is half that of identically constructed linear coils Polarization patterns in light emerging from a q-plate A proof of the impossibility of continuous, anonymous, and unanimous two-party aggregation rules in social choice theory Möbius loop roller coasters, a form of dual-tracked roller coaster in which the two tracks spiral around each other an odd number of times, so that the carriages return to the other track than the one they started on World maps projected onto a Möbius strip with the convenient properties that there are no east–west boundaries, and that the antipode of any point on the map can be found on the other printed side of the surface at the same point of the Möbius strip Scientists have also studied the energetics of soap films shaped as Möbius strips, the chemical synthesis of molecules with a Möbius strip shape, and the formation of larger nanoscale Möbius strips using DNA origami. In popular culture Two-dimensional artworks featuring the Möbius strip include an untitled 1947 painting by Corrado Cagli (memorialized in a poem by Charles Olson), and two prints by M. C. Escher: Möbius Band I (1961), depicting three folded flatfish biting each others' tails; and Möbius Band II (1963), depicting ants crawling around a lemniscate-shaped Möbius strip. It is also a popular subject of mathematical sculpture, including works by Max Bill (Endless Ribbon, 1953), José de Rivera (Infinity, 1967), and Sebastián. A trefoil-knotted Möbius strip was used in John Robinsons Immortality (1982). Charles O. Perry's Continuum (1976) is one of several pieces by Perry exploring variations of the Möbius strip. Because of their easily recognized form, Möbius strips are a common element of graphic design. The familiar three-arrow logo for recycling, designed in 1970, is based on the smooth triangular form of the Möbius as was the logo for the environmentally-themed Expo '74. Some variations of the recycling symbol use a different embedding with three half-twists instead of and the original version of the Google Drive logo used a flat-folded three-twist Möbius strip, as have other similar designs. The Brazilian Instituto Nacional de Matemática Pura e Aplicada (IMPA) uses a stylized smooth Möbius strip as their logo, and has a matching large sculpture of a Möbius strip on display in their building. The Möbius strip has also featured in the artwork for postage stamps from countries including Brazil, Belgium, the Netherlands, and Möbius strips have been a frequent inspiration