PENROSE TILING Meaning and
Definition
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Penrose tiling refers to a non-periodic tiling pattern discovered by mathematician Roger Penrose in the 1970s. It is characterized by a unique arrangement of geometrical shapes that covers a plane without any gaps or overlaps, while lacking translational symmetry. The concept of Penrose tiling has become an intriguing subject in the fields of mathematics, physics, and art, known for its remarkable visual appeal and intricate mathematical properties.
The Penrose tiling pattern consists of two types of rhombus-shaped tiles, often referred to as "kite" and "dart" tiles, which are combined to form a highly symmetric arrangement. These tiles are not congruent, meaning their sizes and shapes vary, but they possess certain distinct properties that allow them to fit together in specific ways. The arrangement of the Penrose tiling is governed by a set of five rules, known as the "matching rules," which dictate how neighboring tiles can connect with each other.
One of the unique characteristics of Penrose tiling is its aperiodicity, which means the pattern does not exhibit any repeating units or traditional symmetries found in periodic tilings. This property sets it apart from regular periodic tilings, such as those formed by square or hexagonal tiles. Penrose tiling exhibits a type of long-range order, where certain patterns repeat but without regularity, resulting in mesmerizing complex designs.
Penrose tiling has significant implications in various scientific disciplines. In mathematics, it has been used to explore the concept of quasi-crystals, which are materials exhibiting long-range order similar to Penrose tilings. The study of Penrose tilings also has connections to areas such as aperiodic order, fractal geometry, and the field of quasicrystallography. Additionally,
Etymology of PENROSE TILING
The word "Penrose tiling" is named after Sir Roger Penrose, a British mathematician and physicist who first discovered and studied this type of tiling in the 1970s. The specific term "Penrose tiling" was coined in honor of his significant contributions to the field of mathematics and his pioneering work in the study of aperiodic tilings, specifically the Penrose tiles.
