Astronomers have discovered a planet with the longest known orbital period. Exoplanet Kepler-421b has been identified through the Kepler observatory, a space-based telescope. It circles its star once every 704 days. More than 1800 exoplanets have been discovered so far, but compared to Kepler-421b, those had much shorter orbital periods, like a few weeks or even a few days. The host star for Kepler-421b is much like the sun, but it is little bit smaller and relatively cooler. With an orbital distance of 177 million kilometers, Kepler-421b gets about one-fourth the light from the host star as the Earth receives from the sun, which makes the exoplanet as cold as -100 °C. The unusual orbit places Kepler-421b beyond the “snow line,” which is accepted as the dividing line between rocky and gaseous planets. Outside of the snow line, water condenses into ice grains that stick together to build planets known as “gas giants.” Since gas giant planets are very close to their stars, theorists believe that many exoplanets migrate inward early in their history. However, Kepler-421b is the first example of why such migration may not be necessary.

Sunflowers’ internal clock

Plants are known to grow toward the sun to maximize the amount of energy they absorb. Sunflowers (Helianthus annuus) show the most fascinating behavior during summer, when they follow the sun as it rises in the east every morning and sets in the west every evening. In a recent study, scientists challenged the obvious explanation for this plant’s behavior: are flowers solely responding to sunlight or are there other unknown mechanisms at work? They designed a clever yet simple experiment where they grew sunflowers in chambers with a fixed overhead light that was continuously on. Surprisingly, for several days, the sunflowers under constant light kept moving as if the sun were rising in the east and setting in the west. This unexpected result suggests that sunflowers were not responding only to the direction of the light but also to an internal biological clock. Furthermore, they discovered that sunflowers bend when one side of the stem grows faster than the other. For example, the west side of the stem seems to grow faster to bend the plant towards the east in the morning. Scientists now hope to understand how an internal biological clock in sunflowers has the opposite effects on opposite sides of the stem. Sunflowers are not the only plants performing this diurnal dance; other agriculturally important crops such as soybeans and cotton exhibit the very same behavior. Solar tracking is known to boost plant yield and discovering the mechanisms of how plants track the sunlight might have important implications for improving global agricultural yields.

Friends linked by genes

It is a common observation that close friends look alike. Even centuries ago, Plato noted the tendency that good friends usually have similar appearances. Recently, a group of geneticists took this idea even further and suggest that people on average tend to choose friends who are genetically similar. The study provided convincing evidence that we have more DNA sequences in common with the people we pick as friends than we do with strangers in the same population. Researchers performed a genome-wide analysis of approximately 1.5 million markers of gene variations from 1,932 subjects of the Framingham Heart Study, which is one of the most comprehensive genetic databases. They identified 1300 pairs of non-relative friends and compared their genetic information to each other. The analyses showed that friends share similar genetic variations (around 1% genomewide), to the degree that it is as if they have the same great-great-great-grandparent – in other words, as if they were fourth cousins. Notably, friend pairs seem to have the greatest similarity in the genes that are responsible for a sense of smell and they show the most difference in immunity-related genes. Friendship entails spending a lot of time together and looking out for each other. Odors are strong behavioral cues in human psychology and people with similar olfactory preferences might like to prefer living or hanging out in similar environments. Likewise, it is potentially a big advantage that friends don’t get infected from the same microbes at the same times, so that one of them can take care of the other. As much as these anthropological implications are merely speculations with many caveats – and despite there being many obvious social, ethnical, and cultural factors that help determine friendships – the genetic basis of friendship and other social interactions may hold answers to at least some of the mysteries of human behavior.

No matter how fast or how far a person runs, the horizon will always be beyond them. This being the case, the real distance and depth of the horizon is inside a person, it is in their mind and perception…

A race I will always remember

Not too long ago, when I was still a little boy, I found myself running from my father’s village to my mother’s, and from my mother’s to another and to another, in the hope of catching up with something that was neither a ball, some other toy, nor a bird, but rather the point, the line where the sky seemed to touch the earth. We call it the “horizon.” That line, that “place,” first presented itself to me hiding right behind the trees to the left of my father’s house. I started out that day walking rather leisurely because the distance between me and the horizon seemed so short. When I observed that the sky had moved, or rather seemed to have moved further away, I hastened my steps. Then I noticed that the sky moved further and further away. Well, being determined to reach the place where the sky certainly touched the ground, I kept walking faster and faster until I found myself running.

I ran for quite a while until I realized that “there”, where the sky and the earth met, was still further away, that it would take me more time and effort than I had thought. I went back—I had to go back—to my father’s village, back to my usual village life because I saw that perhaps much more was involved, that maybe much more effort was called for in order to achieve what I desired, namely, to get to the point where I could touch the sky, where I could climb the sky. I went back to the ordinary, the normal life and experience of the village and of my people. But I did not tell anyone, I did not discuss the experience with anyone, even though I did not stop and could not stop thinking about it. I thought to myself that perhaps a week, a month, maybe a year would suffice for me to reach the place where the sky and the earth embraced. I was absolutely certain that right there in front of me, over there, not too far away, the sky touched the ground. And I thought that perhaps all I needed to do was keep walking, keep running, and keep racing forward, without stopping, without interruptions, without distractions in order to get to where the sky kissed the ground.

Today, thirty-five years later, I have realized that I was not wrong. I was right. The sky did touch the ground. It touches the ground all the time. You may ask “but where and how?” The sky touches the ground in our perception. Look across from your window into the distance. What do you see? Or, go outside and look in the distance. What do you see? The sky is right there, over there, touching the ground, the road, the houses, the trees, the mountains, the sea, and remaining there. But keep in mind that this is all happening in our perception. In perception, things are the way they appear, the way they seem. No rigorous, critical thinking is involved. And this happens so many times, and in fact is happening now; it happens every time that we are not thinking deeply, with attention and effort. It happens every time we fail to allow other perspectives, other possibilities and other possible interpretations to emerge.

The sky touches the earth, embraces and kisses the ground, right there in a fixed position, as long as you do not move. Once you move, it moves. And when you run after it, it too runs, not towards you though, but rather away from you. If you stand still, it stands still. If you stay where you are, it remains where it is. If you move even an inch, it will move. It will never allow you to catch up with it, to touch it; it will never allow you to possess it, to tame it; it will never allow you to take possession of it. And yet, it is always there, “putting everything into perspective.” By that I mean the horizon enables us to see, for without horizon one cannot see much of anything. Think about it! Everything presents itself in horizon. Everything dwells in the horizon, everything is within the confines of the horizon, and depends more or less on this phenomenon. And if I may borrow an expression from Saint Paul’s speech at the Areopagus (Acts 17:28) and be at liberty to use it as I see fit in this context (just as some scholars say he himself was at liberty to do with the same expression from the writing of Epimenides of Knossos (6th Century B.C.)), one can say that “that in which we live and move and have our being” is the horizon.

Standing still, remaining in one fixed position is not in the nature of the horizon. Its every stop (or what appears to be its end, its boundary) is temporary and transitory, like a pilgrim’s stop on a journey whose destination is still far away. It keeps moving, and it invites us to keep moving too, keep working, keep meeting people, keep exploring, keep digging, keep sowing, keep cultivating, keep harvesting, keep looking, keep reading, keep writing, keep thinking, keep talking, keep wondering.

We hear, not infrequently, the expression, “on the horizon/in the horizon.” What does it mean? It means in view, in the possible future, in sight. That which is in or on the horizon appears close, and seems to be approaching; it is as if it’s right there among the things that one hopes to do soon, as something squarely within one’s reach, among the things that one’s abilities can handle. What is in the horizon, then, is something that appears “present” and seems quite achievable.

What is a horizon? And what does it do?

A horizon is inseparable from a living, perceiving human being who is in the open or in the frontier of the open. There are no horizons in closed spaces, closed places. The distance between a living human being and the line where the sky and the earth meet is very wide. It is infinite. It is far, far away. You can only measure it with your eyes, your mind and your soul. You can figure out how long it is only to the extent that your eyes, your mind and your soul can go. An application of any other measuring device will only frustrate you because the moment you start going after it to measure it, it will recede. But the truth is that what you are actually seeing of the horizon is only a small part of it. The bigger part is on the other side of the horizon. Every horizon has at least two parts: a front and a back. The front of the horizon consists of the part you are seeing, and its back consists of the part hidden from you because of the hills and mountains, the earth, the road, the trees, the sea. In fact, the line where the sky seems to touch the earth is really only a perceived curve or a perceived point of contact, but the horizon really goes far and farther away, without end: it stretches into infinity.

All the things we are seeing are in fact standing in the way of the horizon. Similarly, all the things we are thinking right now, all our thoughts and ideas, everything that is presently on our minds can be an obstacle to a deeper and fuller understanding and appreciation of the horizon. We have to let go of all of these things in order to begin to have an idea of the depth and richness of the horizon.

For now, let us focus on the part of the horizon that is visible to us. It is a world, the world that we live in or would like to live in. Normally, it consists of people, people of different religions and/or of no religion at all, people of different languages and cultures, different experiences, different states and walks of life, different situations and aspirations, people driven by different desires, values and visions, people of very deep opinions, inspirations, beliefs and deep convictions other than our own, people heading in a thousand and one directions. This world, this visible side of the horizon also includes animals of many different types and habitats, which eat different kinds of food and have different spans of life. It also includes many different trees, bushes and flowers, and different types of grasses, etc. Mountains and hills and valleys too, rivers and big oceans, streams and creeks, are all part of this side of the horizon. Small and big houses, low and high buildings, shelters and palaces, mud houses and ghettoes are all part of this side of the horizon that we are seeing. But we do not actually see everything that we know is out there, that is all around us, that is over there in front of us…

How do we even know that there is anything out there, that other people are out there? A long walk, travels, meeting people, doing business with people, education, etc. confirm that there are other people out there, other lifestyles, other ways of thinking, other ways of doing things, other attractions, other things that people consider as very precious and worth dying for. We read about these things, have actually met and seen them with our own eyes, have lived with people of different orientations and values, have had some great opportunities to exchange ideas with them. But neither our reading and studying nor our investigative and explorative eyes can exhaust the visible side of the horizon because even the visible side has its own invisible aspects and invisible faces. Let us take for example persons, situations and objects.

From time to time, a person whom I have known for many years, not only surprises me, but also seems to be a surprise to herself/himself whenever s/he says something or does something I could never have thought or imagined her or him doing. And people of this nature are not uncommon.

How about situations? They are similar. Even the most familiar situations often have aspects that are new and different, which we can see if and when we look with more attention and care. And the moment we become used to these, even newer different aspects of the same situation emerge. The same goes for things such as books, clocks, chairs, doors, and so on. A book often presents us with information that we did not see the first time we read it. And if you read it again, you will again see something you missed the second time you read it. If you wish, you can read it again and again, and you will see something new every time. The book will never fail to make you see something new and/or think something new.

Can a chair or a door do something similar? That is, can a chair or a door make you see something new or think something new every time you encounter them? Let us see. A chair, unlike a book, seems to have no generative power. It seems mute and sterile. But can a chair speak and make us think? The answer is yes, it can speak and make us think. No one would disagree that the chair of Pontius Pilate, the chair of a Court Judge, the chair of Saint Peter, and so forth do have a powerful message. Although these chairs I have cited are special, every chair can say something to us and really make us think. For example, chairs for children and for adults make us think different thoughts, which by the way, make us give children appropriate chairs and to adults what is suitable for them. If we did not think differently of these chairs, chances are we would give adults the chairs meant for children and vice-versa, or give the same kind of chairs to everybody, children and adults alike, seriously compromising comfort. And some chairs would even fall apart (that is, if children’s chairs are given to heavy people like me to sit on).

Doors too make us think. For example, the Door of No Return in Goree Island in Dakar, Senegal, and the Door of Hope in Johannesburg, South Africa, makes every visitor think. But again, although these specific references are special, every door, including those that may seem unimposing and insignificant, can really make us think. Every door has a message.

The bottom line is that even the most visible side of the horizon can have aspects that may not be totally obvious and immediately accessible. Therefore, the visible, that which seems completely clear can still make us think because it often has layers, folds, dimensions, messages that lie beneath its surface. There are always other meanings, other messages behind the obvious. And the moment we finish harvesting one message, the moment we finish reading one meaning, the horizon presents us another one, and yet another, and so on and so forth. Inexhaustible indeed, this horizon can constantly give new meaning, hope, color, shape, style, texture, depth, taste and strength to our lives for endless joy and delight, even under very difficult circumstances. Why? Because the horizon has power to liberate us from the present, the immediate, the obvious. As it draws back, so to speak, that is, when we attempt to respond to its invitation into the open, when we dare to go after it, go with it into the deep, when we allow ourselves to move with it and flow with it, then it can open new doors, generate new ideas, launch new beginnings, reveal inroads, illuminate new bridges, disclose exits, uncover new faces, make terrains of other possibilities visible, make cooperation and collaboration possible, make teamwork possible, bring along other solutions, other fertile soils. With the horizon, there are no closed doors, no human being is a finished project, no done deal, no finished once-and-for-all discussions, no insurmountable barriers. The horizon’s open field stretches into infinity.

All of this is but an invitation to read between the lines, i.e., “to resist simplistic interpretations that dogmatically ascribe fixed significations to [things]” (G. Weiss, Refiguring the Ordinary, Indiana University, Bloomington, 2008, p.58).

It is about the need to go on researching other possible meanings and interpretations of a text, to go on searching for other possible answers to certain problems, to appreciate the expanding limits, and to devote more time and energy to the lifelong project of exploration of self and of the world (and of God) (see P. Okogie’s “Horizon: the birthing world” in the Journal of Horizons of Horizons, Vol. 1, no. 1, Duquesne University, Pittsburgh, 2012, p.10).

Rev. Dr. Okogie is Assistant Professor of Philosophy and Bioethics, University of Saint Anselm, Rome, Italy.

With half the world living on less than $2.50 per day and with 46.2 million people in the United States living below the poverty line, poverty is a growing concern.

The United States is known all over the world to be a very powerful and rich country. It is not just American people who believe in the American Dream, but also many people from other countries have been dreaming of coming to the US to live in better conditions. Although the US is thought to be a rich country, we still see hungry and homeless people, especially women and children in the streets. Women, who are either married or unmarried, whether supported by their husbands or single mothers with no support, struggle to earn money for food, clothes, safe shelter, and other intangible needs such as love and happiness. When observed closely, it is easy to understand the reasons why this is so. It is because of the wage gap between men and women, the decreased amount of opportunities in having high income jobs, and the fact that more women are the head of their household compared to men, means that the ratio of poor women is rising, and the increased need for governmental help makes “welfare” necessary.

Understanding the definition of poverty becomes very important because it categorizes people into groups which are poor and wealthy. Richard Ropers states that poverty can be understood and described in numerous ways, and that people will not understand the meaning of poverty if they do not recognize the situation of the poor. To be poor means to not have any sustenance, shelter, or any support from family. However nowadays, living alone, or being pushed out of society, being under depression of unchanging destitution also describes poverty. Being fired from a job, losing self-esteem, having no power, or being away from cultural values are also other parameters to describe poverty (Ropers, 25). Ropers also describes “widespread poverty” as a disloyalty to the democratic values’ failure to gain optimism. Successful leaders must aim to provide economical comfort for their citizens. If the majority of the people are not happy because of poverty, it means the government is not as strong to deal with the problems.

The official poverty line is inadmissible as an accurate system to determine the number of poor people. “The US government identifies the poverty line by multiplying the cost of a minimally nutritious diet by three,” then the number of people who live in the same house is calculated (Popers 35). According to the Census data for 2011, 46.2 million people in the United States lived below the poverty line. According to Peter Edelman, a law professor in Georgetown University, even though there are so many hard working people, they are still living in poverty or just barely above the poverty line (Bilitteri, 723). These people are not given the necessary governmental support. There is also a huge gap between the poor and the wealthy people in the US (Cooper, 337). The highest income is $102,000 for households, just 1% of the population, and the lowest earning is $250 for people, who make up 90% of the population, explains Thomas Piketty and Emmanuel Saez (Bilitteri, 723).

One given image portrayed in the media is that “the poor have only themselves to blame” (Mantsios, 638). The problem of poverty is not just one individual’s problem. There is a strong connection between the poor and society. How can a defenseless child be responsible for being poor, not having shelter, and for not earning any money? How can a single or divorced mother with a little baby, without any family help, be expected to work full time without feeding the little one for hours. The term “poor are eyesores” (Mantsios, 637) is not a responsible and thoughtful depiction, rather, it is a way of not being able to see the problems of the people outside and breaking away from the realities of the poor.

More and more women, especially single mothers, are experiencing poverty at a higher rate than the rest of society. Ropers notes that 58% of women are facing poverty, and in this category 48% of the women are the head of their household. According to Albelda and Tilly, 50% of single women are below the poverty line with no support of a husband. In 1993, while 16% of families struggled against poverty, simultaneously, 52% of single mothers, bereft of husband or family support, experiences real difficulty to provide for their basic needs. Most women work at least two jobs at the same time. On the one hand they work at home without earning any money, and on the other hand work outside to earn money (Albelle & Tilly 307). In 1947, about 38% of women were working mostly in paid labor jobs; however, in 1954, the number of working women who were African American, doubled to 54%. Then in 1996 the ratio of working women rose up to 88%, as reported by Albella and Tilly. Even though the number of hard working women is increasing year by year, they are still, except for a small percentage, earning low income and their situation still remains below the poverty line. According to Albelda and Tilly, “women’s earnings are considerably lower than men’s, approximately 70 cents to the man’s dollar.” This difference makes women’s lives miserable as they try to work outside and head the household all at the same time.

For so many years, women have been endeavoring to have the same rights, opportunities, and benefits as men have in their working lives. Although women’s working situations are not as bad as some years ago, women still face graceless and unpleasant discrimination when they look for jobs. Even though women are more educated nowadays and have more opportunities to get a job, there are distinctive wage gaps between men and women. Being the head of the family (Bernstein, 370), giving birth to a child, being under differentiation of occupation, and being sexually abused by employers are some of the common reasons as to why women are behind men when it comes to the benefits of the jobs (Wage Project, 373).

Family responsibilities are one of the most common reasons why women work in a part time job instead of having a full time job (Bernstein, 371). There are so many married or single women who do most of the household responsibilities while trying to work in a job. It is hard to deal with the chores and manage the expectations at work at the same time. For this reason, women in these kinds of situations prefer to work in part time jobs. According to Bernstein, only 25% of women are able to work full day, for the rest of the women cannot dedicate their whole day for work. This being the case, women cannot get the equal remuneration like other women who work in full time jobs. Interestingly, there is also a huge payment gap between women who work full time and men who work full time. Bernstein explains that “on average women work a lot less than men: 1,498 hours a year, vs. 2,219 worked by the typical man.” According to The Wage Project, part time women employees make only 38% of men’s full time yearly salary. Bernstein also mentions the Hartmann and Rose’s data which shows that women employees can have the same benefits if they leave all the family responsibilities behind and come to work behaving like a “traditional man.” The continuation of such unfair treatment is sure to wear down woman, a situation that’s already strained them enough.

Another reason for the wage gap between men and women is the choice a women makes to have a child (Wage Project, 378). Bernstein says after quoting Bergland that after delivering a child, women have to work part time or stay away from work for a while because they do not receive the necessary help from the society.

Nowadays, the position of women employees is assumed to not be as powerful as men’s by most bosses (Wage Project, 377). Even if men and women have the same educational level (Bernstein, 372) and women show more talent, the suggestions made by women are mostly not considered important until, of course, there is no other choice but to accept (Wage project, 375). Bernstein states that women’s yearly salary is much less than men’s, even when they are at the same educational level.

Sexual harassment is another important factor for women to leave their jobs (Wage Project, 377). Sometimes in situations like these, women are unfortunately seen as sexual means by their bosses. If the women, even if they are educated, do not accept the advances of their bosses, they have no choice but to leave or drop out of their jobs, benefits, emotional solidity, and sometimes even their lives (Wage Project, 377). Women encounter such discriminatory situations at the same time while they are dealing with difficulties which they have in their personal lives.

Some people think that people are getting welfare because they are too lazy and they don’t want to work. This theory can be true for just a few people. Making this kind of generalization for all people who are in poverty is derogatory against them. Albelda and Tilly say that the reasons for the poverty experience by single mothers and their families is not because of their laziness or lack of ambition. They are in poverty because they don’t have parent support, they face job discrimination, they earn less than men, and they have the added responsibility of taking care of their children. Blaming the poor is so easy, but being aware of their situation and helping them out of it would be the best thing for all.

Making reforms on the welfare program will make it work well. Some malicious people display themselves as poor to get support from welfare. Under the welfare program, the situation of the applicant must be clarified through an attentive investigation. Determining the really needy persons, eliminating their needs, and opening free high qualified career courses will make welfare a more beneficial program for the poor and will reduce the complaints made against the program.

Being in poverty is mostly not a personal choice. People in poverty don’t just lack food or safe shelter, but they have also lost their hope and happiness. Women, especially single mothers with no support, encounter the most difficult situations of all. Having an income less than men, taking care of their children without any support, facing job discrimination, and heading the family are the most common adversities faced by women today. Receiving no government support will not help reduce their problems; on the contrary, having access to effective government support will let people in poverty know that there are people with helping hands, people who care about them and who think about them. Poor people need helping hands, at least to not let them give up their hopes and dreams.

References

• Albelda, Randy.,& Tilly, Chris. 2001. “‘Women, Income, and Poverty’: There’s a Family connection.” Race, Class, and Gender in The United States. Ed. Paula S. Rothenberg. New Jersey: Worth,. 305-314.
• Billitteri, Thomas J. “Gender Pay Gap.” CQ Researcher 18.11 (2008): 241-264. CQ Researcher Online. CQ Press. Elisabeth Sturn Library, Reno, NV. “Domestic Poverty.” CQ Researcher 17.31 (2007): 721-744. CQ Researcher Online. CQ Press. Elisabeth Sturn Library, Reno, NV. Cooper, Mary H. “The Working Poor.” CQ Researcher 5.41 (1995): 969-992. CQ Researcher Online. CQ Press. Elisabeth Sturn Library, Reno, NV. 5 Nov. 2008 “Income Inequality.” CQ Researcher 8.15 (1998): 337-360. CQ Researcher Online. CQ Press. Elisabeth Sturn Library, Reno, NV. 5 Nov. 2008
• Glazer, Sarah. “Welfare Reform.” CQ Researcher 11.27 (2001):601-632. CQ Researcher Online. CQ Press. Elisabeth Sturn Library, Reno, NV. 5 Nov. 2008 Berstein, Aoron. 2007. “‘Women’s Pay: Why the Gap Remains A Chasm.” Race, Class, And Gender in The United States. Ed. Paula S. Rothenberg. NJ: Worth. 370-372. Mantsios, Gregory. 2007. “‘Media Magic: Making Class Invisible.’” Race, Class, And Gender in The United States. Paula S.Rothenberg. New Jersey: Worth. 636-643. Ropers, H. Richard. 1991. Persistent Poverty, New York: Plenum. Rothenberg, Paula S. (Ed.). 2007. The Wage Gap And Its Costs. Race, Class, And Gender in The United States. NJ: Worth. 373-378.

Let us imagine the earth as a small sphere before us. If we throw an object from the North Pole toward point A on the equator line, the object follows a curved line towards the right side and reaches point B, not point A. Likewise, an object thrown from the South Pole towards the same point A will follow a similar line curved in the opposite direction. These cases have a common point. An object rolling on a rotating ground moves on a curved line. This curved line, instead of a straight one, is explained with reference to the force of acceleration. This force is named after the French engineer, Coriolis who explained it in 1835. If this force-which is generated by the earth rotating around its own axis-did not exist, then air movements and ocean currents, and consequently the climate conditions of our world, would be different than they are. The objects in our example, thrown from the two poles, go in different directions, because the world rotates counter-clockwise when looked from the North Pole, and clockwise from the South Pole.

The air over the equator receives the sun’s rays at a broad angle. It rises up after gaining heat and is replaced by colder air coming from distant latitudes. Air convection begins in connection with these heat changes. So if the world did not rotate, the air on the Poles would get heavier with cold air and come down. Then, it would be replaced by hot air from lower latitudes. The air at the equator would rise up with gaining heat and would move until reaching the Poles where it would come down after losing heat. Then, it would return to the equator, this time very close to the ground. In this case, the world would probably be an uninhabitable place with cold and fierce winds blowing all around. And of course, the side facing the sun would be very hot and the other side would be very cold.

Instead, the Coriolis effect makes these great atmospheric air masses move over our rotating earth. The hot air rising up from the equator moves towards the poles with a curved course thanks to the Coriolis effect (Figure 4). As this air current approaches the latitudes around 30 degrees, it loses heat and descends. A part of the descending air begins to move back toward the equator, but it follows a curved line again owing to the Coriolis effect. So this last curving forms the “trade winds.” In the past, sailing ships traveled from Europe to America for the purpose of trade; thus, these winds were named as trade winds. This air circulation between the equator and the 30-degree meridians is known as Hadley circulation. These air currents cause heavy rainfall in the equatorial region and the consequent formation of rain forests, which are considered as the lungs of our planet, and also they cause the formation of deserts around the region where the dry and hot weather are pure blessings for us. They are a blessing because the airborne dust rising from the desert fertilizes the rainclouds and plays a critical role for rainfall.

The air over the poles becomes cold, and it causes another air current as it becomes heavier and starts to descend. As the lowered air moves toward the equator, it changes course with the Coriolis effect. At the same time it begins to gain heat and ascend. At the latitudes where water ascends by gaining heat, a rain climate prevails. This polar air cycle is seen between latitudes of 60-90 degrees.

Some part of the air current, which descends down around 30 degrees of latitude, moves toward the poles at a low level. Also, some part of the air which comes from the poles and ascends begins to move towards the equator. So a third air cycling begins between the altitudes between 30-60 degrees. The “western winds” are brought forth from this third cycle. During the time of sailing ships, these winds were used to traveling from America to Europe (Figure 4).

In order for these air cycles to happen, the earth’s rotation around its own axis is not sufficient; its speed and atmospheric mass also play an important role. If the earth rotated slower, the Coriolis Effect would be too weak to give way to a triple air cycle. For example, since Venus rotates too slowly, there is only a single air cycle in its atmosphere. Another factor, as we mentioned, is the mass of the atmosphere. Since the atmosphere of Mars is thin and its mass is relatively less, the Coriolis Effect is too weak and there is only a single air cycle.

Coriolis Effect prevents the air current from following a straight course and the isobars form twisters as they proceed. Therefore, hurricanes in the Northern hemisphere move counter-clockwise, and those in the south move clockwise (Figure 5). Naturally, these main atmospheric movements are not the only ones. A region’s climate is dependent on several factors such as landscape, night-day heat differences, and the like. Therefore, the climatic conditions on the earth have a very complex structure. Even when we consider just these few factors discussed here, it is evident that there are countless parameters that make human life possible in our planet, and each one is finely adjusted. Even slight changes in rotation and the mass of the atmosphere would result in a dramatically different planet Earth.

The ocean currents

Movement of air masses affects the water on the ocean surface as well. Thus, wind-generated surface currents are born. These currents are parallel with the relevant winds. It is a well-known fact that these huge bodies of water change the climate of the regions they pass. Therefore, two places at 54 degrees of latitude show a surprising difference: there can be a polar bears’ park in Ontario, whereas palm trees and tropical fruits can grow in Belfast thanks to the Gulf Stream. There are other warm ocean currents that pass from Brazil, and the north and south of the equator. Some of major cold surface currents pass from Labrador, Canada, the Falkland Islands, and Peru. Warm currents soften the climate of the regions they pass, while cold currents provide sea creatures with rich food, and they are important areas of fishing.

The impact of the wind on ocean water normally reaches as deep as 100-200 meters, and even 1,000 meters in some cases. The Coriolis effect has a determining role on the direction of the currents. These currents on the move make a turn when their way is blocked by land. Thus, the succession of ocean currents becomes a cycle, and they form the great current cycles named as “gyre.” They turn clockwise in the Northern Hemisphere and counter-clockwise in the south.

There are five main ocean circulations on earth and each of them consists of four streams. These currents are at the north and south of the Atlantic Ocean, the north and south of the Pacific Ocean, and one in the Indian Ocean. The North Atlantic circulation is made up of the Northern Equator Current, the Gulf Stream, North Atlantic Current, and the Canary Current.

With the Coriolis effect, a blessing of wondrous scale, food chains are brought to life in the ocean and around coastal regions. The ocean waters are set in motion by the winds generated by the Coriolis effect, but they do not strictly follow the winds that activated them. With a deflection of nearly 45 degrees they move right in the Northern Hemisphere and to left in the Southern Hemisphere.

The effect of the winds weakens in the deeper ocean waters, and then the Coriolis effect becomes dominant. Thus the direction of ocean water carried in the Northern Hemisphere is vertical to the wind direction and towards the right. This condition causes ocean waters to be pushed towards the circulatory center, and the water level there rises about 2 meters.

As rising waters move down with the effect of gravity, the Coriolis effect comes to the stage again to give way to another current in the same direction within that current. The waters that were rising toward the center begin to sink, and they form a new vertical current. For the same reason, the separation of the water current to the right and left directions around the equatorial regions gives way to the waters at the bottom which then come to the surface. At these places, the water level decreases a little. This “upwelling” phenomenon has very important results. Dead organisms sinking down are broken down by bacteria in the deep waters. When this nutrient-rich water returns to the surface, it is a great blessing for so many sea creatures. It is a striking fact that the rotating of the earth is a means for providing many living beings with sustenance. All of these finely adjusted balances on our planet, which we mostly take for granted, provide reflecting minds with food for thought.

She might as well save her breath. After carrying water in pails and plastic bins from the first to the fourth floor of the building where we live, I know better than to waste a drop of it.

Moms love to warn though, so there she goes again: “We have so little left. Use it sparingly. Make it last until evening.”

In the evening my sister and I will start our summer ritual-water carrying-like the rest of our neighbors who don’t live on the first floor. The town’s water reserve level drops so low in the summer that the water pushes itself up the pipes to the first floor, but no further. On the first floor the water flows from the taps while in the higher floors it carries only growling sounds, like a monster in a bad mood.

So we use it sparingly, only when strictly necessary.

In winter the water runs through the taps of the whole building, not discriminating on the terms of the floors, three times a day for an hour and a half. Every household is busy filling every useable container in their possession during that time.

In the summer our survival grimly depends on the mercy of our first floor neighbors. Twelve families, three for each floor, carry their water up four flights of stairs, utilizing pails, bins, bottles, even cauldrons for this vital cause. Children are the most diligent carriers.

The clock on the wall reminds me that I need to get ready for the water’s evening course. The water won’t come for fifteen more minutes, but I must get in line at my first floor neighbor’s door to be ready.

I grab a pail and two bottles in a plastic bag. I run down the worn smooth stairs.

Soon, other neighbors join the march.

I am third in line.

The first is our next door neighbor, Auntie Jazja. She handles the ordeal quite normally. “I have seen worse,” tell her eyes.

Lina comes second. She lives in the fifth floor, above us. Three years older than me, but not much stronger, she holds an aluminum pail with a blackened bottom. Who knows how many times it has been used to heat water on the stove?

Behind me, fourth in line, is my best friend, Dita. She is restlessly switching hands with her glass bottles clinking noisily. She will break them sooner than she fills them with water. The line grows longer each minute.

Everybody talks with those nearby. Lina and Dita are chatterboxes. I am caught in the crossfire of their words.

I worry that our buzz will annoy our gracious first floor neighbor and she will shoo us away.

When the water starts gushing in we fall silent, listening in reverie. It is proper to wait ten to fifteen minutes for the household to fill their share of water, before the first in line is urged to knock.

I am glad Auntie Jazja is to do that today. A senior lady is always hard to turn down.

Soon enough she goes inside, greeting and blessing the benevolence of the neighbor who seems unpleased opening the door to a bunch of thirsty people. As we hear the water fill Aunties Jazja’s glass bottle, we let out a breath of relief.

Meanwhile the chatting resumes. We talk of anything but water.

Lina runs inside with her pail when Auntie Jazja calls her name, letting her know that she is almost done.

Auntie Jazja comes out carrying four one-liter glass bottles, two in each hand. A thin layer of condensation has formed on them. I think that is the picture of perfection. Those drops forming and dripping on the transparent glass refresh my soul.

Lina, shouts my name. It’s my turn. My heart beats in panic for fear that the moment I place my bottle under the tap, the water will stop flowing. Instead, I will hear that horrible whistle which I dread so much.

I enter, greet the lady of the house and head toward the bathroom. Lina is filling her pail, keeping a short hose in it. The water is forming turbulence, increasing in level, making me feel dizzy a bit with impatience.

When she withdraws her pail, I very quickly put my own under the hose, not wasting a drop of water or a second of time. We have to race with time as well, you see. There are people in line waiting.

I fill my container and call my best friend who appears in a second by my side.

I thank my neighbor, although I will return for more water in a few minutes. She knows that a pail and a few bottles of water are not enough for a family of six. I will make two more rounds if the time permits.

As I go up the stairs, I see a trail of water drops. Lina’s pail must be leaking. How silly! By the time she reaches home, half of the water will be gone. I look behind me to see if my pail is leaking, too. I am glad it is not.

At the second floor I feel my arm tighten. Warm numbness creeps up to my shoulders. The pail is heavy; my limbs stretch while my back complains. I put down my burden and I notice a fine red line forming in my palm by the handle of the pail.

I feel hot, and sweat is roller coasting down the bones of my spine. I will drink half a bottle of water to quench my thirst.

I take a deep breath, grab the pail and the bottle and step up the stairs. A frightful thought invades my mind. I had heard from Lina that carrying heavy weight was extremely harmful to young girls. It could badly damage the back, and also be disabling in childbearing. Although nine times out of ten I don’t believe what Lina tells me, this time I worry. Could it be true? My breathing becomes heavier and my muscles tenser. Tears swell around my eyes. I decide not to worry. Why have children anyway? To send them downstairs to carry water until they break their backs?

As I approach the third floor, I come across my little sister hurrying down the steps with one-liter plastic bottles under each arm. She smiles. I remember once when I was her age, I fell on the last steps of the fourth floor. I hurt my knee and my bottles rolled down, mercilessly spilling the water. I couldn’t stop crying, pretending that it was my knee that made me cry so much when it was the waste of water that broke my heart.

I leave the pail and the bottles in front of my door and as I catch my breath, I listen to Lina’s mother scold her daughter for carelessly spilling half of the pail on the stairs. It’s not her fault. The pail is leaking. But I would rather not interfere.

I ring the bell. Mom appears with a worried look. A shade of pity lingers on her face as she takes the full containers inside, and with an air of apology hands me the empty ones. “My poor girl” her eyes lament. I have noticed that the more I go up and down to make Mom happier with the abundance of water she could use, the sadder she gets. That’s when I feel most miserable.

As she closes the door, I overhear her curse the incompetent government, blaming the infrastructure for our misery. I know the government blames the lack of rain. When the rain vindicates itself in fall showers the government will blame it again, this time for the flood. You see how hopeless it is?

I go down the stairs, this time with two plastic pails. I feel so light that I wish I would never reach the first floor, but I do. Lina is again in front of me. The chatting continues as intensely as the flow of water.

Lina produces a photo from her dress pocket. A young man poses in front of greenest garden I have ever seen. The blue of the sky and the whiteness of his teeth contrast attractively, but I can’t take my eyes off the vast lawn behind him.

“This is my cousin, Alban,” Lina says. “You remember? He immigrated to France four years ago. He is doing quite well. He works in the Luxembourg Gardens in Paris,” she says proudly, as if her cousin had become the mayor of the city.

I am busy sorting out something confusing though. Isn’t Luxembourg a country in Europe? Then what business do Luxembourg Gardens have in Paris, the capital of France? I doubt Lina has any idea where France or Luxembourg is, so I keep my peace.

“Do you know they water the grass in this humongous garden with sprinklers that turn on automatically?” she asks.

And before I express my admiration, she goes on about her cousin’s high salary, the car he drives, his clothes and the gifts he sent to them last year.

“I envy him, you know,” she concludes. Her eyes are daydreaming.

“I envy the grass,” I think to myself, but I don’t say it aloud. I would break into tears if I pronounced how worthless I felt, and then I would have the whole line asking what was wrong. What is it like to lie under the sun and be sprinkled with thousands of silvery droplets that replenish every cell of your being? What makes the grass of Luxembourg luckier than me? A surge of envy fills my heart.

Lina counts with delight all the things her cousin has, unaware that she is counting all the things we lack as well. She gets on my nerves. I am saved only when her name is called. She goes in, leaving me with pails full of despair.

I did five rounds of water carrying today. Some neighbors had gone out of town leaving the line, ever so graciously, to us. After dinner I fell asleep listening to the news anchor woman explaining that this year’s drought was the worst ever.

With her drought-warning words echoing in my head, I dived into the world of sleep, and I dreamed. I saw my town was flooded. Angry rivers of water carried furniture, cars, and trees floating in the streets. Among them I saw a body floating, undisturbed. Then I recognized that it was my body. My eyes were closed peacefully. I looked like I was sleeping. In dreams you can do anything, even sleep on a flood’s current. A radiant smile of intact elation lingered on my face. I remember thinking out loud, “I don’t know whether I am dead or not. Yet, no doubt I am happy. So happy that I don’t envy the grass of Luxembourg anymore.”

Mirkena Ozer is pursuing MA in women studies at the University of Georgia, Atlanta. 

instead of a picture, multiplication table adorns my kitchen wall.

I have 8 arms like an octopus reaching in every direction.

Nobody can worry as much as I do.

There is always some stain on my clothes that detergent won’t remove.

I am a mother,

my notebook has dinosaurs drawn on it

the wall of my bedroom a little artist’s exhibition.

Me and my cell phone fall apart too often.

I lose my keys every other day.

I am a mother

and a pediatrician though I never went to medical school.

I play the cook, the nurse, the teacher, the driver, the singer

selfless like the rain, the earth, the sun.

I am a mother,

small things make me cry for joy.

like little notes that say “luv mom”

or sketched portrait with ugly teeth and fuzzy hair,

every line reflecting admiration and care.

I am a mother,

my heart deep and vast like an ocean.

I am a mother,

paradise lies under my feet.

Mirkena Ozer pursues MA in creative writing at the University of Georgia, Atlanta.

A group of scientists attempted to do just this; they used focused electron rays as their writing implement, rather than a pencil. Some researchers at Liverpool University developed a power source that can draw a line of light no thicker than the width of two atoms. This line is so narrow that if millions of them were to come together they would still fit inside the line drawn by the thinnest pencil lead. Drawing such lines would certainly not be something one could do by hand. The smallest vibration would cause the lines to converge. The only way to successfully do this is to send the electron rays by computer.

If we think that nearly 4 trillion atoms can fit on the head of a pin, which is accepted as being equal to one millimeter square, then we can understand how small atoms are. If we arrange the atoms as squares consisting of 100 atoms each, with 10 atoms at every edge, this means that we can get 40 billion of these squares on the head of a pin. We then put one letter into every one of those squares, with some squares being used as blank spaces between the words. If we think that on average there are six letters in a word, we can use 4.7 billion words to fill only 28 billion of our squares. There are nearly 50 million words in the Encyclopedia Britannica. Previously, it was thought that it would not be possible to fit the encyclopedia on the head of a pin, but now we can see that only one percent of the pinhead would be used up. Even if every letter were written ten times larger, it would still fit on the head of the pin. What a huge area a pinhead is! To see if their theory would work the researchers at Liverpool University placed one page of the encyclopedia on the pinhead.

One may wonder what use writing an encyclopedia on a pinhead could possibly be. We wouldn’t be able to read it, so is it not just a futile exercise? In the future, this technology may lead to some new developments, but for now, we can give an example about how this technology could be used by looking at the works of art created by the Divine Power. One of the wonderful examples of “books” in which atoms are used as letters is in the cell of a chromosome. God Almighty writes with His Pen of Power the coded programs and characteristics for living beings in the DNA molecules. The Human Genome Project has made it possible for us to read the genes in chromosomes; each of these can be compared to a library or a data bank. This development has shed a great deal of light on the biological secrets and features of the human being, which can be considered to be a “minor universe.”

How can so much knowledge fit into the DNA? DNA molecules are found in the chromosomes, which are packaged in the form of chromatin in the nucleus of a cell. If a DNA molecule was unfolded and each piece was to be laid side by side, it would measure up to 6 meters. In order to understand how many atoms can be found on such a long DNA, the following example may be of some assistance: if we place 75 million hydrogen atoms next to one another we make a hydrogen chain that is 1 cm. long. As each chromosome is 6 meters, and there are 46 chromosomes in a cell, the total length of the chromosomes in just one cell is approximately 300 meters. Now, if we remember the two-atom wide line drawn by the researchers at Liverpool University with the electron rays, (i.e., a million times thinner than the line drawn by a pencil), then we can imagine how small the DNA chain is in its folded state. In fact, this means to compress human being called micro cosmos as chromosome in 1/100.000 or 1/1.000.000 of one cm. Of course, this miraculous task is not the work of lifeless and unconscious beings called atoms or the result of confused coincidences, but must be the work of God, Whose every job is miraculous and Whose knowledge and power is eternal.

The Qur’an on an atom

Now, can the Qur’an be written on an atom? Since atoms are too small to be seen with the naked eye, let’s think of an apple that is the size of the earth; thus we will better be able to see the atoms, and the subject will be more easily understood.Like everything, an apple is also made of atoms. In such a huge apple, an atom is the size of a football. But still we cannot see the nucleus of the atom, including the neutron and proton. The space between the nucleus and the electron is a vast distance in the scale we are using. The radius of this distance is a ratio of 1/100,000 for the electron to the atom. If we imagine this electron to be in the size of a marble with a radius of 1 cm, this means that the nucleus is 1,000 meters away from the marble. When we enlarge the nucleus to the size of a football, the smallest atom (e.g. the hydrogen atom) is a sphere with a 2,000 meter radius. Then, how many Qur’an copies can we write using electrons, which are as big as marbles, or neutrons and protons which are 1,836 times larger than electrons, as letters. The Qur’an can be written 10 times, maybe even a 100 times on such a huge surface. One of the important things to note in these examples is that atom are almost entirely hollow. If we try to fill atom with nuclei, we need as many nuclei as 1015. If we write the Qur’an not only on the surface of the atom, but also on the inside and the cavities of that huge sphere, then thousands of Qur’an copies, each of which has 300,620 letters, can be written using atom nuclei as letters.

Amazing similarity

There are a hundred trillion cells in one person, whereas, the science of the human being can be summarized in just one cell. But from the aspect of what is contained in just one cell, the human being is more profound than the greatest written works. If a cell were conscious, most probably it would be just as amazed that it can be the index of humans as we are amazed at the concept that we are the index for the universe.

A human being is 1028 times larger than an atom. The sun is 1028 times larger than a man. This cannot be coincidence; therefore, must there not be some relation between the human, the atom and the sun?

The world is nothing more than one point in the solar system; a person is also like one point in the world. The Owner of the Book of the Universe, when summarizing this Divine Book known as the universe, encapsulated it in the human being, and when summarizing humans He encapsulated them in the tiny book written with the atoms called the genome. It is an interesting fact that the Exalted Creator created the solar system similar to the system in the atom. This indicates that the Creator of the universe is the same as the Creator of human beings. He created spheres like the sun and all other complicated systems and the atom to make us think about His artistry and to astonish us with their beauty.

In this article, we will delve a little deeper into this magnificent miracle of God: the mathematics of nature.

FLOWERS:

For example, look at the pictures given below. For 1-petalled flowers, we offer white calla lilies; for 2-petalled flowers, we offer the very rare euphorbia; and for 3-petalled flowers trilliums, lilies, and irises.

<cellpadding=”15″ cellspacing=”15″>White Calla Lilly

Trilliums

Did you ever wonder why 4-petalled flowers are so rare, and why everyone gets excited when they find a 4-leaf clover? The reason for this is because such flowers are very rare, for 4 is not a Fibonacci number. Some violets and bluets also have 4 petals.

Flowers with 5 petals are rather common. Among them are buttercups, wild roses, larkspurs, and columbines.

Examples of 8-petalled flowers are bloodroots and delphiniums. Examples of 13-petalled flowers are ragworts, corn marigolds, and cinerarias; those with 21 petals are daisies, asters, and chicories; and those with 34 petals are oxeye daisies, sunflowers, plantains, and pyrethrums.

Some families of daisies, such as the michaelmas daisies from the asteraceae family, have 55 and 89 petals.

Seed and flower heads

The echinacea purpura is a member of the daisy family native to the Illinois prairie. You can see in Figure 1 that the orange œpetals seem to form spirals curving both to the left and to the right. At the edge of the picture, if you count those spiraling to the right as you go outwards, you will notice that there are 55 spirals (a Fibonacci number). A little further toward the center, you can count 34 spirals (another Fibonacci number). If you count the spirals going the other way, you will see that the pair of numbers (counting the spirals curving toward the left and toward the right) are neighbors in the Fibonacci number series.

The same happens in many seeds and flower heads, among them sunflower seeds, daisies, pineapples, and pine cones. The reason for this is that such an arrangement packs the optimal number of seeds so that no matter how large the seed head is, the seeds are always packed uniformly at any stage. As they are the same size in any given area, there is no crowding in the center and no scarcity at the edges.

The spirals form a pattern: The œcurvier ones

appear near the center, while the flatter ones, which are more numerous, appear the further out you go. Thus the number of spirals we see in either direction differs according to the size of the flower’s head. On a large flower head, we see more spirals further out than we do near the center. The numbers of spirals in each direction are (almost always) neighboring Fibonacci numbers!

Let’s observe the spirals in these beautiful arts of the Infinite Artist. Consider the daisy. In the close-packed arrangement of tiny florets in the daisy blossom’s core, you can see the phenomenon in an almost two-dimensional form. As shown in Figure 2 there are 21 (a Fibonacci number) counterclockwise spirals and 34 (another Fibonacci number) logarithmic or equiangular spirals. In any daisy, the combination of counterclockwise and clockwise spirals generally consists of successive terms in the Fibonacci sequence.

The Math Behind It

Botanists have shown that plants grow from a single tiny group of cells right at the tip of any branch or twig belonging to a growing plant or tree. This tip is called the meristem. They grow in size after their formation, but new cells are formed only at such growing points. Cells further down the stem expand, and thus cause the growing point to rise. This means that a growing plant produces seeds at the flower’s center, and that those seeds then push the other seeds outward. Each seed settles into a location that turns out to have a specific constant angle of rotation relative to the previous seed. This constant rotation forms the spirals.

Consider the following case. There are n seeds in the arrangement. The nearest seed is seed 1, the next one is seed 2, and so on. If each seed has an area of 1, we have a total area of n and a circle with a radius of from the area formula (Area= ). Given this, the distance from the center to each seed is proportional to the square root of its seed number. If we call this angle alpha, the angle of seed k will be alpha*k. So we can easily describe the location of any seed in polar coordinates with and theta=k*alpha.

If we chose an angle of 0.15 (54A) the result will be far better. But we will be done again after 20 seeds, for 20*0.15=3, so after 3 complete turns we will be back on the same line. If we choose 0.48, which is a little bit better than 0.15, we will come back to the original line in 25 rotations.

Therefore, speaking logically, if we choose an irrational number we will not return to the original line. Of course we will get close to it, since every irrational number has some kind of rational approximation. In nature, we mostly observe the so-called golden ratio, an irrational (1.618 = ), which is the root of the equation , which is the limit of the ratio of two consecutive Fibonacci numbers.

With this angle of rotation, each seed is rotated approximately 1.618 revolutions from the previous seed (i.e., 0.618 revolutions or 0.618*360=222.5A). Notice how well distributed the seeds appear; for there is no clumping and very little wasted space. Although the pattern grows quite large, the distances between neighboring seeds appear to stay constant. In nature, you can see that plants grow their seeds simply where there is the most room.

It is really amazing that a single fixed angle can produce the optimal design no matter how large the plant becomes. For example, once a leaf’s angle is fixed, that leaf will œdo its best not to obscure the leaves below and œdo its best not to be obscured by any leaves that will grow above it. Similarly, once a seed is positioned on a seed head, the new seeds continue to push the older ones out in a straight line. However, it retains the seed head’s original angle. The seeds will always be packed uniformly on the seed head regardless of the head’s size. The principle that a single angle produces uniform packing no matter how much growth appears thereafter was proved mathematically only in 1993 by the French mathematicians Douady and Couder.

We frequently observe the golden ration in nature. In addition, we can try flowers and flowers, at least mathematically and as models.

Conclusion

We look at nature and see God’s creation. Most people just look at the general design, but others also study the seeds and their designs. As the Qur’an’s first verse tells us to œRead, in the sense of reading the signs in nature (the Qur’an was revealed to a largely illiterate people who had no significant body of written literature), we should understand this as an indication to analyze nature.

As a mathematician, I see that God has arranged everything in nature according to a mathematical order. He puts the maximum number of seeds in a minimum area. Bees use hexagons to store the maximum amount of honey in a minimal space. This fact is even mentioned in Qur’an 16:68: Your Lord revealed to the bee. Those who believe in evolution say that the picture is very clear. But there is a great art in front of us, one which is very well balanced and in perfect accord with mathematical harmony. This shows that there is no luck or chance in the world, and that everything is based on the rules that God has laid down for His creation.

Footnote

1. Fibonacci (Leonardo da Pisa, c1175-1250): The son of a Pisan merchant who also served as a customs officer in North Africa. He travelled widely in Barbary (Algeria) and was later sent on business trips to Egypt, Syria, Greece, Sicily and Provence. In 1200 he returned to Pisa and used the knowledge that he had gained on his travels to write Liber abaci, in which he introduced the Latin-speaking world to the decimal number system. Fibonacci numbers begin with 1,1 and the next term is the sum of the two previous terms. The first ones in the series are 1,1,2,3,5,8,13,21,34,55,89,

References

Mathematics Magazine 75:3 (June 2002): 163-73.

http://ccins.camosun.bc.ca/~jbritton/fibslide/jbfibslide.htm.

G. J. Mitchison, œPhyllotaxis and the Fibonacci Series, Science 1965, 270-75.

P. Stevens, Patterns in Nature (New York: Little Brown and Co.,1974).