Results 81 to 90 of about 99 (99)
Function Art: Linking Mathematics, Technology, and Visual Arts
School Science and Mathematics, EarlyView.ABSTRACT This study investigated students' understanding of mathematical functions and strategies to create artwork using GeoGebra. It was framed by the principles of constructionism and examined how students use functions in creating artworks. We gathered data from students' artworks using the Algebra view and the Construction Protocol in the GeoGebra
Guillermo Bautista Jr +5 more
wiley +1 more source
Where Mathematical Symbols Come From
Topics in Cognitive Science, EarlyView.Abstract There is a sense in which the symbols used in mathematical expressions and formulas are arbitrary. After all, arithmetic would be no different if we would replace the symbols ‘+$+$’ or ‘8’ by different symbols. Nevertheless, the shape of many mathematical symbols is in fact well motivated in practice.
Dirk Schlimm
wiley +1 more source
Parallel Architecture: From Problems and Mysteries to Solutions and Explanations
Topics in Cognitive Science, EarlyView.Abstract We argue that Jackendoff's Parallel Architecture (PA) is the right way to think about the architecture of the language faculty. The critical property of this architecture is that it allows for genuine explanation by allocating different aspects of linguistic phenomena to appropriate corresponding representations and capacities.
Peter W. Culicover, Giuseppe Varaschin
wiley +1 more source
The birational geometry of GIT quotients
Bulletin of the London Mathematical Society, EarlyView.Abstract Geometric invariant theory (GIT) produces quotients of algebraic varieties by reductive groups. If the variety is projective, this quotient depends on a choice of polarisation; by work of Dolgachev–Hu and Thaddeus, it is known that two quotients of the same variety using different polarisations are related by birational transformations.
Ruadhaí Dervan, Rémi Reboulet
wiley +1 more source
Removing scalar curvature assumption for Ricci flow smoothing
Bulletin of the London Mathematical Society, EarlyView.Abstract In recent work of Chan–Huang–Lee, it is shown that if a manifold enjoys uniform bounds on (a) the negative part of the scalar curvature, (b) the local entropy, and (c) volume ratios up to a fixed scale, then there exists a Ricci flow for some definite time with estimates on the solution assuming that the local curvature concentration is small ...
Adam Martens
wiley +1 more source
Noncompact surfaces, triangulations and rigidity
Bulletin of the London Mathematical Society, EarlyView.Abstract Every noncompact surface is shown to have a (3,6)‐tight triangulation, and applications are given to the generic rigidity of countable bar‐joint frameworks in R3${\mathbb {R}}^3$. In particular, every noncompact surface has a (3,6)‐tight triangulation that is minimally 3‐rigid. A simplification of Richards' proof of Kerékjártó's classification
Stephen C. Power
wiley +1 more source
Étale motives of geometric origin
Bulletin of the London Mathematical Society, EarlyView.Abstract Over qcqs finite‐dimensional schemes, we prove that étale motives of geometric origin can be characterised by a constructibility property which is purely categorical, giving a full answer to the question ‘Do all constructible étale motives come from geometry?’ which dates back to Cisinski and Déglise's work.
Raphaël Ruimy, Swann Tubach
wiley +1 more source
Presentation of kernels of rational characters of right‐angled Artin groups
Bulletin of the London Mathematical Society, EarlyView.Abstract In this note, we characterise when the kernel of a rational character of a right‐angled Artin group, also known as generalised Bestiva–Brady group, is finitely generated and finitely presented. In these cases, we exhibit a finite generating set and a presentation.
Montserrat Casals‐Ruiz +2 more
wiley +1 more source
Graphical models for topological groups: A case study on countable Stone spaces
Bulletin of the London Mathematical Society, EarlyView.Abstract By analogy with the Cayley graph of a group with respect to a finite generating set or the Cayley–Abels graph of a totally disconnected, locally compact group, we detail countable connected graphs associated to Polish groups that we term Cayley–Abels–Rosendal graphs.
Beth Branman +3 more
wiley +1 more source
Thurston obstructions and tropical geometry
Bulletin of the London Mathematical Society, EarlyView.Abstract We describe an application of tropical moduli spaces to complex dynamics. A post‐critically finite branched covering φ$\varphi$ of S2$S^2$ induces a pullback map on the Teichmüller space of complex structures of S2$S^2$; this descends to an algebraic correspondence on the moduli space of point‐configurations of P1$\mathbb {P}^1$.
Rohini Ramadas
wiley +1 more source