about pi. Circles appear throughout the natural world, whether they’re a soap bubble or the moon in the night sky.

 A Gif showing the clever play on the letters “pi”

Sinuosity of rivers

Pi has a direct relationship with rivers. But how? To figure this out, we need to measure the length of a river in two different ways. Assume that we know the starting and ending point of the river. First, we need the actual length to see how bendy the river is. In other words, the distance that you need to swim from the beginning point to the ending point. This whole length will be “L”. Second, we need to find a straight length. In other words, this time we need to fly from the beginning to the end. And this direct route will be a lowercase “l”. Now we can write the formula for the sinuosity by dividing L by l. The sinuosity is a ratio and measures how bendy the river is.

What is important here is there’s no limit to how high sinuosity can be. Rivers can be really bendy. However, Hans-Henrik Stølum proved that theaverage sinuosity of rivers around the world is pi. If you find the sinuosity of all the rivers and take the average sinuosity of them, you should get pi (Meandering River).

There is another interesting fact about sinuosity. Rivers can be very bendy at some points. But suddenly, those rivers become straight and make the sinuosity around pi. So, it is hard to find the sinuosity of a river equal to 7 because of fluid dynamics. Mathematicians found the highest sinuosity to be around 3.5 and the lowest sinuosity around 2.7.

At the extremely bendy point, rivers cut off after the bend point and make a shortcut to become straight again. This phenomenon is known as an oxbow lake, which controls the sinuosity of rivers. This keeps the sinuosity of a river around Pi.

Pi in Space

There is a mathematical order inherent in our universe. For instance, to understand our solar system, we need pi. We know that our planet moves in front of its host star. And the light comes from host stars. To talk about that light, we need to know how big the host star is. In other words, we need the surface area of the host star. The formula for the surface area of a sphere is 4πr², with r being the star’s radius. The size of a planet also helps scientists to guess whether it is habitable or not.

Another good example to show the relationship between pi and the universe is electrostatic force, which is the force between two electric charges. An electron exerts a force in all directions and forms a sphere field. Electrons also interact with each other on an electric field. To figure out that interaction, we need to find the surface area of spheres, where again pi comes up.

There is also a connection between pi and gravity. If you have had a chance to see Einstein’s field equations, you might notice that pi is there also:

The formula above calculates how objects with a large mass, such as stars and galaxies, can curve space and time with their gravity. Einstein said that, just like a ball sitting on a bedsheet, any form of momentum and energy can also curve space-time around it. In words, the formula is saying:

Gravity = 8 x π x Energy & Momentum

Lastly, if you take the square root of Earth’s gravity, you almost get pi.

Pi Day

After so many years studying pi, people decided to organize an official celebration of pi on March 14th. Since 1988, people have celebrated this magical constant. Coincidentally, Albert Einstein was born on pi day – March 14, 1879. Einstein also published his theory of general relativity on pi day.

The Google logos for Pi Day.

This essay evaluates an example of violence theme books, claimed to be written for both children and adults. We shall analyze Harry Potter, which has been marketed through commercials and campaigns, in terms of content and language, adequate and overriding themes.

The author: Joanne Kathleen Rowling was born in 1965 in England and graduated from Exeter University with a degree in French literature. She started writing the series after an instant inspiration while riding a train. The Harry Potter series, which has sold more than 200 million copies and has been translated into 47 languages, has made the author one of the highest taxpayers (’60 million sterling) in England.

The hero: Harry Potter is a child who survived a tragedy in which his parents, both wizards, were killed by black magic. As an infant, he was sent to live with his mother’s sister and her husband, both opposed to magic and therefore openly hostile to Harry. After realizing that he has inherited supernatural powers, Harry dedicates himself to fighting evil. He acquires many magic skills that no one else has.

Themes: The science-mystic series starts on a Tuesday morning in London. Throughout, good-bad and positive-negative elements are inseparable, for there is neither a hierarchy of values nor a moral code. Furthermore, the characters’ morals shift morals throughout the books. The series affects children, leaving traces of subjective behaviors based on imitation and changing ethics. As a result, they use their fathers’ cars without permission, lie to cover up incidents, and become apparently disobedient at school.

In such books, there usually is an overwhelming idea: The universe is ordered and good always triumphs over evil. But in this series, there is no good side apart from Harry’s hereditary supernatural powers.

Language: Another interesting feature is the unacceptable language full of swear words, even though it is said to be written for children. It is evident that the author tried to maintain the readers’ interest through inappropriate metaphors and negative terminology.

Main theme: The usual design of the universe can be changed through magic, and the only way to overcome evil is to use mysterious forces and sorcery. Thus everything is build on a theme of sorcery. The author successfully tells the story for children by using normal objects and places and by incorporating the real world with an artificial world based on sorcery.

Magic is used to overcome evil and help the good, but is portrayed as a positive element to be used in daily life. Thus, all daily behaviors are associated with magic. This emphasis asserts that adults and children must use magic to resolve issues that can be resolved through human willpower and effort. In this case, there is the possibility to believe in sorcery’s power, and thereby be drawn into helplessness and pessimism and forgetfulness of Divine power.

The absolute evils in the books (vampires, witches, bloodsuckers) are around all the time and can exert evil constantly. Such a world concept has the potential to increase the number of unhappy children, as well as those who already are aggressive and cause trouble for others.

Up until the eighteenth century, people believed in white (good) and black (bad) magic and that white magic somehow helped goodness to prevail. However, in Harry Potter, white and black magic are inseparable, use the same weapons, and both use the apparatuses used in black magic (e.g.,corps, urine, blood, crow, cemetery soil). However, it is implied that black magic is used for murder and death. Black magic and spells replace mercy, forgiveness, warning, and short-term punishment with methods of terminating and disappearing. As a consequence, children are manipulated toward magic (particularly black magic) and the so-called dark sciences.

Religion and Divine Power: This series emphasizes a universe without any design and owner, one having no concept of God or Destiny. Creation, killing, and reviving are associated with a mysticism originating from an arbitrary and Godless universe. The concepts attributed to God in all religions are tied to the power of magicians and sorcery. In a sense, therefore, sorcery has replaced religion. Harry has an almost divine role due to the supernatural powers he possesses, which have come to him from an unknown source.

Mental violence: In the series, both the good and evil forces use violence against each other. In fact, violence against violence is the primary theme. All of these violent messages sent to the subconscious are constantly repeated and thus leave negative impacts. Moreover, even the fairy used as the symbol of good in such books is portrayed as an evil fairy. It is well known that mental violence is more harmful to one’s personality than physical violence.

Interaction with the Devil and Satanism: The series contains many satanic motifs, among them Harry’s interaction with the snake in the zoo and owls carrying a letter to him. Both of these animals are apparent signs of the world of sorcery. In fact, the Qur’n refers to the snake as the ‘€œdevil who leads people astray.’€ The victims of satanic scarifies are unfortunately innocent girls. The author even writes about such a girl who is killed in this way, a murdered cat whose blood is drunk tree days after, and a way of suicide that the Satanists call Satan suicide. Furthermore cemeteries, which also attract Satanists, appear frequently in the books. The Satanists’ œblood drinking ritual, based on their belief that they become more powerful by drinking the blood of a cat killed by torture, is also depicted.

We do not know why blood, another element that feeds mental violence, is used so much in books written for children. However, if we consider that blood is not shown on TV news programs, we find it difficult to comprehend the author’s intentions. The frequent use of such terms as ‘blood, death, soul suckers’ cannot lead to anything but mental terror for small children whose perception cannot go beyond physical means.

Conclusion

The Harry Potter series emphasizes an unorganized universe; ignores moral codes; implants mental violence; injects helplessness, fear, and pessimism; replaces religion and Divine Power with sorcery and magic; overlooks the effects of God and Destiny in the flow of events; encourages Satanism, violence, and suicide; and reflects a perception of the consumer society as an appetizing market without any social concern.

Regardless of the author’s intention, all of the images and descriptions of violence stored in the subconscious will bear violent people, who will play a role in creating a violent society. We should expect one consequence to be rising rates of children terror, death, and suicide on the nightly news.

From this perspective, this overlooking of moral values, children’s pure minds, and the beautiful world of tomorrow for the sake of earning more and reaching greater markets could be countered by the efforts of those striving for goodness and their consciousness of these dangerous games. Children, to whom we one day will hand over the future, can be saved only in this way.

There are two major theories about the origin or essence of mathematics. One of these theories is attributed to Plato, and the other to the so-called Formalist school. According to Plato, mathematics exists independently of man. What man does is to discover its objective reality, just as other ‘laws of nature’, which we tend to call ‘Divine laws of nature’, are discovered. The Formalist school by contrast asserts that mathematics is a product of human thinking. In order to understand the difference between these two schools, we may cite as an example their view of prime numbers (that is, numbers like 7, 17, 41 which can only be divided exactly by themselves and the number 1). Platonists argue that the prime numbers exist independently of us: before we discovered their existence, they existed in infinite number. Whereas, Formalists are of the opinion that the prime numbers exist because we have defined them as such, and it is meaningless to think about whether they are of infinite number or not.

The language of numbers

Formalists assert that numbers came into existence when human beings began to count. A well-known account of how this happened is that of a shepherd who used to put a stone in his bag for each of his sheep and by matching a stone with a sheep could find out whether any of his sheep had been lost or not. Later on, people began to call numbers each by a different name and since there were two fingers in the two hands, they found it easier to make calculations by the decimal system. This was followed by the operations of addition and subtraction.

According to the Formalists, even the simplest mathematical operations like the four basic ones consist in some logical rules based on certain axioms. They say that we do mathematics by expressing certain rules with certain symbols. That is, we take, say, 5 and 7, a couple of signs whose meaning in the physical world we do not know, and put between them the plus sign, a third sign whose meaning in the physical world we do not know, followed by an equals sign. And we know we must write 12 after the equals sign because that is a requirement of the axioms and rules of logic we are using. This is just what a calculating machine does, that is, it goes through the operation required of it without knowing what it is doing.

Let us suppose that an adding operation consists only in applying axioms or certain logical rules, and has nothing essential to do with the physical world. If we were to take our number signs and apply them to physical objects like stones and sheep, we should be surprised, amazed even, as if by a miracle, that 5 and 7 stones or sheep added together (according to the same rules as 5+7) make 12 stones or 12 sheep. We would come to know that the abstract, conceptual realities in our mind correspond to physical realities in the outer world. According to Paul Davies, the renowned physicist, if we lived in a universe where different physical realities prevailed, in a space where, for example, there were not any countable things, we would not be able to make most of the calculations we make today. David Deutsch claims that counting emerged as the result of experiences. According to him, we can do arithmetic because physical laws allow the existence of physical models convenient for arithmetics.

Richard Feynman, regarded as the greatest physicist after Einstein, says about mathematics that the problem of existence is a very interesting and difficult problem. When you take the third power of certain numbers and then add them with each other, you obtain interesting results. For example, the third power of I is 1, of 2 is 8, and of 3 is 27. The addition of these numbers gives the result of 36. The addition of 1, 2 and 3 is 6 and the second power of 6 is also 36. When you add to this the third power of 4, which is 64, the result is 100. The addition of 6 and 4 is 10 and the second power of 10 is also 100. Added to this the third number of 5, which is 125, the result is 225. 225 is the second number of 10 plus 5, i.e. 15. And so on. According to Feynman, we may not have known this typical characteristic of numbers before but when we do come to know such characteristics of numbers, we feel that they exist independently of us, and that they existed before we discovered them. However, we cannot determine a certain space for their existence. We feel their existence as conceptions only.

Let us take another example. Ibrahim Haqqi of Erzurum, a Turkish Sufi, religious scholar and scientist of the 18th century, discovered a way of checking the correctness of an operation of addition which may still be unknown to modern mathematicians. In order to check or prove the addition, we first add up the digits of each of the two numbers we are going to add up. Let us say, we are going to add 154 to 275, for which we get the answer 429. Adding the digits of each of the first two numbers, we get 1+5+4 = 10 and 2+7+5 = 14. The next step is to subtract 9 from each of these two sums, giving us 1 and 5 respectively. The third step is to add these two results together, 1+5 = 6. Now we do the same thing with the digits of the answer we are wanting to check, namely 429, and again subtract 9: 4+2+9 = 15, 15-9 = 6. The fact that we end up with the same number (i.e.6) means that our addition was correct. This way of checking an addition exists independently of us. We did not create it, we discovered it.

As water had the force of lifting objects of certain weight before Archimedes discovered it and, again, objects thrown into air or a fruit disconnected from its branch fell before Newton discovered the law of gravity so also numbers have many characteristics only some of which have been discovered.

Heinrich Herzt, a physicist, says that we cannot help but feel that the mathematical formulas discovered so far exist out there independently of us. We know that these formulas existed before we discovered them but we cannot determine a space for them. Rudy Rucker, a mathematician, is of the opinion that there is, besides the physical space, a space of mind, which he calls ‘mindspace’ and it is that that mathematician study.

Most of the distinguished mathematicians follow the view of Plato. Kurt Godel is one of them. Before Godel, it was almost a generally accepted view that mathematics is a function of the working of mans brain consisting in the collection of the logical rules which we establish between the symbols of two sets. Godel persuasively argued that there have always been correct mathematical expressions even though their correctness cannot always been proved. Another Platonist mathematician, Roger Penrose, believes that beyond the thoughts of mathematicians there are profound truths or realities in mathematical conceptions. Human thought is directed to extend into these eternal realities and they are there to be discovered as mathematical facts by any one of us. Penrose mentions complex numbers as an example for his argument. According to him, there is a profound, timeless truth in complex numbers. Penrose cites the set of Mandelbrot as another example to prove his argument. The reality this set reveals is the fact that even the lines, twists and shapes of mountains and clouds were or are formed according to certain mathematical formulas. 

What flowers reveal

Almost everyone has heard of the series of Fibonacci. This series, named after the famous mathematician, Leonardo Fibonacci, progresses as 1,1, 2,3,5,8,13,21,34,55,89,144, and so on, each term being equal to the addition of the previous two. That is, I and I make 2, and I and 2 make 3, and 2 and 3 make 5, and 3 and 5 make 8, and so on. This is the series found in nature. For example, when we count the spirals formed of the seeds in a sunflower, we find that those arranged clockwise are 55 and the others arranged anti-clockwise are 89. Both of these figures are among the consecutive terms in the Fibonacci series. These figures may vary according to the size of the sunflower: we may find the figures of 34 and 55 in a relatively small flower, and 55 and 89 in a normal sized one, but the arrangement is always as consecutive numbers in the Fibonacci series. The spirals are arranged in pine cones in 5 to 8. We may encounter the same figures in the arrangement of tobacco leaves. Another extremely interesting characteristic is found in the numbers of petals of flowers. A lily has 3 petals, while a buttercup has 5, a velvet 13, a dahlia 21, and a daisy 34 or 55 or 89, varying according to its family. It is impossible to attribute this miraculous arrangement to chance or ignorant nature. If the DNA of a sunflower or a pine cone determines random numbers for its petals or spirals, how can you explain their correspondence with the terms of the series of Fibonacci? The ratio between the consecutive terms in the series of Fibonacci is quite near what is called the golden ratio’ and known in classical art as the ratio most pleasing to human eye. In order to explain the origin of this miraculous reality, you have to either accept that flowers know what is most pleasing to human eye or that the ‘Hand’ of One, the All- Knowing, the All-Wise and the All-Beautiful, is working in nature.

In short, what Fibonacci did is to discover this characteristic in nature. This means that the universe has a mathematical order or mathematics is the branch of science studying the miraculous order of the universe, the order which the Absolute Orderer and Determiner, One Who determines a certain measure for everything, has established.