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Bazı Mikromorfolojik Yapılarda Geometrik Modellemeler

Year 2021, Issue: 28, 270 - 274, 30.11.2021
https://doi.org/10.31590/ejosat.996946

Abstract

Bu çalışmada, bitkilerin bazı mikromorfolojik yapılarının geometrik modellere ve matematiksel formüllere sahip olduğunu belirledik. Bitkilerde metobolik faaliyetler sonucu meydana gelen ürünlerin kullanılabilir hale gelmesi, depolanması, iletilmesi gibi görevleri yapan özelleşmiş yapılar bulunmaktadır. Bu yapılar görevlerinin kompleksliğine bağlı olarak farklı şekiller alırlar. Bu şekiller onların görevlerini en verimli şekilde yapabilmelerini sağlar yapıdadır. Mikroskop altında incelemeler sonucunda bu yapılardan bitki kristalleri ve iletim doku elemanlarının onlara az yer kaplama ve dayanıklılık gibi önemli avantajlar sağlayan özel geometrik şekillere sahip oldukları gözlendi. İncelediğimiz bitkilerin mikroskobik gözlemlerinde, kristallerin ve bitkilerde su ve çözünmüş minerallerin iletilmesine hizmet eden bazı iletim doku elemanlarının geometride önemli bir yere sahip olan minimal bir yüzey özelliği gösterdikleri tespit edildi. Minimal yüzeyler sıfır ortalama eğriliği olan yüzeyler olarak tanımlanıp matematiksel formüller ile ifade edilir. Ayrıca bu yapıların helikoid ve uzatılmış üçgen bipiramit (Elongated triangular bipyramid) olarak adlandırılan geometrik modeller gösterdikleri tepit edilmiştir. Bu geometrik modellere ait şematik şekiller ve labaratuvar çalışmaları sonucu bitki örneklerinden mikroskopta çekilmiş fotoğrafları çalışmada verilmiştir.

References

  • Franceschi V.r., H.T., Horner. Calcium oxalate crystals in plants. Botany Review, 1980. 46: 361–427. Vincent R.F., P. Aul. Calcium oxalate in plants: formation and function. Annual Review of Plant Biology, 2005. 56: 41–71.
  • Bouro P.N., S. Weiner, l. Addadi. Calcium oxalate crystals in tomato and tobacco plants: Morphology and in vitro interactions of crystal associated macromolecules. Chemistry European Journal, 2001. 7(9): 1881–1888.
  • Fukuda, H. Tracheary Element for- mation as a Model System of Cell Differentia- tion. Inter. Rev. Cytol. 1992. 136, 289-332.
  • Hofte, H. (2010) Plant Cell Biology: How to Pattern a Wall. Curr. Biol. 20(10), 450-2.
  • Devillard, C.and Walter, C. (2014) Formation of Plant Tracheary Elements in Vitro — A Review. NZ. J. For Sci. 44, 1-14.
  • Oppenheimer, P.E. Real Time Design and Animation of Fractal Plants and Trees. Sig- graph, 20, 55-64. https://doi.org/10.1145/ 15886.15892. 1986.
  • Kaitaniemia, J., S. Hananb, and P.M. Room. Virtual Sorghum: Visualisation of Partitioing and Morphogenesis. Computers and Electronics in Agriculture. 2000. 28, 195—205.
  • Ozdemir, A. Geometrıc Model of Mıcroscopıc Raphıde Crystals In Plant. Botanica. 2021. 27, (1): 62-68.
  • Ozdemir, A. Definiation of annular Type Tracheal Elements of Chard and Numerical Comparision. Journal of Agricultural Faculty of Gaziosmanpaşa University. 2018. 35, (3): 227-230.
  • Bozdag, B., O. Kocabas, Y. Akyol, and C.Ozdemir. New Staining Method For Hand-Cut In Plant Anatomy Studies. Marmara Pharm J. 2016 .20,184-190.
  • William, H.M. and P.Joaquin. The classical Theory of Minimal Surfaces. Bull. Amer. Math. Soc. 2011. 48(3), 325—407.
  • Gray, A. Minimal Surfaces" and "Mini- mal Surfaces and Complex Variables.” Ch. 30 and 31 in Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed.Boca Raton, FL: CRC Press, 681-734. 1997.
  • Lagrange, J.L. Trial of a new method to determine the maxima and minima of indefinite integral formulas. Miscellanea Taurinensia 2, 1760. 325(1), 173-199. (in French).
  • Weisstein, E.W. Catenoid. From Math- World-A Wolfram Web Resource. https://math- world. wolfram. com/Catenoid.html. 2017.
  • Fomenko, A.T. and A.A. TuzhilinEle- ments of the Geometry and Topology of Mini- mal Surfaces in Three-dimensional Space. AMS Bookstore Press, ISBN 978-0-8218-4552-3. 1991.
  • Hoffman, D. and H.M. William. The Global Theory of Properly Embedded Minimal Surfaces. Pacific J. of Math. 1987. 128,361—366.
  • Johnson N.W. Convex solids with regular faces. Canadian Journal of Mathematics, 1966. 18: 169–200.
  • Meusnier, J.B. Memory on the curvature of surfaces. Mem. of foreign scholars. 1776. 10, 477-510. (in French).
  • Hoffman D.: The computer-aided discovery of new embedded minimal surfaces. Mathematical Intelligencer. 19879. 8–21.
  • Robert Br., W. Korn, R. M. Spaldıng, The Geometry of Plant Epıdermal Cells.New Phytol. 1973. 72, 1357-1365.
  • Ozdemir, A. C. Özdemir. Geometrıc defınıtıon of druse crystal ın plant cells. J. Indian bot. 2021. 101 (1&2) 146-151.

Geometric Modeling in Some Micromorphological Structures

Year 2021, Issue: 28, 270 - 274, 30.11.2021
https://doi.org/10.31590/ejosat.996946

Abstract

In this study, we determined that some micromorphological structures of plants have geometric models and mathematical formulas. There are specialized structures in plants that perform tasks such as making usable, storing and transmitting the products formed as a result of metabolic activities. These structures take different shapes depending on the complexity of their functions. These shapes enable them to perform their duties in the most efficient way. As a result of the examinations under the microscope, it was observed that plant crystals and vascular tissue elements from these structures have special geometric shapes that provide them with important advantages such as small space and durability. In the microscopic observations of the plants we examined, it was determined that the crystals and some transmission tissue elements that serve to transmit water and dissolved minerals in plants show a minimal surface feature, which has an important place in geometry. Minimal surfaces are defined as surfaces with zero mean curvature and expressed with mathematical formulas. In addition, it has been determined that these structures show geometric patterns called helicoid and elongated triangular bipyramid. The schematic shapes of these geometric models and the photographs taken from the plant samples under the microscope as a result of laboratory studies are given in the study.

References

  • Franceschi V.r., H.T., Horner. Calcium oxalate crystals in plants. Botany Review, 1980. 46: 361–427. Vincent R.F., P. Aul. Calcium oxalate in plants: formation and function. Annual Review of Plant Biology, 2005. 56: 41–71.
  • Bouro P.N., S. Weiner, l. Addadi. Calcium oxalate crystals in tomato and tobacco plants: Morphology and in vitro interactions of crystal associated macromolecules. Chemistry European Journal, 2001. 7(9): 1881–1888.
  • Fukuda, H. Tracheary Element for- mation as a Model System of Cell Differentia- tion. Inter. Rev. Cytol. 1992. 136, 289-332.
  • Hofte, H. (2010) Plant Cell Biology: How to Pattern a Wall. Curr. Biol. 20(10), 450-2.
  • Devillard, C.and Walter, C. (2014) Formation of Plant Tracheary Elements in Vitro — A Review. NZ. J. For Sci. 44, 1-14.
  • Oppenheimer, P.E. Real Time Design and Animation of Fractal Plants and Trees. Sig- graph, 20, 55-64. https://doi.org/10.1145/ 15886.15892. 1986.
  • Kaitaniemia, J., S. Hananb, and P.M. Room. Virtual Sorghum: Visualisation of Partitioing and Morphogenesis. Computers and Electronics in Agriculture. 2000. 28, 195—205.
  • Ozdemir, A. Geometrıc Model of Mıcroscopıc Raphıde Crystals In Plant. Botanica. 2021. 27, (1): 62-68.
  • Ozdemir, A. Definiation of annular Type Tracheal Elements of Chard and Numerical Comparision. Journal of Agricultural Faculty of Gaziosmanpaşa University. 2018. 35, (3): 227-230.
  • Bozdag, B., O. Kocabas, Y. Akyol, and C.Ozdemir. New Staining Method For Hand-Cut In Plant Anatomy Studies. Marmara Pharm J. 2016 .20,184-190.
  • William, H.M. and P.Joaquin. The classical Theory of Minimal Surfaces. Bull. Amer. Math. Soc. 2011. 48(3), 325—407.
  • Gray, A. Minimal Surfaces" and "Mini- mal Surfaces and Complex Variables.” Ch. 30 and 31 in Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed.Boca Raton, FL: CRC Press, 681-734. 1997.
  • Lagrange, J.L. Trial of a new method to determine the maxima and minima of indefinite integral formulas. Miscellanea Taurinensia 2, 1760. 325(1), 173-199. (in French).
  • Weisstein, E.W. Catenoid. From Math- World-A Wolfram Web Resource. https://math- world. wolfram. com/Catenoid.html. 2017.
  • Fomenko, A.T. and A.A. TuzhilinEle- ments of the Geometry and Topology of Mini- mal Surfaces in Three-dimensional Space. AMS Bookstore Press, ISBN 978-0-8218-4552-3. 1991.
  • Hoffman, D. and H.M. William. The Global Theory of Properly Embedded Minimal Surfaces. Pacific J. of Math. 1987. 128,361—366.
  • Johnson N.W. Convex solids with regular faces. Canadian Journal of Mathematics, 1966. 18: 169–200.
  • Meusnier, J.B. Memory on the curvature of surfaces. Mem. of foreign scholars. 1776. 10, 477-510. (in French).
  • Hoffman D.: The computer-aided discovery of new embedded minimal surfaces. Mathematical Intelligencer. 19879. 8–21.
  • Robert Br., W. Korn, R. M. Spaldıng, The Geometry of Plant Epıdermal Cells.New Phytol. 1973. 72, 1357-1365.
  • Ozdemir, A. C. Özdemir. Geometrıc defınıtıon of druse crystal ın plant cells. J. Indian bot. 2021. 101 (1&2) 146-151.
There are 21 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Ali Özdemir 0000-0001-9330-7084

Canan Özdemir 0000-0003-1316-4146

Publication Date November 30, 2021
Published in Issue Year 2021 Issue: 28

Cite

APA Özdemir, A., & Özdemir, C. (2021). Geometric Modeling in Some Micromorphological Structures. Avrupa Bilim Ve Teknoloji Dergisi(28), 270-274. https://doi.org/10.31590/ejosat.996946