10 research outputs found
Discrete Geometry
A number of important recent developments in various branches of discrete geometry were presented at the workshop. The presentations illustrated both the diversity of the area and its strong connections to other fields of mathematics such as topology, combinatorics or algebraic geometry. The open questions abound and many of the results presented were obtained by young researchers, confirming the great vitality of discrete geometry
Colorful Borsuk--Ulam theorems and applications
We prove a colorful generalization of the Borsuk--Ulam theorem and derive
colorful consequences from it, such as a colorful generalization of the ham
sandwich theorem. Even in the uncolored case this specializes to a
strengthening of the ham sandwich theorem, which given an additional condition,
contains a result of B\'{a}r\'{a}ny, Hubard, and Jer\'{o}nimo on well-separated
measures as a special case. We prove a colorful generalization of Fan's
antipodal sphere covering theorem, we derive a short proof of Gale's colorful
KKM theorem, and we prove a colorful generalization of Brouwer's fixed point
theorem. Our results also provide an alternative between Radon-type
intersection results and KKM-type covering results. Finally, we prove colorful
Borsuk--Ulam theorems for higher symmetry.Comment: 15 page
Discrete Geometry and Convexity in Honour of Imre Bárány
This special volume is contributed by the speakers of the Discrete Geometry and
Convexity conference, held in Budapest, June 19–23, 2017. The aim of the conference
is to celebrate the 70th birthday and the scientific achievements of professor
Imre Bárány, a pioneering researcher of discrete and convex geometry, topological
methods, and combinatorics. The extended abstracts presented here are written by
prominent mathematicians whose work has special connections to that of professor
Bárány. Topics that are covered include: discrete and combinatorial geometry,
convex geometry and general convexity, topological and combinatorial methods.
The research papers are presented here in two sections. After this preface and a
short overview of Imre Bárány’s works, the main part consists of 20 short but very
high level surveys and/or original results (at least an extended abstract of them)
by the invited speakers. Then in the second part there are 13 short summaries of
further contributed talks.
We would like to dedicate this volume to Imre, our great teacher, inspiring
colleague, and warm-hearted friend
Large bichromatic point sets admit empty monochromatic 4-gons
We consider a variation of a problem stated by ErdËťos
and Szekeres in 1935 about the existence of a number
fES(k) such that any set S of at least fES(k) points in
general position in the plane has a subset of k points
that are the vertices of a convex k-gon. In our setting
the points of S are colored, and we say that a (not necessarily
convex) spanned polygon is monochromatic if
all its vertices have the same color. Moreover, a polygon
is called empty if it does not contain any points of
S in its interior. We show that any bichromatic set of
n ≥ 5044 points in R2 in general position determines
at least one empty, monochromatic quadrilateral (and
thus linearly many).Postprint (published version
LIPIcs, Volume 258, SoCG 2023, Complete Volume
LIPIcs, Volume 258, SoCG 2023, Complete Volum
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
The benefits of an additional practice in descriptive geomerty course: non obligatory workshop at the Faculty of Civil Engineering in Belgrade
At the Faculty of Civil Engineering in Belgrade, in the Descriptive geometry (DG) course,
non-obligatory workshops named “facultative task” are held for the three generations of freshman
students with the aim to give students the opportunity to get higher final grade on the exam. The
content of this workshop was a creative task, performed by a group of three students, offering free
choice of a topic, i.e. the geometric structure associated with some real or imagery
architectural/art-work object.
After the workshops a questionnaire (composed by the professors at the course) is given to the
students, in order to get their response on teaching/learning materials for the DG course and the
workshop. During the workshop students performed one of the common tests for testing spatial
abilities, named “paper folding".
Based on the results of the questionnairethe investigation of the linkages between:students’
final achievements and spatial abilities, as well as students’ expectations of their performance on
the exam, and how the students’ capacity to correctly estimate their grades were associated with
expected and final grades, is provided. The goal was to give an evidence that a creative work,
performed by a small group of students and self-assessment of their performances are a good way
of helping students to maintain motivation and to accomplish their achievement.
The final conclusion is addressed to the benefits of additional workshops employment in the
course, which confirmhigherfinal scores-grades, achievement of creative results (facultative tasks)
and confirmation of DG knowledge adaption
The contemporary visualization and modelling technologies and the techniques for the design of the green roofs
The contemporary design solutions are merging the boundaries between real and virtual world. The Landscape architecture like the other interdisciplinary field stepped in a contemporary technologies area focused on that, beside the good execution of works, designer solutions has to be more realistic and “touchable”. The opportunities provided by Virtual Reality are certainly not negligible, it is common knowledge that the designs in the world are already presented in this way so the Virtual Reality increasingly used.
Following the example of the application of virtual reality in landscape architecture, this paper deals with proposals for the use of virtual reality in landscape architecture so that designers, clients and users would have a virtual sense of scope e.g. rooftop garden, urban areas, parks, roads, etc. It is a programming language that creates a series of images creating a whole, so
certain parts can be controlled or even modified in VR. Virtual reality today requires a specific gadget, such as Occulus, HTC Vive, Samsung Gear VR and similar.
The aim of this paper is to acquire new theoretical and practical knowledge in the
interdisciplinary field of virtual reality, the ability to display using virtual reality methods, and to present through a brief overview the plant species used in the design and construction of an intensive roof garden in a Mediterranean climate, the basic characteristics of roofing gardens as well as the benefits they carry.
Virtual and augmented reality as technology is a very powerful tool for landscape architects, when modeling roof gardens, parks, and urban areas. One of the most popular technologies used by landscape architects is Google Tilt Brush, which enables fast modeling. The Google Tilt Brush VR app allows modeling in three-dimensional virtual space using a palette to work with the use of a three dimensional brush.
The terms of two "programmed" realities - virtual reality and augmented reality - are often confused. One thing they have in common, though, is VRML - Virtual Reality Modeling Language.
In this paper are shown the ways on which this issue can be solved and by the way, get closer the term of Virtual Reality (VR), also all the opportunities which the Virtual reality offered us. As well, in this paper are shown the conditions of Mediterranean climate, the conceptual solution and the plant species which will be used by execution of intensive green roof on the motel “Marković”