Which scholar is known as the Father of Geometry?
"uncovered some logical inadequacies in Euclid's reasoning, and some unstated geometric principles to which Euclid sometimes appealed. This critique paralleled the crisis occurring in calculus and analysis regarding the meaning of infinite processes such as convergence and continuity. In geometry, there was a clear need for a new set of axioms, which would be complete, and which in no way relied on pictures we draw or on our intuition of space. Such axioms, now known as Hilbert's axioms, were given by David Hilbert in 1894 in his dissertation ""Grundlagen der Geometrie"" (""Foundations of Geometry""). Some other complete sets of axioms"
"Euclid Euclid (; – ""Eukleídēs"", ; fl. 300 BC), sometimes given the name Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the ""founder of geometry"" or 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 theorems of what"
"They follow the same logical structure as ""Elements"", with definitions and proved propositions. Other works are credibly attributed to Euclid, but have been lost. The European Space Agency's (ESA) Euclid spacecraft was named in his honor. Euclid Euclid (; – ""Eukleídēs"", ; fl. 300 BC), sometimes given the name Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the ""founder of geometry"" or 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"
"Descartes has been dubbed the 'Father of Modern Philosophy', and much subsequent Western philosophy is a response to his writings, which are studied closely to this day. In particular, his ""Meditations on First Philosophy"" continues to be a standard text at most university philosophy departments. Descartes' influence in mathematics is equally apparent; the Cartesian coordinate system — allowing algebraic equations to be expressed as geometric shapes in a two-dimensional coordinate system — was named after him. He is credited as the father of analytical geometry, the bridge between algebra and geometry, important to the discovery of calculus and analysis. The"
"Gaspard Monge Gaspard Monge, Comte de Péluse (; 9 May 1746 – 28 July 1818) was a French mathematician, the inventor of descriptive geometry (the mathematical basis of technical drawing), and the father of differential geometry. During the French Revolution he served as the Minister of the Marine, and was involved in the reform of the French educational system, helping to found the École Polytechnique. Monge was born at Beaune, Côte-d'Or, the son of a merchant. He was educated at the college of the Oratorians at Beaune. In 1762 he went to the Collège de la Trinité at Lyon, where,"
"Geometry Geometry (from the ; ""geo-"" ""earth"", ""-metron"" ""measurement"") is a branch of mathematics concerned with questions of shape, size, 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, areas, and volumes. Geometry began to see elements of formal mathematical science emerging in the West as early as the 6th century BC. By the 3rd century BC, geometry was put into an axiomatic form by Euclid, whose treatment, Euclid's ""Elements"","
"Euclidean geometry Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the ""Elements"". Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated by earlier mathematicians, Euclid was the first to show how these propositions could fit into a comprehensive deductive and logical system. The ""Elements"" begins with plane geometry, still taught in secondary school (High School) as the first axiomatic system and the first examples of formal proof. It goes"
"the ""father of algebra"". Many parts of modern geometry are based on the work of Euclid, while Eratosthenes was one of the first scientific geographers, calculating the circumference of the earth and conceiving the first maps based on scientific principles. The Hellenistic period, following Alexander's conquests, continued and built upon this knowledge. Hipparchus is considered the pre-eminent astronomical observer of the ancient world, and was probably the first to develop an accurate method for the prediction of solar eclipse, while Aristarchus of Samos was the first known astronomer to propose a heliocentric model of the solar system, though the geocentric"
"important textbook in mathematics until the 19th century, built upon the work of the Hellenic era Pythagoreans. Euclid developed proofs for the Pythagorean Theorem, for the infinitude of primes, and worked on the five Platonic solids. Eratosthenes used his knowledge of geometry to measure the circumference of the Earth. His calculation was remarkably accurate. He was also the first to calculate the tilt of the Earth's axis (again with remarkable accuracy). Additionally, he may have accurately calculated the distance from the Earth to the Sun and invented the leap day. Known as the ""Father of Geography "", Eratosthenes also created"
"János Bolyai János Bolyai (; 15 December 1802 – 27 January 1860) or Johann Bolyai, was a Hungarian mathematician, one of the founders of non-Euclidean geometry — a geometry that differs from Euclidean geometry in its definition of parallel lines. The discovery of a consistent alternative geometry that might correspond to the structure of the universe helped to free mathematicians to study abstract concepts irrespective of any possible connection with the physical world. Bolyai was born in the Hungarian town of Kolozsvár, Grand Principality of Transylvania (now Cluj-Napoca in Romania), the son of Zsuzsanna Benkő and the well-known mathematician Farkas"
"others; and bearing their names in various combinations in various contexts. Another of his papers in the volume for 1783 relates to the production of water by the combustion of hydrogen. Monge's results had been anticipated by Henry Cavendish. Gaspard Monge Gaspard Monge, Comte de Péluse (; 9 May 1746 – 28 July 1818) was a French mathematician, the inventor of descriptive geometry (the mathematical basis of technical drawing), and the father of differential geometry. During the French Revolution he served as the Minister of the Marine, and was involved in the reform of the French educational system, helping to"
"are Hydrostatics, Optics, Navigation, &c. 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. In the historical development of geometry, the steps in the abstraction of geometry were made by the ancient Greeks. Euclid's"
"formula_8 Iamblichus goes on to describe how some systems of linear equations that are not in this form can be placed into this form. Euclid (Greek: ) was a Greek mathematician who flourished in Alexandria, Egypt, almost certainly during the reign of Ptolemy I (323–283 BCE). Neither the year nor place of his birth have been established, nor the circumstances of his death. Euclid is regarded as the ""father of geometry"". His ""Elements"" is the most successful textbook in the history of mathematics. Although he is one of the most famous mathematicians in history there are no new discoveries attributed"
"of a modern formulation in terms of constructive type theory. This development has implications for pedagogy as well. Euclidean geometry Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the ""Elements"". Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated by earlier mathematicians, Euclid was the first to show how these propositions could fit into a comprehensive deductive and logical system. The ""Elements"" begins with plane geometry, still taught in"
"most university philosophy departments. Descartes' influence in mathematics is equally apparent; the Cartesian coordinate system (see below) was named after him. He is credited as the father of analytical geometry, the bridge between algebra and geometry, used in the discovery of infinitesimal calculus and analysis. Descartes was also one of the key figures in the Scientific Revolution. Descartes refused to accept the authority of previous philosophers. He frequently set his views apart from those of his predecessors. In the opening section of the ""Passions of the Soul"", an early modern treatise on emotions, Descartes goes so far as to assert"
"Geometrography In mathematics, in geometry, geometrography is the study of geometrical constructions. The concepts and methods of geometrography were first expounded by Émile Lemoine (1840–1912), a French civil engineer and a mathematician, in a meeting of the French Association for the Advancement of the Sciences held at Oran in 1888. It is well known in elementary geometry that certain geometrical constructions are simpler than certain others. But in many case it turns out that the apparent simplicity of a construction does not consist in the practical execution of the construction, but in the brevity of the statement of what has"
"Pierre Bouguer Pierre Bouguer () (16 February 1698, Croisic – 15 August 1758, Paris) was a French mathematician, geophysicist, geodesist, and astronomer. He is also known as ""the father of naval architecture"". His father, Jean Bouguer, one of the best hydrographers of his time, was regius professor of hydrography at Le Croisic in lower Brittany, and author of a treatise on navigation. He taught his sons Pierre and Jan at their home, where he also taught private students. In 1714, at the age of 16, Pierre was appointed to succeed his deceased father as professor of hydrography. In 1727 he"
"like Leonardo Da Vinci, Michelangelo, Galileo Galilei and Gerolamo Cardano have been considered as the most recognizable polymaths. During the Renaissance, Italians made substantial contributions in science. Leonardo Da Vinci made significant discoveries in paleontology and anatomy. The Father of modern Science, Galileo Galilei, made key improvements on the thermometer and telescope which allowed him to observe and clearly describe the solar system. Descartes was not only a pioneer of analytic geometry but formulated a theory of mechanics and advanced ideas about the origins of animal movement and perception. Vision interested the physicists Young and Helmholtz, who also studied optics,"
"Jedidiah Morse Jedidiah Morse (August 23, 1761June 9, 1826) was a notable geographer whose textbooks became a staple for students in the United States. He was the father of the telegraphy pioneer and painter Samuel Morse, and his textbooks earned him the sobriquet of ""father of American geography."" Born to a New England family in Woodstock, Connecticut, Morse did his undergraduate work and earned a divinity degree at Yale University (M.A. 1786). While pursuing his theological studies under Jonathan Edwards and Samuel Watts, he established a school for young women in 1783 in New Haven. In the summer of 1785,"
"Girard Desargues Girard Desargues (; 21 February 1591 – September 1661) was a French mathematician and engineer, who is considered one of the founders of projective geometry. Desargues' theorem, the Desargues graph, and the crater Desargues on the Moon are named in his honour. Born in Lyon, Desargues came from a family devoted to service to the French crown. His father was a royal notary, an investigating commissioner of the Seneschal's court in Lyon (1574), the collector of the tithes on ecclesiastical revenues for the city of Lyon (1583) and for the diocese of Lyon. Girard Desargues worked as an"
"basis for an orderly universe — as the first proposal for a scientific ordering principle of the cosmos. Like the Pythagoreans, Plato (c. 427–c. 347 BC) found the ordering principle of the universe in mathematics, specifically in geometry. A later account has it that Plato had inscribed at the entrance to his school, the Academy, ""Let no man ignorant of geometry enter."" The story is a myth, but like all myths it has a grain of truth, for in his writings Plato repeatedly tell us of the importance of geometry. Plato is known more for his contributions to the philosophical"
"some early work in this area by Hellenistic geometers, notably Pappus (c. 340). The greatest flowering of the field occurred with Jean-Victor Poncelet (1788–1867). In the late 17th century, calculus was developed independently and almost simultaneously by Isaac Newton (1642–1727) and Gottfried Wilhelm Leibniz (1646–1716). This was the beginning of a new field of mathematics now called analysis. Though not itself a branch of geometry, it is applicable to geometry, and it solved two families of problems that had long been almost intractable: finding tangent lines to odd curves, and finding areas enclosed by those curves. The methods of calculus"
"Eratosthenes Eratosthenes of Cyrene (; , ; – ) was a Greek mathematician, geographer, poet, astronomer, and music theorist. He was a man of learning, becoming the chief librarian at the Library of Alexandria. He invented the discipline of geography, including the terminology used today. He is best known for being the first person to calculate the circumference of the Earth, which he did by comparing altitudes of the mid-day sun at two places a known North-South distance apart. His calculation was remarkably accurate. He was also the first to calculate the tilt of the Earth's axis, again with remarkable"
"a considerable influence on the development of non-Euclidean geometry among later European geometers, including Witelo (c. 1230–c. 1314), Gersonides (1288–1344), Alfonso, John Wallis, and Giovanni Girolamo Saccheri. In the early 17th century, there were two important developments in geometry. The first was the creation of analytic geometry, or geometry with coordinates and equations, by René Descartes (1596–1650) and Pierre de Fermat (1601–1665). This was a necessary precursor to the development of calculus and a precise quantitative science of physics. The second geometric development of this period was the systematic study of projective geometry by Girard Desargues (1591–1661). Projective geometry is"
"Gino Fano Gino Fano (5 January 18718 November 1952) was an Italian mathematician, best known as the founder of finite geometry. He was born in Mantua, in Italy and died in Verona, also in Italy. Fano made various contributions on projective and algebraic geometry. His work in the foundations of geometry predates the similar, but more popular, work of David Hilbert by about a decade. He was the father of physicist Ugo Fano and electrical engineer Robert Fano and uncle to physicist and mathematician Giulio Racah. Fano was an early writer in the area of finite projective spaces. In his"
"(proposed by Henri Brocard). He died in Lyon. Girard Desargues Girard Desargues (; 21 February 1591 – September 1661) was a French mathematician and engineer, who is considered one of the founders of projective geometry. Desargues' theorem, the Desargues graph, and the crater Desargues on the Moon are named in his honour. Born in Lyon, Desargues came from a family devoted to service to the French crown. His father was a royal notary, an investigating commissioner of the Seneschal's court in Lyon (1574), the collector of the tithes on ecclesiastical revenues for the city of Lyon (1583) and for the"
"Galileo Galilei Galileo Galilei (; 15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Galileo has been called the ""father of observational astronomy"", the ""father of modern physics"", the ""father of the scientific method"", and the ""father of modern science"". Galileo studied speed and velocity, gravity and free fall, the principle of relativity, inertia, projectile motion and also worked in applied science and technology, describing the properties of pendulums and ""hydrostatic balances"", inventing the thermoscope and various military compasses, and using the telescope for scientific observations of celestial objects. His"
"geometry"") is the name given to an hypothetical geometry supposedly used and perhaps created by an alleged megalithic civilization of Britain and Brittany, France, according to British authors Alan Butler and Christopher Knight, and French author Sylvain Tristan. This geometry, whose origin is claimed to go back to c. 3500 BC, would have used a 366-degree circle rather than a 360-degree circle as we do today. 366 geometry is mainly viewed as pseudoscience by mainstream science; defenders of the theory claim that anyone (scholars and laymen alike) may easily verify the truthfulness of their assertions, the ""facts"" being, in their"
"many points, found applications in coding theory and cryptography. With the advent of the computer, new disciplines such as computational geometry or digital geometry deal with geometric algorithms, discrete representations of geometric data, and so forth. History of geometry Geometry (from the ; ""geo-"" ""earth"", ""-metron"" ""measurement"") arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers (arithmetic). Classic geometry was focused in compass and straightedge constructions. Geometry was revolutionized by Euclid, who introduced mathematical rigor and the axiomatic method still in use"
"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. Euclid is the anglicized version of the Greek name Εὐκλείδης, which means ""renowned, glorious"". Very few original references to Euclid survive, so little is known about his life. He was likely born c. 325 BC, although the place and circumstances of both his birth and death are unknown and may only be estimated roughly relative to other people mentioned with him. He is rarely mentioned by name by other Greek mathematicians from Archimedes (c. 287"
"of geometry including early versions of sun clocks. In the 7th century BC, the Greek mathematician Thales of Miletus used geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. Pythagoras established the Pythagorean School, which is credited with the first proof of the Pythagorean theorem, though the statement of the theorem has a long history. Eudoxus (408–c. 355 BC) developed the method of exhaustion, which allowed the calculation of areas"
"""father of modern observational astronomy"", the ""father of modern physics"", the ""father of science"", and ""the Father of Modern Science"". His original contributions to the science of motion were made through an innovative combination of experiment and mathematics. Galileo was one of the first modern thinkers to clearly state that the laws of nature are mathematical. In ""The Assayer"" he wrote ""Philosophy is written in this grand book, the universe ... It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures;..."" His mathematical analyses are a further development of a tradition employed"
"a geography text, and Richard Cary Morse (1795-1868), who assisted his father in his geographical work and founded with brother Sidney the ""New York Observer"". The senior Morse died in 1826 and was buried at the Grove Street Cemetery. Jedidiah Morse Jedidiah Morse (August 23, 1761June 9, 1826) was a notable geographer whose textbooks became a staple for students in the United States. He was the father of the telegraphy pioneer and painter Samuel Morse, and his textbooks earned him the sobriquet of ""father of American geography."" Born to a New England family in Woodstock, Connecticut, Morse did his undergraduate"