Year: 2022

BIOINSPIRED MATHEMATICS. "Early in his career he drew inspiration from nature, making studies of insects, landscapes, and plants such as lichens, all of which he reused as details in his artworks. He travelled in Italy and Spain, sketching buildings, townscapes, architecture and the tilings of the Alhambra and La Mezquita, Cordoba, and became steadily more interested in their mathematical structure." https://en.m.wikipedia.org/wiki/M._C._Escher View in LinkedIn

SELF-TAUGHT. "Although Escher considered that he had no mathematical ability, he interacted with mathematicians George Pólya, Roger Penrose, and Harold Coxeter; read mathematical papers by these authors and by the crystallographer Friedrich Haag; and conducted his own original research into tessellation." https://en.m.wikipedia.org/wiki/M._C._Escher View in LinkedIn

DIVISION OF THE PLANE. "M.C. Escher became fascinated by the regular Division of the Plane, when he first visited the Alhambra, a fourteen century Moorish castle in Granada, Spain in 1922." https://lnkd.in/dKF_WPx View in LinkedIn

TESSELLATIONS. "Regular divisions of the plane, called tessellations, are arrangements of closed shapes that completely cover the plane without overlapping and without leaving gaps. Typically, the shapes making up a tessellation are polygons or similar regular shapes, such as the square tiles often used on floors." (Reminiscent of the basic geometry of spider webs). https://lnkd.in/d_HZ4K8 View in LinkedIn

METAMORPHOSIS. "Escher, however, was fascinated by every kind of tessellation—regular and irregular—and took special delight in what he called “metamorphoses,” in which the shapes changed and interacted with each other, and sometimes even broke free of the plane itself." There metamorphoses of geometry also obsessed Gaudí in the Sagrada Familia. https://lnkd.in/d_HZ4K8 View in LinkedIn

GARDEN OF DELIGHTS. "In mathematical quarters, the regular division of the plane has been considered theoretically…Does this mean that it is an exclusively mathematical question? In my opinion, it does not. [Mathematicians] have opened the gate leading to an extensive domain, but they have not entered this domain themselves. By their very nature they are more interested in the way in which the gate is opened than in the garden lying behind it." (MCE). https://lnkd.in/d_HZ4K8 View in LinkedIn

ELABORATED ANIMALIA. "Escher exploited these basic patterns in his tessellations, applying what geometers would call reflections, glide reflections, translations, and rotations to obtain a greater variety of patterns. He also elaborated these patterns by distorting the basic shapes to render them into animals, birds, and other figures." https://lnkd.in/d_HZ4K8 View in LinkedIn

SYMMETRY. "These distortions had to obey the three, four, or six-fold symmetry of the underlying pattern in order to preserve the tessellation. The effect can be both startling and beautiful." (Reminiscent of the six-fold symmetry of snowflakes). https://lnkd.in/d_HZ4K8 View in LinkedIn

PLATONIC SOLIDS. "There are only five polyhedra with exactly similar polygonal faces, and they are called the Platonic solids: the tetrahedron, with four triangular faces; the cube, with six square faces; the octahedron, with eight triangular faces; the dodecahedron, with twelve pentagonal faces; and the icosahedron, with twenty triangular faces." These were an artistic foundation for MCE. https://lnkd.in/d_HZ4K8 View in LinkedIn

STELLATIONS. "There are many interesting solids that may be obtained from the Platonic solids by intersecting them or stellating them. To stellate a solid means to replace each of its faces with a pyramid, that is, with a pointed solid having triangular faces; this transforms the polyhedron into a pointed, three-dimensional star. A beautiful example of a stellated dodecahedron may be found in Escher’s Contrast (Order and Chaos)." https://lnkd.in/d_HZ4K8 View in LinkedIn