Список литературы
- Baker D.E. A geometric method for determining shape of bird eggs. Auk. 2002;119:1179–1186. doi: 10.1642/0004-8038(2002)119[1179:AGMFDS]2.0.CO;2
- Preston F.W. The shapes of birds’ eggs. Auk. 1953;70:160–182. doi: 10.2307/4081145
- Carter T.C. The hen’s egg: A mathematical model with three parameters. Br. Poult. Sci. 1968;9:165–171. doi: 10.1080/00071666808415706
- Smart I.H.M. The method of transformed co-ordinates applied to the deformations produced by the walls of a tubular viscus on a contained body: The avian egg as a model system. J. Anat. 1969;104:507–518.
- Smart I.H.M. Egg-shape in birds. In: Egg Incubation: Its Effects on Embryonic Development in Birds and Reptiles. Eds. Deeming D.C., Ferguson M.W.J. Cambridge: Cambridge University Press, 1991. P. 101–116. doi: 10.1017/CBO9780511585739.009
- Todd P.H., Smart I.H. The shape of birds' eggs. J. Theor. Biol. 1984;106:239–243. doi: 10.1016/0022-5193(84)90021-3
- Narushin V.G. The avian egg: geometrical description and calculation of parameters. J. Agric. Eng. Res. 1997;68:201–205. doi: 10.1006/jaer.1997.0188
- Narushin V.G. Shape geometry of the avian egg. J. Agric. Eng. Res. 2001;79:441–448. doi: 10.1006/jaer.2001.0721
- Stoddard M.C., Yong E.H., Akkaynak D., Sheard C., Tobias J.A., Mahadevan L. Avian egg shape: form, function, and evolution. Science. 2017;356:1249–1254. doi: 10.1126/science.aaj1945
- Biggins J.D., Thompson J.E., Birkhead T.R. Accurately quantifying the shape of birds’ eggs. Ecol. Evol. 2018;8:9728–9738. doi: 10.1002/ece3.4412
- Birkhead T.R., Thompson J.E., Biggins J.D., Montgomerie R. The evolution of egg shape in birds: selection during the incubation period. Ibis. 2019;161:605–618. doi: 10.1111/ibi.12658
- Stoddard M.C., Sheard C., Akkaynak D., Yong E.H., Mahadevan L., Tobias J.A. Evolution of avian egg shape: underlying mechanisms and the importance of taxonomic scale. Ibis. 2019;161:922–925. doi: 10.1111/ibi.12755
- Biggins J.D., Montgomerie R., Thompson J.E., Birkhead T.R. Preston’s universal formula for avian egg shape. Ornithology. 2022;139. Article No. ukac028. doi: 10.1093/ornithology/ukac028
- Edwards L. The Vortex of Life: Nature's Patterns in Space and Time. Edinburgh, Scotland: Floris Press, 1993.
- Narushin V.G., Orszulik S.T., Romanov M.N., Griffin D.K. A novel approach to egg and math: Improved geometrical standardization of any avian egg profile. Ann. N. Y. Acad. Sci. 2023;1529:61–71. doi: 10.1111/nyas.15059
- Narushin V.G., Romanov M.N., Lu G., Cugley J., Griffin D.K. Digital imaging assisted geometry of chicken eggs using Hügelschäffer's model. Biosyst. Eng. 2020;197:45–55. doi: 10.1016/j.biosystemseng.2020.06.008
- Narushin V.G., Romanov M.N., Griffin D.K. Egg and math: introducing a universal formula for egg shape. Ann. N. Y. Acad. Sci. 2021;1505:169–177. doi: 10.1111/nyas.14680
- Almon C. Path Curves and Plant Buds: An Introduction to the Work of Lawrence Edwards. IIASA Professional Paper PP-79-005. Laxenburg, Austria: IIASA, 1979. https://pure.iiasa.ac.at/1204 (accessed 02.10.2025).
- Almon C. Path curves, an introduction to the work of L. Edwards on bud forms. Open Syst. Inf. Dyn. 1994;2:265–277. doi: 10.1007/BF02228852
- Signage. Fitting a Path Curve to a Bud: the Math of the Method. The Bud Workshop, 2016. http://budwork.hopto.org/bw_fitting_a_path_curve.html#signage (accessed 02.10.2025).
- Narushin V.G., Orszulik S.T., Romanov M.N., Griffin D.K. The pros and cons of the Preston–Biggins egg shape model: A reconsideration case based on mathematical modeling and simulation. Nonlinear Sci. 2025;4. Article No. 100038. doi: 10.1016/j.nls.2025.100038
- Narushin V.G., Volkova N.A., Dzhagaev A.Yu., Griffin D.K., Romanov M.N., Zinovieva N.A. Smart and smarter: Improving on a classic egg shape model. Theory Biosci. 2025:1–14. doi: 10.1007/s12064-025-00447-6
- Narushin V.G., Griffin A.W., Romanov M.N., Griffin D.K. Measurement of the neutral axis in avian eggshells reveals which species conform to the golden ratio. Ann. N. Y. Acad. Sci. 2022;1517:143–153. doi: 10.1111/nyas.14895
- Narushin V.G., Romanov M.N., Griffin D.K. A novel model for eggs like pears: How to quantify them geometrically with two parameters? J. Biosci. 2023;48. Article No. 35. doi: 10.1007/s12038-023-00361-3
- Makridakis S., Andersen A., Carbone R., Fildes R., Hibon M., Lewandowski R., Newton J., Parzen E., Winkler R. The accuracy of extrapolation (time series) methods: Results of a forecasting competition. J. Forecast. 1982;1:111–153. doi: 10.1002/for.3980010202
- Narushin V.G., Romanov M.N., Griffin D.K. Egg-inspired engineering in the design of thin-walled shelled vessels: a theoretical approach for shell strength. Front. Bioeng. Biotechnol. 2022;10. Article No. 995817. doi: 10.1111/10.3389/fbioe.2022.995817
- Narushin V.G., Volkova N.A., Dzhagaev A.Yu., Griffin D.K., Romanov M.N., Zinovieva N.A. Coupling artificial intelligence with proper mathematical algorithms to gain deeper insights into the biology of birds’ eggs. Animals. 2025;15:292. doi: 10.3390/ani15030292
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