# September 1963 - Vol. 6 No. 9

## Features

A semi-iterative process for evaluating arctangents

The technique of obtaining arctangents by inverse interpolation [1] is a relatively long process not suitable for a subroutine. The Taylor series expansion for arguments less than unity converges rather slowly for those near unity. The method of small increments of the argument [2] is again inconvenient for a subroutine. A more rapid series expansion in terms of Chebyshev polynomial [3] is given in terms of a new argument, which is less than 0.1989. This method requires the storage of &pgr;, √2 - 1 and seven coefficients and is perhaps widely used. However, for multiple precision not only the coefficients have to be evaluated to the precision desired, but more must be used. Therefore the following alternative method may prove to be convenient and efficient.

MIRFAC: a compiler based on standard mathematical notation and plain English

A pilot version of the compiler MIRFAC, now in the operation, is described. The chief features of the system, which is intended for the solution of scientific problems, are the presentation of mathematical formulas entirely in standard textbook notation. The use of plain English for organizational instructions, automatic error diagnosis indicating the actual location of the error in the uncompiled program, and an attempt to minimize that fragmentation of the original problem statement which is a normal feature of programming systems.

On the approximate solution of Δ u=F(u)

Three-dimensional Dirichlet problems for &Dgr;u = F(u), Fu ≧ 0, are treated numerically by an exceptionally fast, exceptionally accurate numerical method. Programming details, numerous examples and mathematical theory are supplied. Extension of the method in a natural way to n-dimensional problems is indicated by means of a 4-dimensional example.

A general program for the analysis of square and rectanglar lattice designs

This paper describes a general-purpose program that will handle those incomplete block designs known as square and rectangular lattices. Flow diagrams are given so that the method of calculation may be programmed for any digital computer.

Group participation computer demonstration

Engelbart1 has reported on some demonstrations in which a group functions as various parts of a digital computer. These demonstrations are concerned with binary operations including addition. However, there are occasions when it is desirable to have a group participate in a simulation which is not at this detailed level of computer operation. This note suggests a demonstration which allows a group to simulate the execution of a computer routine itself.