Search results for "01A55"

showing 5 items of 5 documents

The forgotten mathematical legacy of Peano

2019

International audience; The formulations that Peano gave to many mathematical notions at the end of the 19th century were so perfect and modern that they have become standard today. A formal language of logic that he created, enabled him to perceive mathematics with great precision and depth. He described mathematics axiomatically basing the reasoning exclusively on logical and set-theoretical primitive terms and properties, which was revolutionary at that time. Yet, numerous Peano’s contributions remain either unremembered or underestimated.

PeanoPeano's axioms of arithmeticPeano's counterexamplesWeierstrass maximum theoremabstract measuresGeneral MathematicsClosure (topology)tangencyinterioranti-distributive familiesfoundationdefinitions by abstractionlinear differential equationsaxiom of choiceLogical conjunctionPeano axiomsproofFormal languageAxiom of choiceMSC: Primary 01A55 01A6003-03 26-03 28-03 34-03 54-03; Secondary15A75 26A03 26A2426B25 26B05 28A1228A15 28A75.affine exterior algebra[MATH]Mathematics [math]reduction formulaeMathematicsnonlinear differential equationsoptimality conditionsdifferentiation of measuressweeping-tangent theoremPeano's axioms of geometryPeano's filling curvereduction of mathematics to setssurface areaclosuremean value theoremDirichlet functionNonlinear differential equationssubtangentsEpistemologymeasure theoryplanar measurelower and upper limits of setsdistributive familiescompactnessmathematical definitions1886 existence theoremdifferentiabilityDissertationes Mathematicae
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Historical Origins of the nine-point conic -- The Contribution of Eugenio Beltrami

2020

In this paper, we examine the evolution of a specific mathematical problem, i.e. the nine-point conic, a generalisation of the nine-point circle due to Steiner. We will follow this evolution from Steiner to the Neapolitan school (Trudi and Battaglini) and finally to the contribution of Beltrami that closed this journey, at least from a mathematical point of view (scholars of elementary geometry, in fact, will continue to resume the problem from the second half of the 19th to the beginning of the 20th century). We believe that such evolution may indicate the steady development of the mathematical methods from Euclidean metric to projective, and finally, with Beltrami, with the use of quadrat…

HistoryMathematical problemMathematics - History and OverviewGeneral MathematicsHistory and Overview (math.HO)06 humanities and the artsAlgebraic geometrySettore MAT/04 - Matematiche Complementari01A55 51-03AlgebraEuclidean distanceEugenio Beltrami060105 history of science technology & medicineConic sectionQuadratic transformationsNine-point conicFOS: Mathematics0601 history and archaeologyNine-point conicPoint (geometry)Development (differential geometry)Period (music)Mathematics
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The strange case of Paul Appell's last memoir on Monge's problem: "sur les déblais et remblais"

2016

International audience; We analyze a case of plagiarism that appears in a work published in 1928 by Paul Appell (1855–1930) in the collection Mémorial des sciences mathématiques. Appell's memoir entitled Le problème géométrique des déblais et remblais contains a verbatim copy of several pages from a memoir published in 1886 by Albert de Saint-Germain (1839–1914). By tracing back Appell's last years, we have found historical evidences that might cast a shadow of doubt on Appell's full responsibility by the plagiarism that appeared under his name.

HistoryGeneral Mathematics010102 general mathematicsFrench mathematicsArt historyGeometryPaul Appell16. Peace & justice[ MATH.MATH-HO ] Mathematics [math]/History and Overview [math.HO]MSC: 01A55 01A6001 natural sciencesPlagiarism010305 fluids & plasmasMemoir[MATH.MATH-HO]Mathematics [math]/History and Overview [math.HO]0103 physical sciences0101 mathematicsMathematicsShadow (psychology)
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From the theory of “congeneric surd equations” to “Segre's bicomplex numbers”

2015

We will study the historical pathway of the emergence of Tessarines or Bicomplex numbers, from their origin as "imaginary" solutions of irrational equations, to their insertion in the context of study of the algebras of hypercomplex numbers.

HistoryPure mathematicsGeneral MathematicsHistory and Overview (math.HO)Context (language use)01 natural sciencesCorrado SegreBiquaternionJames CockleStoria dell'Algebra BicomplessiFOS: MathematicsBiquaternion0601 history and archaeology0101 mathematics01A55 08-03 51-03The ImaginaryMathematicsHypercomplex numberTessarineMathematics::Complex VariablesMathematics - History and Overview010102 general mathematics06 humanities and the artsSettore MAT/04 - Matematiche Complementari060105 history of science technology & medicineIrrational numberBicomplex numberMathematics::Differential GeometryWilliam Rowan Hamilton
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Robert de Montessus de Ballore's 1902 theorem on algebraic continued fractions : genesis and circulation

2013

Robert de Montessus de Ballore proved in 1902 his famous theorem on the convergence of Pad\'e approximants of meromorphic functions. In this paper, we will first describe the genesis of the theorem, then investigate its circulation. A number of letters addressed to Robert de Montessus by different mathematicians will be quoted to help determining the scientific context and the steps that led to the result. In particular, excerpts of the correspondence with Henri Pad\'e in the years 1901-1902 played a leading role. The large number of authors who mentioned the theorem soon after its derivation, for instance N\"orlund and Perron among others, indicates a fast circulation due to factors that w…

01A55 01A60[MATH.MATH-HO]Mathematics [math]/History and Overview [math.HO]Mathematics - History and Overview[MATH.MATH-HO] Mathematics [math]/History and Overview [math.HO][ MATH.MATH-HO ] Mathematics [math]/History and Overview [math.HO]
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