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Giovanni Ceva
Giovanni Ceva (September 1, 1647 – May 13, 1734) was an Italian mathematician widely known for proving Ceva's theorem in elementary geometry. His brother, Tommaso Ceva was also a well-known poet and mathematician. Life Ceva received his education at a Jesuit college in Milan. Later in his life, he studied at the University of Pisa, where he subsequently became a professor. In 1686, however, he was designated as the Professor of Mathematics at the University of Mantua and worked there for the rest of his life. Work Ceva studied geometry for most of his long life. In 1678, he published a now famous theorem on synthetic geometry in a triangle called Ceva's Theorem. The theorem, already known to Yusuf Al-Mu'taman ibn Hűd in 11th century, states that if three line segments are drawn from the vertices of a triangle to the opposite sides, then the three line segments are concurrent if, and only if, the product of the ratios of the newly created line segments on each side of the tri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Pisa
The University of Pisa ( it, Università di Pisa, UniPi), officially founded in 1343, is one of the oldest universities in Europe. History The Origins The University of Pisa was officially founded in 1343, although various scholars place its origins in the 11th century. It is certain, however, that from the middle of the 12th century Pisa had a “Universitas” in the original sense of the word, that is, a group of students who gathered around masters. It was during this period that Leonardo Fibonacci was born and worked. He was one of the greatest mathematicians in history who, through his work, synthesized the spirit and processes of Greek geometry and the tools of Arabic mathematics for the first time in Europe. The papal seal “In Supremae dignitatis”, issued by Pope Clement VI on 3 September 1343, granted the Studium in Pisa the title of Studium Generale with various exclusive privileges, making it universally recognised. In medieval times, the Studium Generale wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Menelaus's Theorem
Menelaus's theorem, named for Menelaus of Alexandria, is a proposition about triangles in plane geometry. Suppose we have a triangle ''ABC'', and a transversal line that crosses ''BC'', ''AC'', and ''AB'' at points ''D'', ''E'', and ''F'' respectively, with ''D'', ''E'', and ''F'' distinct from ''A'', ''B'', and ''C''. A weak version of the theorem states that : \frac \times \frac \times \frac = 1, where '', AB, '' is taken to be the ordinary length of segment ''AB'': a positive value. The theorem can be strengthened to a statement about signed lengths of segments, which provides some additional information about the relative order of collinear points. Here, the length ''AB'' is taken to be positive or negative according to whether ''A'' is to the left or right of ''B'' in some fixed orientation of the line; for example, ''AF''/''FB'' is defined as having positive value when ''F'' is between ''A'' and ''B'' and negative otherwise. The signed version of Menelaus's theorem stat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scientists From Milan
A scientist is a person who conducts scientific research to advance knowledge in an area of the natural sciences. In classical antiquity, there was no real ancient analog of a modern scientist. Instead, philosophers engaged in the philosophical study of nature called natural philosophy, a precursor of natural science. Though Thales (circa 624-545 BC) was arguably the first scientist for describing how cosmic events may be seen as natural, not necessarily caused by gods,Frank N. Magill''The Ancient World: Dictionary of World Biography'', Volume 1 Routledge, 2003 it was not until the 19th century in science, 19th century that the term ''scientist'' came into regular use after it was coined by the theologian, philosopher, and historian of science William Whewell in 1833. In modern times, many scientists have Terminal degree, advanced degrees in an area of science and pursue careers in various Sector (economic), sectors of the economy such as Academy, academia, Private industry, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1734 Deaths
Events January– March * January 8 – Salzburgers, Lutherans who were expelled by the Roman Catholic Bishop of Salzburg, Austria, in October 1731, set sail for the British Colony of Georgia in America. * February 16 – The Ostend Company, established in 1722 in the Austrian Netherlands (modern-day Belgium) to compete for trade in the West Indies (the Caribbean islands) and the East Indies (south and southeast Asia), ceases business as part of the agreement by Austria in the Second Treaty of Vienna. * March 12 – Salzburgers arrive at the mouth of the Savannah River in the British Colony of Georgia. April–June * April 25 – Easter occurs on the latest possible date (the next time is in 1886). * May 15 – Prince Charles of Spain (later King Charles III) becomes the new King of Naples and Sicily, five days after his arrival in Naples. * May 25 – Spanish forces under the command of José Carrillo de Albornoz, 1st Duke of Mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1647 Births
Events January–March * January 2 – Chinese bandit leader Zhang Xianzhong, who has ruled the Sichuan province since 1644, is killed at Xichong County, Xichong by a Qing archer after having been betrayed one of his officers, Liu Jinzhong. * January 7 – The Westminster Assembly begins debating the biblical proof texts, to support the new Westminster Confession of Faith, Confession of Faith. * January 16 – Citizens of Dublin declare their support for Giovanni Battista Rinuccini, Rinuccini, and refuse to support the army of the Marquis of Ormond. * January 17 – Posten Norge was founded as Postvesenet. * January 20 – A small Qing force led by Li Chengdong captures Guangzhou and kills the Zhu Yuyue, the List of emperors of the Ming dynasty, Shaowu Emperor of the Southern Ming dynasty in China. * February 5 – The Yongli Chinese era name, era is proclaimed as Zhu Youlang is declared the Yongli Emperor of the Southern Ming. * February 24 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cevian
In geometry, a cevian is a line that intersects both a triangle's vertex, and also the side that is opposite to that vertex. Medians and angle bisectors are special cases of cevians. The name "cevian" comes from the Italian mathematician Giovanni Ceva, who proved a well-known theorem about cevians which also bears his name. Length Stewart's theorem The length of a cevian can be determined by Stewart's theorem: in the diagram, the cevian length is given by the formula :\,b^2m + c^2n = a(d^2 + mn). Less commonly, this is also represented (with some rearrangement) by the following mnemonic: :\underset = \!\!\!\!\!\! \underset Median If the cevian happens to be a median (thus bisecting a side), its length can be determined from the formula :\,m(b^2 + c^2) = a(d^2 + m^2) or :\,2(b^2 + c^2) = 4d^2 + a^2 since :\,a = 2m. Hence in this case :d= \frac\sqrt2 . Angle bisector If the cevian happens to be an angle bisector, its length obeys the formulas :\,(b + c)^2 = a^2 \le ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Po River
The Po ( , ; la, Padus or ; Ligurian language (ancient), Ancient Ligurian: or ) is the longest river in Italy. It flows eastward across northern Italy starting from the Cottian Alps. The river's length is either or , if the Maira (river), Maira, a right bank tributary, is included. The headwaters of the Po are a Spring (hydrology), spring seeping from a stony hillside at Pian del Re, a flat place at the head of the Val Po under the northwest face of Monviso. The Po then extends along the 45th parallel north before ending at a delta projecting into the Adriatic Sea near Venice. It is characterized by its large Discharge (hydrology), discharge (several List of rivers by length, rivers over 1,000 km have a discharge inferior or equal to the Po). It is, with the Rhône and Nile, one of the three Mediterranean rivers with the largest water discharge. As a result of its characteristics, the river is subject to heavy flooding. Consequently, over half its length is controlled with Leve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hydraulics
Hydraulics (from Greek: Υδραυλική) is a technology and applied science using engineering, chemistry, and other sciences involving the mechanical properties and use of liquids. At a very basic level, hydraulics is the liquid counterpart of pneumatics, which concerns gases. Fluid mechanics provides the theoretical foundation for hydraulics, which focuses on the applied engineering using the properties of fluids. In its fluid power applications, hydraulics is used for the generation, control, and transmission of power by the use of pressurized liquids. Hydraulic topics range through some parts of science and most of engineering modules, and cover concepts such as pipe flow, dam design, fluidics and fluid control circuitry. The principles of hydraulics are in use naturally in the human body within the vascular system and erectile tissue. Free surface hydraulics is the branch of hydraulics dealing with free surface flow, such as occurring in rivers, canals, lakes, estuar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oscillation
Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum and alternating current. Oscillations can be used in physics to approximate complex interactions, such as those between atoms. Oscillations occur not only in mechanical systems but also in dynamic systems in virtually every area of science: for example the beating of the human heart (for circulation), business cycles in economics, predator–prey population cycles in ecology, geothermal geysers in geology, vibration of strings in guitar and other string instruments, periodic firing of nerve cells in the brain, and the periodic swelling of Cepheid variable stars in astronomy. The term ''vibration'' is precisely used to describe a mechanical oscillation. Oscillation, especially rapid oscillation, may be an undesirable phenomenon in proc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statics
Statics is the branch of classical mechanics that is concerned with the analysis of force and torque (also called moment) acting on physical systems that do not experience an acceleration (''a''=0), but rather, are in static equilibrium with their environment. The application of Newton's second law to a system gives: : \textbf F = m \textbf a \, . Where bold font indicates a vector that has magnitude and direction. \textbf F is the total of the forces acting on the system, m is the mass of the system and \textbf a is the acceleration of the system. The summation of forces will give the direction and the magnitude of the acceleration and will be inversely proportional to the mass. The assumption of static equilibrium of \textbf a = 0 leads to: : \textbf F = 0 \, . The summation of forces, one of which might be unknown, allows that unknown to be found. So when in static equilibrium, the acceleration of the system is zero and the system is either at rest, or its center of mas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Economics
Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. Often, these applied methods are beyond simple geometry, and may include differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, or other computational methods. Proponents of this approach claim that it allows the formulation of theoretical relationships with rigor, generality, and simplicity. Mathematics allows economists to form meaningful, testable propositions about wide-ranging and complex subjects which could less easily be expressed informally. Further, the language of mathematics allows economists to make specific, positive claims about controversial or contentious subjects that would be impossible without mathematics. Much of economic theory is currently presented in terms of mathematical economic models, a set of stylized and simplified mathematical relationships asserted to clarify ass ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinitesimal Calculus
Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. It has two major branches, differential calculus and integral calculus; the former concerns instantaneous rates of change, and the slopes of curves, while the latter concerns accumulation of quantities, and areas under or between curves. These two branches are related to each other by the fundamental theorem of calculus, and they make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit. Infinitesimal calculus was developed independently in the late 17th century by Isaac Newton and Gottfried Wilhelm Leibniz. Later work, including codifying the idea of limits, put these developments on a more solid conceptual footing. Today, calculus has widespread uses in scien ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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