Visualization of Enneper’s surface by line graphics

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 387-405 ◽  
Author(s):  
Vesna Velickovic
Keyword(s):  
Minimal Surface ◽  
Graphical Representations ◽  
Lines Of Curvature ◽  
Geodesic Lines

Here we study Enneper?s minimal surface and some of its properties. We compute and visualize the lines of self-intersection, lines of intersections with planes, lines of curvature, asymptotic and geodesic lines of Enneper?s surface. For the graphical representations of all the results we use our own software for line graphics.

A CHARACTERIZATION OF THE CATENOID AND HELICOID

2013 ◽  
Vol 24 (06) ◽  
pp. 1350045 ◽  
Author(s):  
CARLOS M. C. RIVEROS ◽  
ARMANDO M. V. CORRO
Keyword(s):  
Minimal Surface ◽  
Minimal Surfaces ◽  
Geodesic Curvature ◽  
Lines Of Curvature ◽  
Asymptotic Lines

In this paper we show that a connected non-planar minimal surface whose asymptotic lines have the same geodesic curvature up to sign is a catenoid. As an application of this result we show that a connected non-planar minimal surface whose lines of curvature have the same geodesic curvature up to sign is a helicoid. Moreover, we show that the coordinates curves of the associate minimal surfaces to catenoid have the same geodesic curvature up to sign.

Proof Theory of the Cut Rule

2018 ◽  
Author(s):  
J. R. B. Cockett ◽  
R. A. G. Seely
Keyword(s):  
Proof Theory ◽  
Graphical Representation ◽  
Basic Component ◽  
Graphical Representations ◽  
Mathematical Language ◽  
Basic Logic ◽  
Cut Rule ◽  
Structural Rules ◽  
The One ◽  
Categorical Semantics

This chapter describes the categorical proof theory of the cut rule, a very basic component of any sequent-style presentation of a logic, assuming a minimum of structural rules and connectives, in fact, starting with none. It is shown how logical features can be added to this basic logic in a modular fashion, at each stage showing the appropriate corresponding categorical semantics of the proof theory, starting with multicategories, and moving to linearly distributive categories and *-autonomous categories. A key tool is the use of graphical representations of proofs (“proof circuits”) to represent formal derivations in these logics. This is a powerful symbolism, which on the one hand is a formal mathematical language, but crucially, at the same time, has an intuitive graphical representation.

Binding of Alkenes and Ionic Liquids to B–H-Functionalized Boron Nanoparticles: Creation of Particles with Controlled Dispersibility and Minimal Surface Oxidation

2015 ◽  
Vol 7 (18) ◽  
pp. 9991-10003 ◽  
Author(s):  
Jesus Paulo L. Perez ◽  
Jiang Yu ◽  
Anna J. Sheppard ◽  
Steven D. Chambreau ◽  
Ghanshyam L. Vaghjiani ◽  
...  
Keyword(s):  
Ionic Liquids ◽  
Minimal Surface ◽  
Surface Oxidation

Reducing misperceptions through news stories with data visualization: The role of readers’ prior knowledge and prior beliefs

Journalism ◽  
2021 ◽  
pp. 146488492110287
Author(s):  
Paul Mena
Keyword(s):  
Experimental Design ◽  
Prior Knowledge ◽  
Data Visualization ◽  
Accurate Information ◽  
Graphical Representations ◽  
Prior Beliefs ◽  
News Stories ◽  
Issue Involvement

Amid the global discussion on ways to fight misinformation, journalists have been writing stories with graphical representations of data to expose misperceptions and provide readers with more accurate information. Employing an experimental design, this study explored to what extent news stories correcting misperceptions are effective in reducing them when the stories include data visualization and how influential readers’ prior beliefs, issue involvement and prior knowledge may be in that context. The study found that the presence of data visualization in news articles correcting misperceptions significantly enhanced the reduction of misperceptions among news readers with less than average prior knowledge about an issue. In addition, it was found that prior beliefs had a significant effect on news readers’ misperceptions regardless of the presence or absence of data visualization. In this way, this research offers some support for the notion that data visualization may be useful to decrease misperceptions under certain circumstances.

scholarly journals From surfaces in the 5-sphere to 3-manifolds in complex projective 3-space

2002 ◽  
Vol 66 (3) ◽  
pp. 465-475 ◽  
Author(s):  
J. Bolton ◽  
C. Scharlach ◽  
L. Vrancken
Keyword(s):  
Projective Space ◽  
Minimal Surface ◽  
Complex Projective Space ◽  
Lagrangian Submanifold ◽  
3 Dimensional ◽  
Ellipse Of Curvature ◽  
Complex Projective

In a previous paper it was shown how to associate with a Lagrangian submanifold satisfying Chen's equality in 3-dimensional complex projective space, a minimal surface in the 5-sphere with ellipse of curvature a circle. In this paper we focus on the reverse construction.

Clustered Iconography: A Resurrected Method for Representing Multidimensional Data

2020 ◽  
pp. 004912412091494
Author(s):  
Olav Muurlink ◽  
Anthony M. Gould ◽  
Jean-Etienne Joullié
Keyword(s):  
Twentieth Century ◽  
Open Source ◽  
Multidimensional Data ◽  
Statistical Techniques ◽  
Graphical Representations ◽  
Graphical Methods ◽  
History Of ◽  
Research Findings

Development of graphical methods for representing data has not kept up with progress in statistical techniques. This article presents a brief history of graphical representations of research findings and makes the case for a revival of methods developed in the early and mid-twentieth century, notably ISOTYPE and Chernoff’s faces. It resurrects and improves a procedure, clustered iconography, which enables the presentation of multidimensional data through which readers engage more effectively with the presentation’s central message by way of an easier understanding of relationships between variables. The proposed technique is especially well adapted to the needs and protocols of open-source research.

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