The Monge theorem and its application in engineering practice

Balajti, Zsuzsanna; Dudás, Illés

doi:10.1007/s00170-016-9763-1

Cited by 9 publications

(7 citation statements)

References 5 publications

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“…MT implies that the projections arising from three separated objects (i.e., two- or three-dimensional circles) give rise to a line that is external to the three objects. MT has been operationally used to calculate the correct camera position for the wearing examination of the cutting edge of the hob, by calculating the inner points of the Monge cuboid and their parallel shifting (defined by the bijective Monge projections) bordered by a surface [ 123 ]. Further, MT is still valid even if the plane is equipped with non-Euclidean metrics [ 124 ].…”

Section: Mathematics and Visual Perceptionmentioning

confidence: 99%

Unusual Mathematical Approaches Untangle Nervous Dynamics

Tozzi

Mariniello

2022

Biomedicines

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The massive amount of available neurodata suggests the existence of a mathematical backbone underlying neuronal oscillatory activities. For example, geometric constraints are powerful enough to define cellular distribution and drive the embryonal development of the central nervous system. We aim to elucidate whether underrated notions from geometry, topology, group theory and category theory can assess neuronal issues and provide experimentally testable hypotheses. The Monge’s theorem might contribute to our visual ability of depth perception and that the brain connectome can be tackled in terms of tunnelling nanotubes. The multisynaptic ascending fibers connecting the peripheral receptors to the neocortical areas can be assessed in terms of knot theory/braid groups. Presheaves from category theory permit the tackling of nervous phase spaces in terms of the theory of infinity categories, highlighting an approach based on equivalence rather than equality. Further, the physical concepts of soft-matter polymers and nematic colloids might shed new light on neurulation in mammalian embryos. Hidden, unexpected multidisciplinary relationships can be found when mathematics copes with neural phenomena, leading to novel answers for everlasting neuroscientific questions. For instance, our framework leads to the conjecture that the development of the nervous system might be correlated with the occurrence of local thermal changes in embryo–fetal tissues.

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Section: Mathematics and Visual Perceptionmentioning

confidence: 99%

Unusual Mathematical Approaches Untangle Nervous Dynamics

Tozzi

Mariniello

2022

Biomedicines

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“…Due to their excessive extent, we consider the justifying calculus can be omitted here. The value of the tilt angle α k with respect to (8), becomes (9)…”

Section: The Geometric Model Of the Relieving Operationmentioning

confidence: 99%

The Improvement of the Precision of the Archimedean Spiral Toothline Gear Cutting Mill

Gyéresi

Cristea

Máté

2021

Műszaki Tudományos Közlemények

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The precision of gears has a major influence on the quality of the transmission. If the gear cannot be finished by grinding, the precision of the generating tool becomes essential. Archimedean spiral toothline cylindrical gears are obtained by reciprocate meshing using a milling cutter built up by individual cutters, organized in groups. The profiles of edges must be realized with a minimal profile error. In order to ensure the quality and the precision of the meshed tooth surface, and also the profile constancy after re-sharpening, relief faces must be realized by a grinding relieving operation. A secondary effect of the kinematics of relieving end the spatial extent of the grinding wheel a post undercut results and this produces an inevitable profile error. The present paper discusses a possible grinding wheel setting that produces a maximum theoretical profile error under 1μm along the whole re-sharpening reserve of the cutter. The proposed setting can be realized on a classical relieving lathe.

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“…Monge's theorem (Fig. 5) states that for any three circles in a plane, none of which is completely inside one of the others, the intersection points of each of the three pairs of external tangent lines are collinear [26].…”

Section: Monge's Theoremmentioning

confidence: 99%

“…Each such pair has a unique intersection point in the extended Euclidean plane. Monge's theorem states that the three such points given by each circle are always in a straight line [26]. Monge's theorem can be proved by using Desargues' theorem and Menelaus' theorem [37].…”

Section: Monge's Theoremmentioning

confidence: 99%

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The man who invented descriptive geometry

Cvetković¹,

Stojičević²,

Stachel³

et al. 2019

FME Transactions

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is known as the father of modern descriptive and differential geometry. In 1764, he was engaged to draw a detailed plan of a fortification in his hometown, which was seen by an officer at the École Royale du Génie de Mézières. This plan was a success and his techniques were marked as a military secret for a long period of time. In 1780, he was elected to the Academy of Science and participated in the work of the Commission for Weights and Measures, that was in charge of moving the system from imperial to metric. In 1794, Monge helped setting up the École Centrale des Travaux Publics (later École Polytechnique) where he was lecturing Descriptive Geometry. In 1798, Napoleon undertook a campaign in Egypt. The famous chemist Claude Louis Berthollet was asked to recruit prominent scientists. Among them were Fourier, Monge, Dolomieu and Malus. Institut d'Egypte was established by Napoleon and Monge was named as its first president. Monge passed away on July 28, 1818. His name is inscribed on the base of the Eiffel Tower and it is located on the third façade opposite the Military Academy. Besides descriptive geometry, he carried on many different researches in chemistry and physics.

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The Monge theorem and its application in engineering practice

Cited by 9 publications

References 5 publications

Unusual Mathematical Approaches Untangle Nervous Dynamics

Unusual Mathematical Approaches Untangle Nervous Dynamics

The Improvement of the Precision of the Archimedean Spiral Toothline Gear Cutting Mill

The man who invented descriptive geometry

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