Thinking Geometrically

Pedoe, D.

doi:10.1080/00029890.1970.11992565

Cited by 7 publications

(6 citation statements)

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“…I am not crying with Dieudonné "down with Euclid" [50] or "away with triangle" [51], but I agree that the secure ancient mathematical paradise has been lost [52], for of no formal system one can affirm with certainty that all contentual considerations are representable within it [53]. Thus definitions in analysis are not to be considered as arbitrary; they must satisfy the condition of utility as regards the science to which they belong [54].…”

Section: Volume 50mentioning

confidence: 99%

Mathematical Gateway to Complementary Hidden Variables in Macrophysics

Czajko

2015

ILCPA

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It is shown that even physically meaningful and experimentally confirmed formulas of physics and mathematics can be extended by enabling some previously unrecognized (or considered as just fixed) parameters to either vary independently and thus reveal them as previously hidden variables or to turn them into fixed exposure functions whose cumulative impact varies along yet another formerly hidden variable. Uncovering of hidden variables requires (new) synthetic approach to mathematics. The need for revealing hidden variables is prompted mainly by unanticipated experimental results, whose more precise outcomes apparently challenge the previously espoused paradigms upon which those simpler former formulas had been established. Operational rules of calculus can reveal the hidden variables that could extend the laws of classical physics whose predictions disagree with new experimental evidence. Presence of such variables has already been confirmed in several experiments.

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Section: Volume 50mentioning

confidence: 99%

Mathematical Gateway to Complementary Hidden Variables in Macrophysics

Czajko

2015

ILCPA

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“…The well-known Neuberg-Pedoe inequality is the first inequality involving two triangles [20]. Following Pedoe, a number of inequalities for two simplices have been established (see [15], [21], and [29]). Yang and Zhang in [28] generalized the Neuberg-Pedoe inequality to R n .…”

Section: Some Results Involving Two Simplicesmentioning

confidence: 99%

The Mixed Volume of Two Finite Vector Sets

Leng

2004

Discrete Comput Geom

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“…the three sides of the triangles. The inequality U A,B ≥ 2S A S B , expressing the fact that the discriminant of Equation (10) is always nonnegative, is known in geometry as the Neuberg-Pedoe inequality [13,14]; the equality case is precisely when the two triangles are similar. The diamond configuration occurs when β < 1 < α, i.e.…”

Section: Classification Of 3-rpr Manipulatorsmentioning

confidence: 99%