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Dividing A Square Into Similar Rectangles
Dividing a square into similar rectangles (or, equivalently, tiling a square with similar rectangles) is a problem in mathematics. Three rectangles There is only one way (up to rotation and reflection) to divide a square into two similar rectangles. However, there are three distinct ways of partitioning a square into three similar rectangles: #The trivial solution given by three congruent rectangles with aspect ratio 3:1. #The solution in which two of the three rectangles are congruent and the third one has twice the side length of the other two, where the rectangles have aspect ratio 3:2. #The solution in which the three rectangles are all of different sizes and where they have aspect ratio ''ρ''2, where ''ρ'' is the plastic ratio. The fact that a rectangle of aspect ratio ''ρ''2 can be used for dissections of a square into similar rectangles is equivalent to an algebraic property of the number ''ρ''2 related to the Routh–Hurwitz theorem: all of its conjugates have po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plastic Square Partitions
Plastics are a wide range of synthetic polymers, synthetic or Semisynthesis, semisynthetic materials composed primarily of Polymer, polymers. Their defining characteristic, Plasticity (physics), plasticity, allows them to be Injection moulding, molded, Extrusion, extruded, or Compression molding, pressed into a diverse range of solid forms. This adaptability, combined with a wide range of other properties such as low weight, durability, flexibility, chemical resistance, low toxicity, and low-cost production, has led to their widespread use around the world. While most plastics are produced from natural gas and petroleum, a growing minority are produced from renewable resources like polylactic acid. Between 1950 and 2017, 9.2 billion metric tons of plastic are estimated to have been made, with more than half of this amount being produced since 2004. In 2023 alone, preliminary figures indicate that over 400 million metric tons of plastic were produced worldwide. If global trends ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
