The Practical Application of Combinations of Numbers and of Combinations of Shapes to Buildings

Abstract

The Introduction contends that, with the increasing use of components manufactured off-site, the design of components and their assembly into a building both become complicated unless a numerical discipline such as that of dimensional co-ordination is applied. Dimensional co-ordination is examined. The usefulness of combinations of numbers in dimensional problems is demonstrated and the validity of combinations is shown to be unaffected by adopting any particular module. A literature review includes an appraisal of the author's book* and of the similar and related work of others. A recital of outstanding problems prefaces the general research which examines :- 1 The further development and modification of graphical methods of displaying combinations using up to 6 integers; 2 Graphical means of solving specific problems by isolating the requirements; 3 The patterns displayed by negative numbers and zero; 4 The patterns produced by combinations of numbers below Critical Number (a number such that it and every larger number can be produced); 5 Subordinate Critical Numbers; 6 A modification of Euler's function of relative primeness; 7 A proposition regarding Critical Number and the introduction of third integers. This research precedes the practical application of the subject. Manufacturers, designers, and builders are offered guidance in problem-solving and an examination of the complementary use of standard format and modular format sizes of bricks is made. An economic study of bricks is recommended. The fundamentals of applying shapes (tessellations) to practical building are surveyed. This subject, together with all mathematical theory implied by the whole thesis, is recommended for further study. References are given by chapters. A Contents List and a Bibliography are included. Diagrams, collected at the end for ease of reference, illustrate the work and the Appendices include a translation and hitherto unpublished papers. "Dunstone, P.H. Combinations of Numbers in Building. 1965."