Geometry is a branch of mathematics concerned with questions of shape, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer, Geometry arose independently in a number of early cultures as a practical way for dealing with lengths and volumes. Geometry began to see elements of mathematical science emerging in the West as early as the 6th century BC. By the 3rd century BC, geometry was put into a form by Euclid, whose treatment, Euclids Elements. Geometry arose independently in India, with texts providing rules for geometric constructions appearing as early as the 3rd century BC, islamic scientists preserved Greek ideas and expanded on them during the Middle Ages. By the early 17th century, geometry had been put on a solid footing by mathematicians such as René Descartes. Since then, and into modern times, geometry has expanded into non-Euclidean geometry and manifolds, while geometry has evolved significantly throughout the years, there are some general concepts that are more or less fundamental to geometry.
These include the concepts of points, planes, angles, contemporary geometry has many subfields, Euclidean geometry is geometry in its classical sense. The mandatory educational curriculum of the majority of nations includes the study of points, planes, triangles, similarity, solid figures, Euclidean geometry has applications in computer science and various branches of modern mathematics. Differential geometry uses techniques of calculus and linear algebra to problems in geometry. It has applications in physics, including in general relativity, topology is the field concerned with the properties of geometric objects that are unchanged by continuous mappings. In practice, this often means dealing with large-scale properties of spaces, convex geometry investigates convex shapes in the Euclidean space and its more abstract analogues, often using techniques of real analysis. It has close connections to convex analysis and functional analysis, algebraic geometry studies geometry through the use of multivariate polynomials and other algebraic techniques.
It has applications in areas, including cryptography and string theory. Discrete geometry is concerned mainly with questions of relative position of simple objects, such as points. It shares many methods and principles with combinatorics, Geometry has applications to many fields, including art, physics, as well as to other branches of mathematics. The earliest recorded beginnings of geometry can be traced to ancient Mesopotamia, the earliest known texts on geometry are the Egyptian Rhind Papyrus and Moscow Papyrus, the Babylonian clay tablets such as Plimpton 322. For example, the Moscow Papyrus gives a formula for calculating the volume of a truncated pyramid, clay tablets demonstrate that Babylonian astronomers implemented trapezoid procedures for computing Jupiters position and motion within time-velocity space
France, officially the French Republic, is a country with territory in western Europe and several overseas regions and territories. The European, or metropolitan, area of France extends from the Mediterranean Sea to the English Channel and the North Sea, Overseas France include French Guiana on the South American continent and several island territories in the Atlantic and Indian oceans. France spans 643,801 square kilometres and had a population of almost 67 million people as of January 2017. It is a unitary republic with the capital in Paris. Other major urban centres include Marseille, Lille, Toulouse, during the Iron Age, what is now metropolitan France was inhabited by the Gauls, a Celtic people. The area was annexed in 51 BC by Rome, which held Gaul until 486, France emerged as a major European power in the Late Middle Ages, with its victory in the Hundred Years War strengthening state-building and political centralisation. During the Renaissance, French culture flourished and a colonial empire was established.
The 16th century was dominated by civil wars between Catholics and Protestants. France became Europes dominant cultural and military power under Louis XIV, in the 19th century Napoleon took power and established the First French Empire, whose subsequent Napoleonic Wars shaped the course of continental Europe. Following the collapse of the Empire, France endured a succession of governments culminating with the establishment of the French Third Republic in 1870. Following liberation in 1944, a Fourth Republic was established and dissolved in the course of the Algerian War, the Fifth Republic, led by Charles de Gaulle, was formed in 1958 and remains to this day. Algeria and nearly all the colonies became independent in the 1960s with minimal controversy and typically retained close economic. France has long been a centre of art, science. It hosts Europes fourth-largest number of cultural UNESCO World Heritage Sites and receives around 83 million foreign tourists annually, France is a developed country with the worlds sixth-largest economy by nominal GDP and ninth-largest by purchasing power parity.
In terms of household wealth, it ranks fourth in the world. France performs well in international rankings of education, health care, life expectancy, France remains a great power in the world, being one of the five permanent members of the United Nations Security Council with the power to veto and an official nuclear-weapon state. It is a member state of the European Union and the Eurozone. It is a member of the Group of 7, North Atlantic Treaty Organization, Organisation for Economic Co-operation and Development, the World Trade Organization, originally applied to the whole Frankish Empire, the name France comes from the Latin Francia, or country of the Franks
Mathematics is the study of topics such as quantity, structure and change. There is a range of views among mathematicians and philosophers as to the exact scope, Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof, when mathematical structures are good models of real phenomena, mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, measurement, practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry, rigorous arguments first appeared in Greek mathematics, most notably in Euclids Elements. Galileo Galilei said, The universe cannot be read until we have learned the language and it is written in mathematical language, and the letters are triangles and other geometrical figures, without which means it is humanly impossible to comprehend a single word.
Without these, one is wandering about in a dark labyrinth, carl Friedrich Gauss referred to mathematics as the Queen of the Sciences. Benjamin Peirce called mathematics the science that draws necessary conclusions, David Hilbert said of mathematics, We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules, rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise. Albert Einstein stated that as far as the laws of mathematics refer to reality, they are not certain, Mathematics is essential in many fields, including natural science, medicine and the social sciences. Applied mathematics has led to entirely new mathematical disciplines, such as statistics, Mathematicians engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, the history of mathematics can be seen as an ever-increasing series of abstractions.
The earliest uses of mathematics were in trading, land measurement and weaving patterns, in Babylonian mathematics elementary arithmetic first appears in the archaeological record. Numeracy pre-dated writing and numeral systems have many and diverse. Between 600 and 300 BC the Ancient Greeks began a study of mathematics in its own right with Greek mathematics. Mathematics has since been extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries continue to be made today, the overwhelming majority of works in this ocean contain new mathematical theorems and their proofs. The word máthēma is derived from μανθάνω, while the modern Greek equivalent is μαθαίνω, in Greece, the word for mathematics came to have the narrower and more technical meaning mathematical study even in Classical times
Monte Viso or Monviso, is the highest mountain of the Cottian Alps. It is located in Italy close to the French border, on a very clear day it can be seen from the spires of the Milan Cathedral. It has been suggested that Monte Viso could be one of the mountains which inspired the Paramount logo, in Italy is known as Il Re di Pietra because of his prominence within western Italian Alps landscape. On the northern slopes of Monte Viso are the headwaters of the Po, the longest Italian river, the Monviso group is surrounded by the Valle Po, Valle Varaita and, on the French side, the Guil valley. Its productivity peaked around 5000 BC, the jadeite was used to make cult axes, which are found all over western Europe. In ancient times the mountain was known as Vesulus, Monte Viso was climbed for the first time on August 30,1861 by William Mathews, Frederick Jacomb, Jean-Baptiste Croz and Michel Croz. Monte Viso is mentioned by authors and non-, including Dante, Petrarch. List of Alpine peaks by prominence Monte Viso tunnel McLewin, Will, in Monte Viso’s Horizon, Climbing All the Alpine 4000m Peaks
Kingdom of Sardinia
The Kingdom of Sardinia was a state in Southern Europe which existed from the early 14th until the mid-19th century. It was the state of todays Italy. When it was acquired by the Duke of Savoy in 1720, the Savoyards united it with their possessions on the Italian mainland and, by the time of the Crimean War in 1853, had built the resulting kingdom into a strong power. The formal name of the entire Savoyard state was the States of His Majesty the King of Sardinia and its final capital was Turin, the capital of Savoy since the Middle Ages. Beginning in 1324, James and his successors conquered the island of Sardinia, in 1420 the last competing claim to the island was bought out. After the union of the crowns of Aragon and Castile, Sardinia became a part of the burgeoning Spanish Empire, in 1720 it was ceded by the Habsburg and Bourbon claimants to the Spanish throne to Duke Victor Amadeus II of Savoy. While in theory the traditional capital of the island of Sardinia and seat of its viceroys was Cagliari, the Congress of Vienna, which restructured Europe after Napoleons defeat, returned to Savoy its mainland possessions and augmented them with Liguria, taken from the Republic of Genoa.
In 1847–48, in a fusion, the various Savoyard states were unified under one legal system, with the capital in Turin, and granted a constitution. There followed the annexation of Lombardy, the central Italian states and the Two Sicilies, Venetia, in 238 BC Sardinia became, along with Corsica, a province of the Roman Empire. The Romans ruled the island until the middle of the 5th century, when it was occupied by the Vandals, in 534 AD it was reconquered by the Romans, but now from the Eastern Roman Empire, Byzantium. It remained a Byzantine province until the Arab conquest of Sicily in the 9th century, after that, communications with Constantinople became very difficult, and powerful families of the island assumed control of the land. Starting from 705–706, Saracens from north Africa harassed the population of the coastal cities, information about the Sardinian political situation in the following centuries is scarce. There is a record of another massive Saracen sea attack in 1015–16 from the Balearics, the Saracen attempt to invade the island was stopped by the Judicatus with the support of the fleets of the maritime republics of Pisa and Genoa, free cities of the Holy Roman Empire.
Pope Benedict VIII requested aid from the republics of Pisa. Even the title of Judices was a Byzantine reminder of the Greek church and state, of these sovereigns only two names are known and Salusiu, who probably ruled in the 10th century. The Archons still wrote in Greek or Latin, but one of the first documents of the Judex of Cagliari, their successor, was written in romance Sardinian language. The realm was divided into four kingdoms, the Judicati, perfectly organized as was the previous realm, but was now under the influence of the Pope. That was the cause of leading to a long war between the Judices, who regarded themselves as kings fighting against rebellious nobles
Prussia was a historic state originating out of the Duchy of Prussia and the Margraviate of Brandenburg, and centred on the region of Prussia. For centuries, the House of Hohenzollern ruled Prussia, successfully expanding its size by way of an unusually well-organised, with its capital in Königsberg and from 1701 in Berlin, shaped the history of Germany. In 1871, German states united to create the German Empire under Prussian leadership, in November 1918, the monarchies were abolished and the nobility lost its political power during the German Revolution of 1918–19. The Kingdom of Prussia was thus abolished in favour of a republic—the Free State of Prussia, from 1933, Prussia lost its independence as a result of the Prussian coup, when the Nazi regime was successfully establishing its Gleichschaltung laws in pursuit of a unitary state. Prussia existed de jure until its liquidation by the Allied Control Council Enactment No.46 of 25 February 1947. The name Prussia derives from the Old Prussians, in the 13th century, the Teutonic Knights—an organized Catholic medieval military order of German crusaders—conquered the lands inhabited by them.
In 1308, the Teutonic Knights conquered the region of Pomerelia with Gdańsk and their monastic state was mostly Germanised through immigration from central and western Germany and in the south, it was Polonised by settlers from Masovia. The Second Peace of Thorn split Prussia into the western Royal Prussia, a province of Poland, and the part, from 1525 called the Duchy of Prussia. The union of Brandenburg and the Duchy of Prussia in 1618 led to the proclamation of the Kingdom of Prussia in 1701, Prussia entered the ranks of the great powers shortly after becoming a kingdom, and exercised most influence in the 18th and 19th centuries. During the 18th century it had a say in many international affairs under the reign of Frederick the Great. During the 19th century, Chancellor Otto von Bismarck united the German principalities into a Lesser Germany which excluded the Austrian Empire. At the Congress of Vienna, which redrew the map of Europe following Napoleons defeat, Prussia acquired a section of north western Germany.
The country grew rapidly in influence economically and politically, and became the core of the North German Confederation in 1867, and of the German Empire in 1871. The Kingdom of Prussia was now so large and so dominant in the new Germany that Junkers and other Prussian élites identified more and more as Germans and less as Prussians. In the Weimar Republic, the state of Prussia lost nearly all of its legal and political importance following the 1932 coup led by Franz von Papen. East Prussia lost all of its German population after 1945, as Poland, the main coat of arms of Prussia, as well as the flag of Prussia, depicted a black eagle on a white background. The black and white colours were already used by the Teutonic Knights. The Teutonic Order wore a white coat embroidered with a cross with gold insert
Turin is a city and an important business and cultural centre in northern Italy, capital of the Piedmont region and was the first capital city of Italy. The city is located mainly on the bank of the Po River, in front of Susa Valley and surrounded by the western Alpine arch. The population of the city proper is 892,649 while the population of the area is estimated by Eurostat to be 1.7 million inhabitants. The Turin metropolitan area is estimated by the OECD to have a population of 2.2 million, in 1997 a part of the historical center of Torino was inscribed in the World Heritage List under the name Residences of the Royal House of Savoy. Turin is well known for its Renaissance, Rococo, Neo-classical, many of Turins public squares, castles and elegant palazzi such as Palazzo Madama, were built between the 16th and 18th centuries. This was after the capital of the Duchy of Savoy was moved to Turin from Chambery as part of the urban expansion, the city used to be a major European political center.
Turin was Italys first capital city in 1861 and home to the House of Savoy, from 1563, it was the capital of the Duchy of Savoy, of the Kingdom of Sardinia ruled by the Royal House of Savoy and finally the first capital of the unified Italy. Turin is sometimes called the cradle of Italian liberty for having been the birthplace and home of notable politicians and people who contributed to the Risorgimento, such as Cavour. The city currently hosts some of Italys best universities, academies and gymnasia, such as the University of Turin, founded in the 15th century, in addition, the city is home to museums such as the Museo Egizio and the Mole Antonelliana. Turins attractions make it one of the worlds top 250 tourist destinations, Turin is ranked third in Italy, after Milan and Rome, for economic strength. With a GDP of $58 billion, Turin is the worlds 78th richest city by purchasing power, as of 2010, the city has been ranked by GaWC as a Gamma World city. Turin is home to much of the Italian automotive industry, the Taurini were an ancient Celto-Ligurian Alpine people, who occupied the upper valley of the Po River, in the center of modern Piedmont.
In 218 BC, they were attacked by Hannibal as he was allied with their long-standing enemies, the Taurini chief town was captured by Hannibals forces after a three-day siege. As a people they are mentioned in history. It is believed that a Roman colony was established in 27 BC under the name of Castra Taurinorum, both Livy and Strabo mention the Taurinis country as including one of the passes of the Alps, which points to a wider use of the name in earlier times. In the 1st century BC, the Romans created a military camp, the typical Roman street grid can still be seen in the modern city, especially in the neighborhood known as the Quadrilatero Romano. Via Garibaldi traces the path of the Roman citys decumanus which began at the Porta Decumani. The Porta Palatina, on the side of the current city centre, is still preserved in a park near the Cathedral
MINES ParisTech, created in 1783 by King Louis XVI, is a most prominent and prestigious French engineering schools in France and a member of ParisTech and PSL*. Created by decree of the French Kings Counsel on March 19,1783, the school disappeared at the beginning of the French Revolution but was re-established by decree of the Committee of Public Safety in 1794, the 13th Messidor Year II. It moved to Savoie, after a decree of the consuls the 23rd Pluviôse Year X, after the Bourbon Restoration in 1814, the school moved to the Hôtel de Vendôme. From the 1960s onwards, it created research laboratories in Fontainebleau, Évry, the initial aim of the Ecole des mines de Paris, namely to train high-level mining engineers, evolved with time to adapt to the technological and structural transformations undergone by society. Mines ParisTech has now become one of the most prestigious French engineering schools with a variety of subjects. Its students are trained to have management positions, work in research and development departments, or as operations officers, the Corps of Mines, one of the greatest technical corps of the French state.
It is a third degree, lasting for three years, consisting in two long-term internships both in public and private economical institutions and courses in economics and public institutions. Every year, ten applications are accepted from students around the world according to their academic achievements. Admission in third year is open to one Ph. D graduate. mines-paristech. ensmp. fr ISIGE-MINES ParisTech
Domenico Giovanni Giuseppe Maria Lanza was an Italian politician and the eighth Prime Minister from 1869 to 1873. Lanza was born in the Piedmontese city of Casale Monferrato. He studied and wrote on agriculture developments in both the practical and social aspects. ”Lanza was a member of the Subalpine Agricultural Association of Turin and became its secretary. ”He attached himself to the party of Cavour and devoted his attention chiefly to questions of economy. He became minister of instruction in 1855 in the cabinet of Cavour. Lanza followed Cavour into his retirement in July 1859 after the Treaty of Villafranca. He was minister of the interior in the La Marmora cabinet and he maintained a resolute opposition to the financial policy of Menabrea, who resigned when Lanza was a second time elected, in 1869, chairman of the House. Lanza formed a new cabinet in which he was minister of the interior. With Quintino Sella as minister of finance he sought to reorganize Italian budget and his cabinet had seen the accomplishment of Italian unity and the installation of an Italian government in Rome after the defeat of the Papal States in late 1870.
Works by or about Giovanni Lanza at Internet Archive
Mineralogy is a subject of geology specializing in the scientific study of chemistry, crystal structure, and physical properties of minerals and mineralized artifacts. Specific studies within mineralogy include the processes of mineral origin and formation, classification of minerals, their geographical distribution, the German Renaissance specialist Georgius Agricola wrote works such as De re metallica and De Natura Fossilium which began the scientific approach to the subject. Systematic scientific studies of minerals and rocks developed in post-Renaissance Europe, the modern study of mineralogy was founded on the principles of crystallography and to the microscopic study of rock sections with the invention of the microscope in the 17th century. Nicholas Steno first observed the law of constancy of interfacial angles in quartz crystals in 1669 and this was generalized and established experimentally by Jean-Baptiste L. Romé de lIslee in 1783. In 1814, Jöns Jacob Berzelius introduced a classification of minerals based on their chemistry rather than their crystal structure, james D.
Dana published his first edition of A System of Mineralogy in 1837, and in a edition introduced a chemical classification that is still the standard. It, retains a focus on the structures commonly encountered in rock-forming minerals. An initial step in identifying a mineral is to examine its physical properties and these can be classified into density, measures of mechanical cohesion, macroscopic visual properties and electric properties and solubility in hydrogen chloride. If the mineral is crystallized, it will have a distinctive crystal habit that reflects the crystal structure or internal arrangement of atoms. It is affected by crystal defects and twinning. Many crystals are polymorphic, having more than one crystal structure depending on factors such as pressure and temperature. ”Examples of polymorphs are calcite and aragonite - two minerals with identical chemical composition, distinguished by their crystallography, calcite is rhombohedral and aragonite is orthorhombic. The crystal structure is the arrangement of atoms in a crystal and it is represented by a lattice of points which repeats a basic pattern, called a unit cell, in three dimensions.
The lattice can be characterized by its symmetries and by the dimensions of the unit cell and these dimensions are represented by three Miller indices. The lattice remains unchanged by certain symmetry operations about any point in the lattice, rotation and rotary inversion. Together, they make up an object called a crystallographic point group or crystal class. There are 32 possible crystal classes, in addition, there are operations that displace all the points, screw axis, and glide plane. In combination with the point symmetries, they form 230 possible space groups, most geology departments have X-ray powder diffraction equipment to analyze the crystal structures of minerals. X-rays have wavelengths that are the order of magnitude as the distances between atoms. In a sample that is ground to a powder, the X-rays sample a random distribution of all crystal orientations, powder diffraction can distinguish between minerals that may appear the same in a hand sample, for example quartz and its polymorphs tridymite and cristobalite
The term Engineering is derived from the Latin ingenium, meaning cleverness and ingeniare, meaning to contrive, devise. Engineering has existed since ancient times as humans devised fundamental inventions such as the wedge, wheel, each of these inventions is essentially consistent with the modern definition of engineering. The term engineering is derived from the engineer, which itself dates back to 1390 when an engineer originally referred to a constructor of military engines. In this context, now obsolete, a referred to a military machine. Notable examples of the obsolete usage which have survived to the present day are military engineering corps, the word engine itself is of even older origin, ultimately deriving from the Latin ingenium, meaning innate quality, especially mental power, hence a clever invention. The earliest civil engineer known by name is Imhotep, as one of the officials of the Pharaoh, Djosèr, he probably designed and supervised the construction of the Pyramid of Djoser at Saqqara in Egypt around 2630–2611 BC.
Ancient Greece developed machines in both civilian and military domains, the Antikythera mechanism, the first known mechanical computer, and the mechanical inventions of Archimedes are examples of early mechanical engineering. In the Middle Ages, the trebuchet was developed, the first steam engine was built in 1698 by Thomas Savery. The development of this gave rise to the Industrial Revolution in the coming decades. With the rise of engineering as a profession in the 18th century, similarly, in addition to military and civil engineering, the fields known as the mechanic arts became incorporated into engineering. The inventions of Thomas Newcomen and the Scottish engineer James Watt gave rise to mechanical engineering. The development of specialized machines and machine tools during the revolution led to the rapid growth of mechanical engineering both in its birthplace Britain and abroad. John Smeaton was the first self-proclaimed civil engineer and is regarded as the father of civil engineering.
He was an English civil engineer responsible for the design of bridges, harbours and he was a capable mechanical engineer and an eminent physicist. Smeaton designed the third Eddystone Lighthouse where he pioneered the use of hydraulic lime and his lighthouse remained in use until 1877 and was dismantled and partially rebuilt at Plymouth Hoe where it is known as Smeatons Tower. The United States census of 1850 listed the occupation of engineer for the first time with a count of 2,000, there were fewer than 50 engineering graduates in the U. S. before 1865. In 1870 there were a dozen U. S. mechanical engineering graduates, in 1890 there were 6,000 engineers in civil, mining and electrical. There was no chair of applied mechanism and applied mechanics established at Cambridge until 1875, the theoretical work of James Maxwell and Heinrich Hertz in the late 19th century gave rise to the field of electronics