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Euclid, also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the “Father of Geometry”. He was active in Alexandria during the reign of Ptolemy I (323–283 BC). His Elements is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century.In the Elements, Euclid deduced the principles of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory and rigor.
Although many of the results in Elements originated with earlier mathematicians, one of Euclid’s accomplishments was to present them in a single, logically coherent framework, making it easy to use and easy to reference, including a system of rigorous mathematical proofs that remains the basis of mathematics 23 centuries later.
There is no mention of Euclid in the earliest remaining copies of the Elements, and most of the copies say they are “from the edition of Theon” or the “lectures of Theon”, while the text considered being primary, held by the Vatican, mentions no author. The only reference that historians rely on of Euclid having written the Elements was from Proclus, who briefly in his Commentary on the Elements ascribes Euclid as its author.
Although best known for its geometric results, the Elements also include number theory. It considers the connection between perfect numbers and Mersenne primes, the infinitude of prime numbers, Euclid’s lemma on factorization (which leads to the fundamental theorem of arithmetic on uniqueness of prime factorizations), and the Euclidean algorithm for finding the greatest common divisor of two numbers.
The geometrical system described in the Elements was long known simply as geometry, and was considered to be the only geometry possible. Today, however, that system is often referred to as Euclidean geometry to distinguish it from other so-called non-Euclidean geometries that mathematicians discovered in the 19th century.
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology. Together with Plato and Socrates (Plato’s teacher), Aristotle is one of the most important founding figures in Western philosophy. Aristotle’s writings were the first to create a comprehensive system of Western philosophy, encompassing morality, aesthetics, logic, science, politics, and metaphysics.
Aristotle’s views on the physical sciences profoundly shaped medieval scholarship, and their influence extended well into the Renaissance, although they were ultimately replaced by Newtonian physics. In the zoological sciences, some of his observations were confirmed to be accurate only in the 19th century. His works contain the earliest known formal study of logic, which was incorporated in the late 19th century into modern formal logic.
Archimedes of Syracuse (Greek: Ἀρχιμήδης; c. 287 BC – c. 212 BC) was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and an explanation of the principle of the lever. He is credited with designing innovative machines, including siege engines and the screw pump that bears his name. Modern experiments have tested claims that Archimedes designed machines capable of lifting attacking ships out of the water and setting ships on fire using an array of mirrors.
Archimedes is generally considered to be the greatest mathematician of antiquity and one of the greatest of all time. He used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave a remarkably accurate approximation of pi. He also defined the spiral bearing his name, formulae for the volumes of surfaces of revolution and an ingenious system for expressing very large numbers.
Archimedes died during the Siege of Syracuse when he was killed by a Roman soldier despite orders that he should not be harmed. Cicero describes visiting the tomb of Archimedes, which was surmounted by a sphere inscribed within a cylinder. Archimedes had proven that the sphere has two thirds of the volume and surface area of the cylinder (including the bases of the latter), and regarded this as the greatest of his mathematical achievements.
Unlike his inventions, the mathematical writings of Archimedes were little known in antiquity. Mathematicians from Alexandria read and quoted him, but the first comprehensive compilation was not made until c. 530 AD by isidore of Miletus, while commentaries on the works of Archimedes written by autocues in the sixth century AD opened them to wider readership for the first time. The relatively few copies of Archimedes’ written work that survived through the Middle Ages were an influential source of ideas for scientists during the Renaissance, while the discovery in 1906 of previously unknown works by Archimedes in the Archimedes Palimpsest has provided new insights into how he obtained mathematical results.
Ancient Greek philosopher and natural scientist from Miletus. The edge of the falls in the 6th century BC (died between the years 528 and 525). Anaximenis considered as the beginning of everything “air”, starting from the material body that spreads diffusely around us and his mobility to enable the everyone observes. The “air” is the only item normally distributed in space and as such is suitable for continuous, contain and hold everything. And the most important is that the air is the thinnest material which is identified with the “spirit” or “soul”, the beginning of life. The world is conceived as one large living organism that breathes air and animated by him. And the human soul is but a thin breath of air keeps alive the human body. In the system of Anaximenis seen as the main feature, the transfer of differences of temperature differences in density: warmer – thinner, cooler – denser. So all things fall at a certain level on the cosmic temperature range, which corresponds to a certain extent the elemental density of matter. Excerpts of his philosophy are the writings of Aristotle, Plutarch, and of Hippolytus Aetia.
In mathematics, a conic section (or just conic) is a curve obtained as the intersection of a cone (more precisely, a right circular conical surface) with a plane. In analytic geometry, a conic may be defined as a plane algebraic curve of degree 2. There are a number of other geometric definitions possible. One of the most useful, in that it involves only the plane, is that a conic consists of those points whose distances to some point, called a focus, and some line, called a directrix, are in a fixed ratio, called the eccentricity.
The conic sections were named and studied at least since 200 BC, when Apollonius of Perga undertook a systematic study of their properties.
St. Benedetto School presented the following dossier on conic sections
A science fair experiment is generally a competition where contestants present their science project results in the form of a report, display board, and models that they have created. Science fairs allow students in grade schools and high schools to compete in science and/or technology activities.
At the meeting in San Benedetto, our students participated in a science fair. Each school presented a scientific project and these are the results …
- I’m a sea Turtle Do you know my diet?
In this category we show the items related to the world of mathematics and science. We will design a magazin in each project meeting. The articles are written by students and teachers from each of the schools participating in the project.
Prof. Dr. Oktay Sinanoğlu
He is the youngest person in the past century to attain a status of professor
Oktay Sinanoğlu is a Turkish scientist of theoretical chemistry and molecular biology. He was the youngest person in the past century to attain a status of professor when he earned the status at the age of 28. Also, he has been nominated to Nobel award in chemistry twice. He is also one of the most successful people about protection of Turkish Language.
Sinanoğlu was born on February 25,1935 in Bari, Italy where his father served as a consul general. In 1939 by the commence of World War II, the family returned to Turkey. In 1953, he attended the high school “TED Yenişehir Lisesi” in Ankara, and after graduating won a scholarship for education of chemistry in the USA. In1956, he graduated from Berkeley in chemical engineering with the highest rank. In only eight months, he graduated from MIT in 1957 with the highest degree. In two years, he finished his doctorate at the University of California at Berkeley. In 1960, Sinanoğlu started working as associate professor at Yale University. He theorized the “Many-Electron Theory of Atoms and Molecules” in 1962 by solving a mathematical theorem that had been unsolved for 50 years. The same year, he earned the “Alfred P. Sloan” prize. As appointed professor in 1963 at the age of only 28, he became the youngest person in the past century at Yale to attain the status as a full professor. He got his second life-long chair in Yale in Molecular Biology.
Sinanoğlu was the first to earn the Alexander von Humboldt’s Science Prize in 1973. In 1975, he won the award of Japan’s International Outstanding Scientist. In the 1980s, he theorized a new method from 180 theories concerning mathematics and physics, considered revolutionary, which enables chemists to predict the ways in which chemicals combine in the laboratory and to solve other complex problems in chemistry using simple pictures and periodic tables. Also, he took his place in the Academy of Arts & Sciences. In 1993, he moved to Turkey to teach at the Yıldız Teknik Universitesi, and officially retired at the age of 67. Yet his scientific researches has not ceased.
He received several international and local awards concerning his scientific and social contributions and efforts. He has been to many places includingAsia and Latin America. He tried to establish strong communications between Japan, India and Turkey. Because of his efforts, he was given the title “Special Emissary” of Japan-Turkey. He worked for better education, purified language in Turkey most of his life and strived to form a conscious generation.
Fuat Sezgin: A life devoted to understanding Islam’s golden age of science
Fuat Sezgin founded two museums in İstanbul and Frankfurt that bring together hundreds of replicas of scientific instruments, tools and maps, mostly belonging to the golden age of Islamic science.(PHOTO Sunday’s Zaman)
25 December 2011 /MAHMUT ÇEBI
Fuat Sezgin, a Turkish researcher and historian who has devoted his life to uncovering the roots of Islamic civilization and how big a role the Islamic world played in the emergence of today’s modern civilization, has always found it astonishing that so little is known about the scientific achievements of the Islamic world.
Known as the “conqueror of a missing treasure,” Sezgin was inspired by Helmut Ritter, a renowned 20th century German scholar of oriental studies and someone who used to teach courses on Islamic sciences and orientalism at İstanbul University.
Ritter inspired Sezgin to begin his search for the Islamic scholars’ contributions to modern science. Sezgin defines the moment he met with Ritter as “the time when I was born again.” He said Ritter told him to read at least 17 hours a day if he wanted to become a real scholar.
During one of Ritter’s courses, Sezgin asked him whether or not there was an important Islamic mathematician and was surprised by his answer: “There are as many mathematicians in the Islamic world as there are great figures in Greece and Europe,” Ritter said. The reason why Sezgin was astonished by Ritter’s answer was due to the fact that one of his teachers at primary school told him that Muslims scholars used to believe that the earth was located on the horn of an ox.
Sezgin said it was following the statements by Professor Ritter that he started to take notice of the fact that the Islamic world had made significant contributions to the history of general sciences and decided to search for what those contributions were.
“From that day on, I decided to learn about the contributions of the Islamic world to science and to make a contribution to science myself if possible. Despite my young age, I assumed the responsibility of writing the ‘History of Islamic Sciences.’ I worked day and night on that book,” Sezgin said.
Sezgin decided to first address the question of “when Islamic narration began and from which period on it is possible to talk about written Islamic documents.” After graduating from the faculty of literature of İstanbul University in 1947, Sezgin received his Ph.D. in 1954 for his work on Arab language and literature. In 1954 he became an associate professor with his work titled “Buhari’nin Kaynakları” (Sources of Bukhari).
Bukhari refers to Muhammad al-Bukhari, a Sunni Islamic scholar from Persia who authored the Hadith collection titled “Sahih al-Bukhari.” In his book, Sezgin claims that Bukhari relied on written sources for the Hadith, and not oral sources as is widely believed.
During his years as a student, Sezgin also read Carl Brockelmann’s five-volume “History of Arab Literature,” which was written based on manuscripts in Europe and İstanbul. Sezgin found out that this book, which details chronological information about manuscripts and gives tips to researchers on how to access these manuscripts, did not include information about many Muslim authors. Brockelmann, who used to come to İstanbul occasionally for a one-month’s stay, did not have sufficient time before his death to expand his body of work. Upon noticing that most of the written Islamic sources were not included in Brockelmann’s work, Sezgin decided to complete his work, which would mean examining hundred of thousands of works, something that would last for decades.
Sezgin was not the only person who wanted to complete Brockelmann’s work, as a group of European scholars made a similar attempt in the 1950s under the leadership of the Brill Publishing House, which published German translations of Arabic works. This group of scholars was able to complete Brockelmann’s work thanks to financial support from UNESCO.
Sezgin travelled to Germany for several times during 1957 and 1958, where he worked at University of Bonn. The scholar improved his German to the extent that he began offering his courses in German. Although he was asked to stay at the university, Sezgin declined the offer and returned to Turkey, where he established the Islamic Sciences Research Institute with Zeki Velidi Togan, a Turkish historian.
The May 27, 1960 military coup was a turning point in Sezgin’s life. He said that even though two of his brothers were jailed in the aftermath of the coup, he tried to continue his studies but was shocked by the news of the removal of 147 professors from the university.
“As I was going to the institute one morning, I was shocked to hear a boy selling newspapers telling me about the removal of 147 professors from the university. I was either the 40th or 50th among the professors who were removed. I did not want to leave my country, but when I was removed from the university, I saw that I had no other choice. I went to the Süleymaniye Library and wrote letters to my friends, two Americans and the former rector of Frankfurt University, asking them whether they could find me a place to continue my studies as I had been expelled from the university. I received positive responses from all three of them within a month. I chose to work in Frankfurt. On the evening of my departure from Turkey, I went to the Karaköy side of the Galata Bridge. I watched Üsküdar for about 15 or 20 minutes. It was a beautiful night, but I had to wipe my tears. I was not angry but sad,” he said.
Sezgin began offering courses at the University of Frankfurt as a visiting professor in 1961, where he was very well liked by his students due to his disciplined work ethic and character.
In 1967, the first volume of Sezgin’s “Islam’s Golden Age of Science,” which was an expansion of Brockelmann’s work, was published, receiving widespread acclaim in academic circles.
Visiting more than 60 countries, Sezgin examined works in the fields of physics, chemistry, biology, animal breeding, veterinary medicine, agriculture, medicine, astronomy and geography for the “History of Islamic Sciences,” and brought these works, which were kept on the dusty shelves of the libraries of many countries, to light so that they could be accessed by researchers.
The number of volumes of his study reached 15 over the years.
Sezgin founded a unique museum in 1983, bringing together more than 800 replicas of historical scientific instruments, tools and maps, mostly belonging to the golden age of Islamic science. A similar museum was opened in 2008 in İstanbul.
The 87-year-old Sezgin still works 14 hours a day. He plans to publish the 16th and 17th volumes of his study of Islamic sciences next year, which will deal with “literary sciences in the Arabic language.”
Due to his contribution to science in Europe, Sezgin has been awarded the Great Medal for Distinguished Service of the Federal Republic of Germany Although he has been living abroad away for roughly a half century, he is still a Turkish citizen and declined offers from Germany to be granted German citizenship
Aydogan Ozcan has the Ph.D., the expertise, and the engineering acumen to perfect the world’s most complex medical diagnostic technology. Instead, he’s solving global health issues—with a cell phone.
His UCLA research team has invented a way to turn common cell phones, already in the hands of four billion people worldwide, into imaging tools that will bring accurate medical diagnoses to the most remote, resource-poor corners of the planet.
“Very few of the great technologies we play with in advanced countries can actually be applied in developing parts of the world,” he points out. “You can’t even assume there will be consistent electricity in rural clinics or villages. Because the infrastructure gap is so huge, we aren’t delivering our best thinking to the people who need it most. I find that very disturbing.”
To demonstrate the gap, Ozcan points to sophisticated $100,000 blood count analyzers found in advanced labs. He feels they are already so state of the art that any improvements will be merely incremental. But in developing nations, even basic technology can be transformative. “Since there’s virtually nothing there to start with, it’s much easier to make a huge impact, quickly.”
In many rural villages, patients remain untreated until mobile units reach them. Even then, tools are woefully inadequate. “You can’t afford to take hundreds of blood samples, transport them to a hospital, then return with results,” he explains. “Many diseases remain entirely missed; people are dying from simple infections that could be easily treated if only they were diagnosed.”
Conventional microscopes, the mainstay of diagnosis for centuries, are impractical on a global level. “They are too heavy and powerful to be cost-effectively miniaturized. They also can’t quickly capture and screen the large number of cells needed for statistically viable diagnoses,” he says.
What’s more, because technicians in remote areas may be poorly trained, they often interpret images inaccurately. “In some parts of Africa, 70 percent of malaria diagnoses are incorrect false-positives.”
These constraints convinced Ozcan that rather than inventing another new ultrahigh-performance tool, we need to think like engineers: “Who’s going to use it and how much can I spend?” This mindset led him directly to cell phones.
“Here’s this extremely inexpensive, yet advanced, technology that’s in use almost everywhere. It presents an obvious opportunity that can be leveraged to benefit health environments where cost drives everything,” he says. “So that’s what we’re doing—creating digital technologies that replace microscopes and enable cell phones to make diagnostic decisions, even in a distant desert village.”
Ozcan’s invention solves the dilemma of poorly trained technicians by arming the phones with sophisticated algorithms that do the interpreting. To tackle the most expensive part of microscopes—lenses—his team simply eliminated them.
“With our lens-free imaging platform, instead of detecting the cell, we detect its shadow,” he explains. “When you shine light on a cell, it casts a shadow from which we can reconstruct the cell image, perform advanced processing, and detect signatures of disease. We’re able to do this because unlike flat, dark, human shadows, the shadows of cells are semitransparent, very textured, and contain specific fingerprints.”
Ozcan’s modified phone uses a special light source and the phone’s camera to capture an image of a blood sample, essentially turning the phone into a lens-free microscope. “It’s lightweight, instantly shows us huge numbers of cells, and fits into the palm of your hand.”
Field tests slated to begin this year will distribute hundreds of the devices to mobile health units in rural Africa with a focus on diagnosing malaria. A central, inexpensive PC station will be installed in a hospital. Mobile health workers will collect blood, load images of the samples into the modified phones, and transmit them to the PC station via the Internet. Within minutes, the data will be processed and a summary diagnosis sent back into the field. Records will also be stored, creating an unprecedented database of global disease statistics.
“Treating malaria is actually very simple,” Ozcan notes, “What’s been lacking is the diagnosis.” Using the devices to analyze blood and other bodily fluids will also be crucial in detecting tuberculosis, HIV/AIDS, and other conditions. Additionally, wireless telemedicine platforms can be a much needed breakthrough in monitoring patients. “Today, HIV doesn’t have to be deadly. If patients are monitored regularly it can be controlled. The ability to easily, frequently check patients would allow us to treat HIV like diabetes, saving so many lives.”
The future, Ozcan believes, lies not only in new technologies, but in innovative applications of existing technologies. Blending an engineer’s discipline and a social entrepreneur’s heart, he predicts, “That’s what will transform global health care in powerful, practical ways we’ve never before imagined.”