A novel approach to egg and math: Improved geometrical standardization of any avian egg profile.
Hügelschäffer model
avian eggs
egg geometry
piecewise functions
standard egg shape
Journal
Annals of the New York Academy of Sciences
ISSN: 1749-6632
Titre abrégé: Ann N Y Acad Sci
Pays: United States
ID NLM: 7506858
Informations de publication
Date de publication:
11 2023
11 2023
Historique:
medline:
16
11
2023
pubmed:
29
8
2023
entrez:
29
8
2023
Statut:
ppublish
Résumé
Developing a geometric formulation of any biological object has a number of justifications and applications. Recently, we developed a universal geometric figure for describing a bird's egg in any of the possible basic shapes: spherical, ellipsoidal, ovoid, and pyriform. The formulation proved widely applicable but had a number of drawbacks, including a very obvious join between two parts of the egg. To correct this, we developed the Main Axiom of the universal mathematical formula. This essentially involved making the ordinate of the extremum of the function correspond to half the maximum egg breadth (B), and the abscissa to the reciprocal of the parameter w that reflects the shift of the vertical axis to its coincidence with B. This, in turn, helped us develop a new, simplified mathematical model without a nonbiological join. Experimental verification was performed to confirm the adequacy of the new geometric figure. It accurately described actual avian eggs of various shapes more closely than our previous model. To the best of our knowledge, our new, simplified equation can be applied as a standard for any bird egg that exists in nature. As a rather simple equation, it can be used in a broad range of applications.
Types de publication
Journal Article
Langues
eng
Sous-ensembles de citation
IM
Pagination
61-71Informations de copyright
© 2023 The New York Academy of Sciences.
Références
Ursinus, O. (1944). Kurvenkonstruktionen für den Flugzeugentwurf. Flugsport, 36(9), 15-18.
Petrović, M., & Obradović, M. (2010). The complement of the Hugelschaffer's construction of the egg curve. In M. Nestorović (Ed.), 25th National and 2nd International Scientific Conference moNGeometrija 2010 (pp. 520-531). Belgrade, Serbia: Serbian Society for Geometry and Graphics.
Petrović, M., Obradović, M., & Mijailović, R. (2011). Suitability analysis of Hugelschaffer's egg curve application in architectural and structures’ geometry. Bulletin of the Polytechnic Institute of Iași. Construction, 57(61), 115-122.
Ferréol, R. (2017). Hügelschäffer egg. Encyclopédie des formes mathématiques remarquables. 2D Curves. http://www.mathcurve.com/courbes2d.gb/oeuf/oeuf.shtml
Narushin, V. G., Romanov, M. N., & Griffin, D. K. (2021). Egg and math: Introducing a universal formula for egg shape. Annals of the New York Academy of Sciences, 1505, 169-177.
Narushin, V. G., Romanov, M. N., Mishra, B., & Griffin, D. K. (2022). Mathematical progression of avian egg shape with associated area and volume determinations. Annals of the New York Academy of Sciences, 1513, 65-78.
Rodríguez, H. (2022). Crean la fórmula universal para la forma de los huevos. National Geographic España. https://www.nationalgeographic.com.es/ciencia/crean-la-formula-universal-para-la-forma-de-los-huevos_17301
Redacción. (2021). Los científicos que dicen haber descubierto “la fórmula matemática de la forma de los huevos” (y por qué es importante para la ciencia). BBC News Mundo. https://web.archive.org/web/20230117175703/https://www.bbc.com/mundo/noticias-58469106
Etienne, P. I. (2022). Mathématiques: enfin une équation universelle pour décrire la forme de l’œuf! Science & Vie. https://www.science-et-vie.com/sciences-fondamentales/mathematiques-enfin-une-equation-universelle-pour-decrire-la-forme-de-loeuf-65990.html
Wood, S. (2021). Research finally reveals ancient universal equation for the shape of an egg. News Centre, University of Kent. https://www.kent.ac.uk/news/science/29620/research-finally-reveals-ancient-universal-equation-for-the-shape-of-an-egg
News Staff. (2021). Researchers find universal formula for egg shape. Sci.News. https://www.sci.news/biology/egg-shape-universal-mathematical-formula-10019.html
Hyun, E. (2021). The mathematically perfect egg. Yale Scientific Magazine, 94.3, 4.
Benoit, M. (2021). Mathématiques: l'équation universelle de “la forme de l'œuf” enfin trouvée après des années de recherché. Sciences et Avenir. https://www.sciencesetavenir.fr/fondamental/mathematiques/mathematiques-l-equation-universelle-de-la-forme-de-l-oeuf-enfin-trouvee-apres-des-annees-de-recherche_158789
Goodall, R. (2021). Scientists find a universal formula for bird egg shape. The Boar. https://theboar.org/2021/09/scientists-find-a-universal-formula-for-bird-egg-shape/
Morrison, R. (2021). The ultimate egg-quation! Scientists develop a universal formula for the shape of any bird's EGG-In breakthrough that could shed light on how and why they evolved. Daily Mail, Associated Newspapers Ltd. https://web.archive.org/web/20210913023804https://www.dailymail.co.uk/sciencetech/article-9955329/Universal-formula-birds-egg-created-scientists.html
von Rauchhaupt, U. (2023). Ei und Form. Frankfurter Allgemeine Sonntagszeitung, April 9, 2023, No. 14: 53.
Leonard, D. (2021). A new equation can describe every egg. Scienceline. Science, Health and Environmental Reporting Program, Arthur L. Carter Journalism Institute, New York University. https://scienceline.org/2021/11/a-new-equation-can-describe-every-egg/
Bhattacharyya, S. (2021). The universal equation for eggs! Medium. https://medium.com/predict/the-universal-equation-for-eggs-d9bbb73857a2
Numberphile. (2022). The ultimate egg-quation. Numberphile2, YouTube. https://youtu.be/tjyFw1BX4eM
Shi, P., Gielis, J., & Niklas, K. J. (2022). Comparison of a universal (but complex) model for avian egg shape with a simpler model. Annals of the New York Academy of Sciences, 1514, 34-42.
Shi, P., Gielis, J., Quinn, B. K., Niklas, K. J., Ratkowsky, D. A., Schrader, J., Ruan, H., Wang, L., & Niinemets, Ü. (2022). ‘biogeom’: An R package for simulating and fitting natural shapes. Annals of the New York Academy of Sciences, 1516, 123-134.
Shi, P., Wang, L., Quinn, B. K., & Gielis, J. (2023). A new program to estimate the parameters of Preston's equation, a general formula for describing the egg shape of birds. Symmetry, 15, 231.
Biggins, J. D., Montgomerie, R., Thompson, J. E., & Birkhead, T. R. (2022). Preston's universal formula for avian egg shape. Ornithology, 139, ukac028.
Al-ossmi, L. H. (2023). Nada's curve towards a new curvature produced by the tangent of a circle and an ellipse: The Nada's curve. Iraqi Journal for Computer Science and Mathematics, 4, 1-9.
Holguin, S., & Kreinovich, V. (2022). Shape of an egg: Towards a natural simple universal formula. College of Engineering, ScholarWorks@UTEP, University of Texas at El Paso. https://scholarworks.utep.edu/cs_techrep/1695
Gielis, J., Shi, P., & Caratelli, D. (2022). Universal equations-A fresh perspective. Growth and Form, 3, 27-44.
Deeming, D. C. (2022). Factors determining persistent asymmetry and egg shape in birds: A hypothesis. Ibis, https://doi.org/10.1111/ibi.13175
Petrovic, M., & Malesevic, B. (2022). Hügelschäffer egg curve and surface. Applicable Analysis and Discrete Mathematics, 27. https://doi.org/10.2298/AADM220526027P
Narushin, V. G., Romanov, M. N., Lu, G., Cugley, J., & Griffin, D. K. (2021). How oviform is the chicken egg? New mathematical insight into the old oomorphological problem. Food Control, 119, 107484.
Narushin, V. G., Griffin, A. W., Romanov, M. N., & Griffin, D. K. (2022). Measurement of the neutral axis in avian eggshells reveals which species conform to the golden ratio. Annals of the New York Academy of Sciences, 1517, 143-153.
Weng, Y.-K., Li, C.-H., Lai, C.-C., & Cheng, C.-W. (2022). Equation for egg volume calculation based on Smart's model. Mathematics, 10, 1661.
Aleynikov, A. F. (2022). Methods for noninvasive assessment of sexual dimorphism of embryos in the poultry egg. Siberian Herald of Agricultural Science, 52(5), 105-116.
Levine, B. M., Kaplun, M., & Ribak, E. N. (2022). An asymmetric sparse telescope. Arxiv, arXiv:2206.13862 [astro-ph.IM]. https://doi.org/10.48550/arXiv.2206.13862
Narushin, V. G., Romanov, M. N., & Griffin, D. K. (2022). Egg-inspired engineering in the design of thin-walled shelled vessels: A theoretical approach for shell strength. Frontiers in Bioengineering and Biotechnology, 10, 995817.
Juračka, D., Katzer, J., Kobaka, J., Świca, I., & Seweryn, K. (2023). Concept of a 3D-printed Voronoi egg-shaped habitat for permanent lunar outpost. Applied Sciences, 13, 1153.
Songsheng, Y.-Y., & Wang, J.-M. (2023). Differential interferometric signatures of close binaries of supermassive black holes in active galactic nuclei. II. Merged broad-line regions. The Astrophysical Journal, 945, 89.
Silverman, M. (2020). Egg: Eggfun.io. Version 0.09. Silverware Games, Inc. https://eggfun.io
Narushin, V. G., Romanov, M. N., & Griffin, D. K. (2023). What comes first: The egg or the mathematics? Biology Bulletin of the Russian Academy of Sciences, 50(3), 237-243.
Narushin, V. G., Romanov, M. N., & Griffin, D. K. (2022). Delineating an ovoidal egg shape by length and breadth: A novel two-parametric mathematical model. Biosystems Engineering, 224, 336-345.
Obradović, M., Malesević, B., Petrović, M., & Gordana, Đ. (2013). Generating curves of higher order using the generalisation of Hügelschäffer's egg curve construction. Buletinul Ştiinţific al Universităţii “Politehnica” din Timişoara: Seria Hidrotehnica, 58(72), 110-114.
Narushin, V. G., Romanov, M. N., Lu, G., Cugley, J., & Griffin, D. K. (2020). Digital imaging assisted geometry of chicken eggs using Hügelschäffer's model. Biosystems Engineering, 197, 45-55.
Narushin, V. G., Romanov, M. N., & Griffin, D. K. (2021). Non-destructive measurement of chicken egg characteristics: Improved formulae for calculating egg volume and surface area. Biosystems Engineering, 201, 42-49.
Egbert, N. (2016). Piecewise functions. Purdue University. https://www.math.purdue.edu/~egbertn/fa2016/notes/lesson9.pdf
Orszulik, S. T. (2007). The decomposition of effects in full factorial experimental design into individual treatment combinations. Quality Engineering, 19, 39-52.
Orszulik, S. T. (2021). A method of joining piecewise functions to produce continuous functions of difficult data. Research Square, June 7, 2021, Version 1. https://doi.org/10.21203/rs.3.rs-593915/v1
Orszulik, S. T. (2022). Curve fitting: A method of joining piecewise functions to produce models of complex data. Communications in Statistics - Simulation and Computation. https://doi.org/10.1080/03610918.2022.2067871
Fordyce, K. (2020). Some basics on the value of S curves and market adoption of a new product. Arkieva. https://blog.arkieva.com/basics-on-s-curves/
Narushin, V. G., & Romanov, M. N. (2002). Physical characteristics of chicken eggs in relation to their hatchability and chick weight. In ASAE Annual International Meeting/CIGR World Congress. Chicago, IL. Paper #026066. https://doi.org/10.13031/2013.9226
Narushin, V. G., Bogatyr, V. P., & Romanov, M. N. (2016). Relationship between hatchability and non-destructive physical measurements of chicken eggs. Journal of Agricultural Science, 154, 359-365.
Bondarenko, Yu. V., Tkachik, T. E., Zakharchenko, O. P., Ruda, S. V., Katerinich, O. O., Shekhovtsov, S. S., & Kutnyuk, P. I. (2007). [Morphological quality traits of eggs of subpopulations of Birky meat-egg type chickens]. Ptakhivnytstvo [Poultry Farming], 59, 29-36.
Baydevlyatova, O. N., Ogurtsova, N. S., Shomina, N. V., & Tereshchenko, A. V. (2009). [Morphological indicators of egg quality in a new chicken subpopulation of the meat-egg type of productivity]. Ptakhivnytstvo [Poultry Farming], 64, 109-115.
Shomina, N. V., Tkachenko, S. M., Tagirov, M. T., & Tereshchenko, O. V. (2009). [Monitoring the quality of hatching eggs during storage]. Efektyvne Ptakhivnytstvo [Effective Poultry Farming], 11, 29-33.
Tagirov, M. T., Ogurtsova, N. S., & Tereshchenko, A. V. (2009). [Analysis of hatchability problems for incubated eggs]. Ptakhivnytstvo [Poultry Farming], 63, 199-215.
Romanoff, A. L., & Romanoff, A. J. (1949). The avian egg. John Wiley & Sons Inc.
Biggins, J. D., Thompson, J. E., & Birkhead, T. R. (2018). Accurately quantifying the shape of birds’ eggs. Ecology & Evolution, 8, 9728-9738.
Narushin, V. G., Romanov, M. N., & Griffin, D. K. (2023). A novel model for eggs like pears: How to quantify them geometrically with two parameters? Journal of Biosciences, In press.
Makridakis, S., Andersen, A., Carbone, R., Fildes, R., Hibon, M., Lewandowski, R., Newton, J., Parzen, E., & Winkler, R. (1982). The accuracy of extrapolation (time series) methods: Results of a forecasting competition. Journal of Forecasting, 1, 111-153.