24 “blueprints” that illustrate how the musculoskeletal, cardiovascular, neurological, and reproductive systems evolve through the mechanical deformation of geometric patterns. These images show how the vertebrate body might have evolved from a single cell during the evolutionary time and during individual development.
Though neither rigorous nor exhaustive in an empirical sense, our model offers an intuitive and plausible description of the emergence of form via simple geometrical and mechanical forces and constraints. The model provides a template, or roadmap, for further investigation, subject to confirmation (or refutation) by interested researchers.
The concept of “embryo geometry” suggests that the vertebrate embryo might be produced by mechanical deformation of the blastula, a ball of cells formed when a fertilized egg splits. As these cells multiply, the volume and surface area of the ball expand, changing its shape. According to the hypothesis, the blastula preserves the geometry of the initial eight cells generated by the egg’s first three divisions, which establish the three axes of the vertebrate body.
Though speculative, the model addresses the poignant absence in the literature of any plausible account of the origin of vertebrate morphology. A robust solution to the problem of morphogenesis—currently an elusive goal—will only emerge from consideration of both top-down (e.g., the mechanical constraints and geometric properties considered here) and bottom-up (e.g., molecular and mechano-chemical) influences.
Origin of the vertebrate body plan via mechanically biased conservation of regular geometrical patterns in the structure of the blastula, David B. Edelman, Mark McMenamin, Peter Sheesley, Stuart Pivar
Published: September 2016, Progress in Biophysics and Molecular Biology DOI: 10.1016/j.pbiomolbio.2016.06.007
Uma imagem que representa uma relação muito interessante em matemática.
A soma de cubos pode ser transformada no quadrado da soma de uma PA.
#math #matematica #algebra #geometria #demonstração #ulysses bueno #prof ulysses tdb
M. C. Escher - Metamorphose II
Plate 17. Guide to the construction of Gothic details. 1888.
Internet Archive
Mais uma da série “Olhando demonstrações”!
#geometria #fractal #demonstração matemática #demonstrações matemáticas #prof Ulysses Bueno #profulyssestdb #somas infinitas #PG infinita
Bruno Munari, (1960), The Square, Translation by corrainiStudio, Corraini Edizioni, Mantova, (2006-)2011, pp. 62-63
Calculating the surface area of a sphere. Found on Imgur.
Realmente os matemáticos são muito otimista com relação ao conhecimento, mas isso pode ser frustante para muitos estudantes, pois sem persistência não há como continuar nesse meio!
math problem: *begins with “we know that..”*
me: WE dont know SHIT
@vivalasestrellas
Blog do profº Ulysses TDBueno destinado a curiosidades, demonstrações, links, trabalhos, artigos, imagens e tudo que possa mostrar a matemática no mundo.
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