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WEB GEOMETRY and force vectors based on observations of spider webs. It takes advanced mathematics to even begin to solve the humble spider's ingenuity. https://lnkd.in/dYdY4x3 View in LinkedIn

WIDE VARIATION. "Interestingly, the overall size of different orb webs varies from centimetres to meters, while the ratio of spiral to radial thread diameter varies from ∼0.1 to 1. Concomitantly, the extensibility and elastic modulus of the spiral and radial threads can differ by 1 and 3 orders of magnitude, respectively." https://lnkd.in/d5Wdths View in LinkedIn

POINT FAILURE. "The failure of silk threads occurs at points where the filament is disturbed by that external force, but after failure, the web returns to stability--even in simulations using broad forces, like hurricane-force winds." I have personally observed this. https://lnkd.in/dND28gV View in LinkedIn

SACRIFICIAL FAILURE DESIGN. "When a force strikes the web, such as that from a trapped fly, the web deforms in distinct ways at multiple scales yet fails only where silk threads are under the most stress. The web manages that feat because of slipping that takes place within the spider-silk protein molecules. The result is compensation for some stress, yet sacrificial failure when stress becomes extreme, preserving the web as a whole." https://lnkd.in/dND28gV View in LinkedIn

VORONI DIAGRAMS. https://lnkd.in/dYnv5AY View in LinkedIn

VORONI DIAGRAMS and spider webs. https://lnkd.in/dAawv-v View in LinkedIn

DIRICHLET TESSELLATIONS and spider webs. "Plane pictures of three-dimensional convex polyhedra, plane sections of three-dimensional Dirichlet tessellations, and flat spider webs with tension in all the threads are essentially the same geometric object. At the root of this remarkable coincidence is a single geometric diagram that permits us to offer a unified image of the connections among these and other objects." http://link.springer.com/chapter/10.1007%2F978-0-387-92714-5_18 View in LinkedIn

ON GROWTH AND FORM. "Cell and tissue, shell and bone, leaf and flower, are so many portions of matter, and it is in obedience to the laws of physics that their particles have been moved, moulded and conformed. They are no exceptions to the rule that God always geometrizes. Their problems of form are in the first instance mathematical problems, their problems of growth are essentially physical problems, and the morphologist is, ipso facto, a student of physical science." (D'Arcy Wentworth Thompson). https://lnkd.in/dvUQ__w View in LinkedIn

ON GROWTH AND FORM promoted the idea of nature conforming to exquisite mathematical laws, leading the reader to marvel at the harmony and symmetry of nature's designs. "For the harmony of the world is made manifest in Form and Number, and the heart and soul and all the poetry of Natural Philosophy are embodied in the concept of mathematical beauty". https://lnkd.in/daGvtQB View in LinkedIn

DESCENT WITH MODIFICATION. "The myth here is that evolution equates to progress, an error inherited from Darwin's contemporary Herbert Spencer, who was using the word 'evolution' to support his metaphysical belief in universal progress. Darwin purposefully avoided using the term 'evolution' (preferring “descent with modification”) because of the risk of this misunderstanding." (Spencer's misfeatured shadow). https://lnkd.in/dMZi4Xr View in LinkedIn