J. C. P. Miller
Encyclopedia
Jeffrey Charles Percy Miller (1906–1981) was an English
mathematician
and computing pioneer. He worked in number theory
and on geometry
, particularly polyhedra, where Miller's monster refers to the great dirhombicosidodecahedron
.
He was an early member of the Computing Laboratory of the University of Cambridge
. He contributed in computation to the construction and documentation of mathematical tables, and by the proposal of certain algorithm
s. Miller's recurrence algorithm is mentioned in the Handbook of Mathematical Functions
.
As the reference says, this technique was subsequently much developed and applied, and was enunciated rather casually by Miller in a 1952 book of tables of Bessel function
s.
In volume 2 of The Art of Computer Programming
, Donald Knuth
attributes to Miller a basic technique on formal power series
, for recursive evaluation of coefficients of powers or more general functions.
In the theory of stellation
of polyhedra, he made some influential suggestions to H. S. M. Coxeter. These became known as Miller's rules. The 1938 book on the fifty-nine icosahedra resulted, written by Coxeter and Patrick du Val
. In the 1930s, Coxeter and Miller found 12 new uniform polyhedra, a step in the process of their complete classification in the 1950s. Miller also made an early investigation into what is now known as the Rule 90
cellular automaton
.
England
England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west; the Irish Sea is to the north west, the Celtic Sea to the south west, with the North Sea to the east and the English Channel to the south separating it from continental...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and computing pioneer. He worked in number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
and on geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, particularly polyhedra, where Miller's monster refers to the great dirhombicosidodecahedron
Great dirhombicosidodecahedron
In geometry, the great dirhombicosidodecahedron is a nonconvex uniform polyhedron, indexed last as U75.This is the only uniform polyhedron with more than six faces meeting at a vertex...
.
He was an early member of the Computing Laboratory of the University of Cambridge
University of Cambridge
The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...
. He contributed in computation to the construction and documentation of mathematical tables, and by the proposal of certain algorithm
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...
s. Miller's recurrence algorithm is mentioned in the Handbook of Mathematical Functions
Handbook of mathematical functions
*Abramowitz and Stegun, the informal name for Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables*NIST Handbook of Mathematical Functions...
.
As the reference says, this technique was subsequently much developed and applied, and was enunciated rather casually by Miller in a 1952 book of tables of Bessel function
Bessel function
In mathematics, Bessel functions, first defined by the mathematician Daniel Bernoulli and generalized by Friedrich Bessel, are canonical solutions y of Bessel's differential equation:...
s.
In volume 2 of The Art of Computer Programming
The Art of Computer Programming
The Art of Computer Programming is a comprehensive monograph written by Donald Knuth that covers many kinds of programming algorithms and their analysis....
, Donald Knuth
Donald Knuth
Donald Ervin Knuth is a computer scientist and Professor Emeritus at Stanford University.He is the author of the seminal multi-volume work The Art of Computer Programming. Knuth has been called the "father" of the analysis of algorithms...
attributes to Miller a basic technique on formal power series
Formal power series
In mathematics, formal power series are a generalization of polynomials as formal objects, where the number of terms is allowed to be infinite; this implies giving up the possibility to substitute arbitrary values for indeterminates...
, for recursive evaluation of coefficients of powers or more general functions.
In the theory of stellation
Stellation
Stellation is a process of constructing new polygons , new polyhedra in three dimensions, or, in general, new polytopes in n dimensions. The process consists of extending elements such as edges or face planes, usually in a symmetrical way, until they meet each other again...
of polyhedra, he made some influential suggestions to H. S. M. Coxeter. These became known as Miller's rules. The 1938 book on the fifty-nine icosahedra resulted, written by Coxeter and Patrick du Val
Patrick du Val
Patrick du Val was a British mathematician, known for his work on algebraic geometry, differential geometry, and general relativity. The concept of Du Val singularity of an algebraic surface is named after him....
. In the 1930s, Coxeter and Miller found 12 new uniform polyhedra, a step in the process of their complete classification in the 1950s. Miller also made an early investigation into what is now known as the Rule 90
Rule 90
Rule 90 is an elementary cellular automaton based on the exclusive or function. It consists of a one-dimensional array of cells, each of which can hold either a 0 or a 1 value; in each time step all values are simultaneously replaced by the exclusive or of the two neighboring values...
cellular automaton
Cellular automaton
A cellular automaton is a discrete model studied in computability theory, mathematics, physics, complexity science, theoretical biology and microstructure modeling. It consists of a regular grid of cells, each in one of a finite number of states, such as "On" and "Off"...
.
Further reading
- Doron ZeilbergerDoron ZeilbergerDoron Zeilberger is an Israeli mathematician, known for his work in combinatorics.He is a Board of Governors Professor of Mathematics at Rutgers University...
,The J. C. P. Miller recurrence for exponentiating a polynomial, and its q-analog, Journal of Difference Equations and Applications, Volume 1, Issue 1 1995, pages 57 – 60.