Beevers–Lipson strips were a computational aid for early crystallographers in calculating

Fourier transform A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, ...

s to determine the structure of

crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macros ...

s from crystallographic data, enabling the creation of models for complex molecules. They were used from the 1930s until computers with enough power became generally available in the 1960s. The technique was developed by C. Arnold Beevers (1908–2001), reader in

crystallography Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. Crystallography is a fundamental subject in the fields of materials science and solid-state physics (condensed matter physics). The wor ...

at the

University of Edinburgh The University of Edinburgh ( sco, University o Edinburgh, gd, Oilthigh Dhùn Èideann; abbreviated as ''Edin.'' in post-nominals) is a public research university based in Edinburgh, Scotland. Granted a royal charter by King James VI in 15 ...

, and

Henry Lipson Henry (Solomon) Lipson CBE FRS (11 March 1910 – 26 April 1991) was a British physicist. He was Professor of Physics, Manchester Institute of Science and Technology, 1954–77, then professor emeritus. Background Lipson was born in Liverpo ...

CBE FRS (1910–1991), Professor of

Physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

at the

University of Manchester Institute of Science and Technology The University of Manchester Institute of Science and Technology (UMIST) was a university based in the centre of the city of Manchester in England. It specialised in technical and scientific subjects and was a major centre for research. On 1 Oct ...

. The approach converted the sizable calculations of multi-dimensional Fourier summations needed in crystallography analysis into sums of more manageable one-dimensional values. The folded card strips with numbers were typically stored in two wooden boxes, one for

sine In mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is oppo ...

s and one for cosines. Previously it was necessary to consult sine/cosine tables, a time-consuming process. The approach was used by the

Nobel Prize The Nobel Prizes ( ; sv, Nobelpriset ; no, Nobelprisen ) are five separate prizes that, according to Alfred Nobel's will of 1895, are awarded to "those who, during the preceding year, have conferred the greatest benefit to humankind." Alfr ...

winner

Dorothy Hodgkin Dorothy Mary Crowfoot Hodgkin (née Crowfoot; 12 May 1910 – 29 July 1994) was a Nobel Prize-winning British chemist who advanced the technique of X-ray crystallography to determine the structure of biomolecules, which became essential fo ...

OM FRS (1910–1994). The technique is still used in modern computer programs.

References

{{DEFAULTSORT:Beevers-Lipson strip Crystallography Mathematical tools Fourier analysis History of chemistry History of the University of Edinburgh University of Manchester

See also

References