scholarly journals Demonstration in geometry: historical and philosophical perspectives

2020 ◽  
Vol 8 (18) ◽  
pp. 540-570
Author(s):  
Saddo Ag Almouloud

In this article, we weave historical-philosophical reflections about demonstration in mathematics, based on works of researchers that discuss the different philosophical perspectives on the topic, more specifically on geometry. We focus first on demonstration and its relationship with intuition and figural representations. Second, we criticize Poincaré’s conception of mathematical demonstration. Third, we reflect, in a non-exhaustive way, on the philosophy of demonstration in geometry, confronting Kant’s conceptions with the axiomatizations of the non-Euclidean geometries. In this text, we do not adopt a single definition that would cover all modes of scientific validation, since we admit the possibility of an evolution of ideas about the validity of a proposition. Not to fall into the symmetrical flaws of the glorification of the Ancients or even being ungrateful to them, we must start from the naive idea that the demonstration has a historical origin and, therefore, maintains a historical character, but we should be more attentive to what characterizes, in its particularity or even its uniqueness, the productions of past and present centuries. Keywords: Philosophy of demonstration; Axiomatization; Induction; Intuition; Representation.

2021 ◽  
Vol 2 ◽  
Author(s):  
Rajender Kumar Sharma

Abstract Seeds of Abrus precatorius L. (Fabaceae) were used as weight measure by Indigenous people. Where, the seeds were referred as Ratti; a traditional Indian unit of mass measurement. Seed weight fluctuates depending upon age, moisture, storage-period/conditions. Therefore, use of seeds as a weighing unit become dubious and need to be validated. For this purpose, seeds of A. precatorious were subjected to different moisture conditions and periodically monitored. Surprisingly, there was no change in seed weight was observed, indicating the impermeability of seed coat. The later was confirmed by scarification of seed coat which resulted in 53% increase in seed weight against 0% in control. Further, presence of a potent toxin (abrin) in the seed coat protects it from pests and microbes, and contributes to the maintenance of impermeability for longer period of time. The data validates the use of A. precatorious seeds as a weighing unit (ratti) by the indigenous people and discussed.


Plants ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 584
Author(s):  
Nadia Las Heras Las Heras Etayo ◽  
Félix Llamas ◽  
Carmen Acedo

The species Chiliadenus glutinosus (L.) Fourr. has a large number of therapeutic uses reported in the traditional Spanish medicine. The growing interest in preserving the ethnopharmacological knowledge related to the botanical diversity existing in Spain and the interest in achieving scientific validation of the therapeutic properties of medicinal species has led to the development of this study. To do it, all the known medicinal uses of Ch. glutinosus in Spain were compiled, then an exhaustive bibliographic research on its chemical composition was carried out, and finally, an in silico validation of the bioactive phytochemicals present in a higher proportion in the essential oil of Ch. glutinosus: camphor, borneol, lucinone, glutinone, quercetin, kutdtriol, and kaempferol; in an attempt to justify the reported traditional uses of the species. It was found that much of the traditional medicinal uses of Ch. glutinosus, along with the biological activity of its phytochemicals, are supported by scientific evidence. The results place this species in a prominent position to initiate possible lines of research to develop new, more effective drugs and improve therapies to treat conditions and diseases that affect the different organic systems of the human being.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Barbara Helena Barcaro Machado ◽  
Ivy Dantas De Melo E. Silva ◽  
Walter Marou Pautrat ◽  
James Frame ◽  
Mohammad Najlah

AbstractMeasuring outcomes from treatments to the skin is either reliant upon patient’s subjective feedback or scale-based peer assessments. Three-Dimensional stereophotogrammetry intend to accurately quantify skin microtopography before and after treatments. The objective of this study is comparing the accuracy of stereophotogrammetry with a scale-based peer evaluation in assessing topographical changes to skin surface following laser treatment. A 3D stereophotogrammetry system photographed skin surface of 48 patients with facial wrinkles or scars before and three months after laser resurfacing, followed immediately by topical application of vitamin C. The software measured changes in skin roughness, wrinkle depth and scar volume. Images were presented to three observers, each independently scoring cutaneous improvement according to Investigator Global Aesthetic Improvement Scale (IGAIS). As for the results, a trend reflecting skin/scar improvement was reported by 3D SPM measurements and raters. The percentage of topographical change given by the raters matched 3D SPM findings. Agreement was highest when observers analysed 3D images. However, observers overestimated skin improvement in a nontreatment control whilst 3D SPM was precise in detecting absence of intervention. This study confirmed a direct correlation between the IGAIS clinical scale and 3D SPM and confirmed the efficacy and accuracy of the latter when assessing cutaneous microtopography alterations as a response to laser treatment.


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