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Lectures for high school students

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A series of scientific informative lectures for interested high school students has been organized by the HUN-REN Morphodynamics Research Group.

  • Kocsis Kinga: Ezer tonna márvány, avagy tér-idő utazás Michelangelo kőtömbjeihez (A thousand ton of marble or a time-space travel to the stones of Michelangelo)
  • Szondi Máté: Alakevolúciós egyenlet használata membránfelületek számítására (Application of shape evolution equations for calculating membrane surfaces)
  • Regős Krisztina: A diszkrét Gömböc nyomában (In the wake of a discrete Gömböc)
    (Lovassy László High School, Veszprém, 8 December, 2023)
  • Almádi Gergő: Tetraéderek egyensúlyairól (On equilibria of tetrahedra)
  • Nagy Klaudia: Falak geometriája (The geometry of walls)
  • Regős Krisztina: A diszkrét Gömböc nyomában (In the wake of a discrete Gömböc)
    (Deák Ferenc High School, Budapest, 23 January, 2024) Link
  • Regős Krisztina: A diszkrét Gömböc nyomában (In the wake of a discrete Gömböc)
  • Ferencz Eszter: Repedéshálózatok időfejlődése, avagy a Gilbert-piaffe (Time evolution of crack networks or the Gilbert piaffe)
  • Kocsis Kinga: Ezer tonna márvány, avagy tér-idő utazás Michelangelo kőtömbjeihez (A thousand ton of marble or a time-space travel to the stones of Michelangelo)
    (Árpád High School, Budapest, 27 March, 2024)
  • Almádi Gergő – Regős Krisztina: A diszkrét Gömböc nyomában (In the wake of a discrete Gömböc)
    (Teleki Blanka High School, Budapest, 23 April, 2024)
  • Domokos Gábor: A láthatatlan kocka (The invisible cube)
    (Teleki Blanka High School, Székesfehérvár, 20 June, 2024)
  • Domokos Gábor: Kemény sziklák és lágy cellák (Hard rocks and soft cells)
  • Almádi Gergő: Repedéshálózatok időfejlődése, avagy a Gilbert-piaffe (Time evolution of crack networks or the Gilbert piaffe)
  • Regős Krisztina: A diszkrét Gömböc nyomában (In the wake of a discrete Gömböc)
  • Szondi Máté: Adhat-e ötletet a természetes kopás a héjszerkezetek tervzéséhez? (Can natural abrasion inspire the design of membrane structures?)
    (Camp of Mathematics, organized by the Trefort Ágoston High School of Budapest, Visegrád, 19 October, 2024)

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New paper on soft cells in geometry and biology

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Soft cells and the geometry of seashells
Gábor Domokos, Alain Goriely, Ákos G. Horváth, Krisztina Regős.

Abstract: A central problem of geometry is the tiling of space with simple structures. The classical solutions, such as triangles, squares, and hexagons in the plane and cubes and other polyhedra in three-dimensional space are built with sharp corners and flat faces. However, many tilings in Nature are characterized by shapes with curved edges, nonflat faces, and few, if any, sharp corners. An important question is then to relate prototypical sharp tilings to softer natural shapes. Here, we solve this problem by introducing a new class of shapes, the soft cells, minimizing the number of sharp corners and filling space as soft tilings. We prove that an infinite class of polyhedral tilings can be smoothly deformed into soft tilings and we construct the soft versions of all Dirichlet–Voronoi cells associated with point lattices in two and three dimensions. Remarkably, these ideal soft shapes, born out of geometry, are found abundantly in nature, from cells to shells.

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Awards, Students, Uncategorised

Institutional Scientific Students’ Associations Conference 2023

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At this year’s Institutional Scientific Students’ Associations Conference at the Budapest University of Technology and Economics, five presentations were related to Morphodynamics: Máté Szondi (1st Prize + Pro Progressio Special Prize), Gergő Almádi (1st Prize), Gergő Almádi and Eszter Ferencz (3rd Prize), Kinga Kocsis (Special award of the Department of Geometry and Morphology + Special award for presentation), Emese Sarolta Encz and Gergely Barta (Special award of the Department of Geometry and Morphology).
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Awards, Students, Uncategorised

National Scientific Students’ Associations Conference 2023

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Several presentations were held in the session for Mathematics, Physics and Geosciences of the 36th National Scientific Students’ Associations Conference in relation with the Morphodynamics Research Group. Gergő Almádi has been awarded by 3rd prize for his presentation entitled Inhomogén politópok mechanikai komplexitása – avagy van-e egy tetraédernek lelke?, under the supervision of Gábor Domokos and Krisztina Regős. Ágoston Szesztay (Iteratív módon csonkolt poliéderek statikai egyenúlyáról) and Máté Szondi (A kvantummechanikai állapottér egy felbontása által indukált geometria) got special prizes.
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Institutional Scientific Students’ Associations Conference 2021

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The Morphodynamics Group had a session titled ‘Geometry’ in the 2021 TDK Conference. Five students participated in the session and received numerous awards. Congratulations!
Krisztina Regős (1st Prize + Rector’s Award), Anna Viczián (1st Prize), Ágoston Szesztay (3rd Prize + Csonka Pál Special Prize), Klaudia Nagy (Department’s Special Prize), Máté Szondi (Metszet Journal Special Prize).
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Institutional Scientific Students’ Associations Conference 2020

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At this year’s Institutional Scientific Students’ Associations Conference at the Budapest University of Technology and Economics, 2 presentations were related to Morphodynamics: Ágoston Szesztay (1st Prize + Pro Progressio Special Prize), Klaudia Nagy (Csonka Pál Special Prize).
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New paper on Balancing polyhedra

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Balancing polyhedra
G. Domokos, F. Kovács, Z. Lángi, K. Regős and P.T. Varga, Balancing polyhedra, Ars Math. Contemp., accepted, arXiv:1810.05382 [math.MG]

Abstract: We define the mechanical complexity C(P) of a convex polyhedron P, interpreted as a homogeneous solid, as the difference between the total number of its faces, edges and vertices and the number of its static equilibria, and the mechanical complexity C(S,U) of primary equilibrium classes (S,U)E with S stable and U unstable equilibria as the infimum of the mechanical complexity of all polyhedra in that class. We prove that the mechanical complexity of a class (S,U)E with S,U>1 is the minimum of 2(f+v−S−U) over all polyhedral pairs (f,v), where a pair of integers is called a polyhedral pair if there is a convex polyhedron with f faces and v vertices. In particular, we prove that the mechanical complexity of a class (S,U)E is zero if, and only if there exists a convex polyhedron with S faces and U vertices. We also give asymptotically sharp bounds for the mechanical complexity of the monostatic classes (1,U)E and (S,1)E, and offer a complexity-dependent prize for the complexity of the Gömböc-class (1,1)E.

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Institutional Scientific Students’ Associations Conference 2018

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At this year’s Institutional Scientific Students’ Associations Conference at the Budapest University of Technology and Economics, 3 presentations were related to Morphodynamics: Krisztina Regős (1st Prize + Pro Progressio Special Prize), Dániel Csallóközi (2nd Prize + Csonka Pál Special Prize), Péter Tamás Varga (3rd Prize).
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