Algebra of sphero-cylinders and refractive errors, and their means, variance, and standard deviation

Am J Optom Physiol Opt. 1988 Oct;65(10):794-802. doi: 10.1097/00006324-198810000-00003.


Sphero-cylinders and refractive errors can be represented by matrices. Matrix algebra provides methods whereby sphero-cylinders can be added, subtracted, multiplied, inverted, and raised to powers and can have roots extracted. These operations are defined for sphero-cylinders and examples are given. In terms of these operations a number of means of refractive errors are defined: the arithmetic, harmonic, and quadratic means. Furthermore it is possible to define a variance and standard deviation for refractive errors. These quantities should provide a basis for a formal approach to the statistical analysis of populations of refractive errors.

MeSH terms

  • Humans
  • Mathematics*
  • Refractive Errors / physiopathology*
  • Statistics as Topic*