Pythagoras as a mathematician

AbstractIn this article, two questions are posed: Just how reliable is the evidence concerning Pythagoras's mathematical studies, and can we reconstruct his contribution to mathematics? All known fragments of evidence by fourth-century B.C. authors on Pythagoras's mathematical investigations are examined, and it is shown that all the discoveries they mentioned belong to the sixth century B.C. The opinion that the Pythagoreans ascribed their own discoveries to Pythagoras is refuted, and it is shown that we are able to establish logically his contribution to mathematics

The Extremal Structure Of Locally Compact Convex Sets

Let X be a locally compact closed convex subset of a locally convex Hausdorff topological linear space E. Then every exposed point of X is strongly exposed. The definitions of denting (strongly extreme) ray and strongly exposed ray are given for convex subsets of E. If X does not contain a line, then every extreme ray is strongly extreme and every exposed ray is strongly exposed. An example is given to show that the hypothesis that X be locally compact is necessary in both cases. © 1976 Pacific Journal of Mathematics. All rights reserved

Non Linear System for a Veritable PID Substitute

The paper deals with a non-linear system largely used in biology, which, in certain conditions and for particular coefficient values, becomes linear, with a linear diagram over a large range of time. It can be used as a veritable regulator in systems' controlComment: 4 pages, exposed on 2nd "European Conference on Computer Sience and Applications" - XA2008, Timisoara, Romani

Inductive Constructions In Logic And Graph Theory

Just as much as mathematics is about results, mathematics is about methods. This thesis focuses on one method: induction. Induction, in short, allows building complex mathemati- cal objects from simple ones. These mathematical objects include the foundational, like logical statements, and the abstract, like cell complexes. Non-mathematicians struggle to find a common thread throughout all of mathematics, but I present induction as such a common thread here. In particular, this thesis discusses everything from the very foundations of mathematics all the way to combina- torial manifolds. I intend to be casual and opinionated while still providing all necessary formal rigor. This way, the content can be as readable as possible while still being complete

Visual Perceptual Difficulties and Under-Achievement at School in a Large Community-Based Sample of Children

Difficulties with visual perception (VP) are often described in children with neurological or developmental problems. However, there are few data regarding the range of visual perceptual abilities in populations of normal children, or on the impact of these abilities on children's day-to-day functioning. Methods Data were obtained for 4512 participants in an ongoing birth cohort study (Avon Longitudinal Study of Parents and Children; ALSPAC). The children's mothers responded to questions designed to elicit indications of visual perceptual difficulties or immaturity, when their children were aged 13 years. We examined associations with standardised school test results in reading and in mathematics at age 1314 years (SATS-KS3), accounting for potential confounders including IQ. Results Three underlying factors explained half the variance in the VP question responses. These correlated best with questions on interpreting cluttered scenes; guidance of movement and face recognition. The adjusted parameter estimates (95% CI) for the cluttered-scenes factor (0.05; 0.02 to 0.08; p<0.001) suggested positive associations with the reading test results whilst that for the guidance-of-movement factor (0.03; 0.00 to 0.06; p = 0.026) suggested positive association with the mathematics results. The raw scores were associated with both test results. Discussion VP abilities were widely distributed in this sample of 13-year old children. Lower levels of VP function were associated with under-achievement in reading and in mathematics. Simple interventions can help children with VP difficulties, so research is needed into practicable, cost-effective strategies for identification and assessment, so that support can be targeted appropriately