AN APPROACH TO INTEGER FACTORISATION - WITH SAMPLE PROGRAMS

Book Cover

It is easy to multiply any two numbers together and obtain a result. Trying to discover which numbers were multiplied together to result in a given number is a rather different proposition. Factorisation has fascinated mathematicians both amateur and professional since the history of numbers began. Integers have their own special appeal, and finding which pairs of integers give rise to a specified third integer is the domain of Number Theorists.

However, Mathematics belongs to nobody and it seems a shame to leave such an entertaining diversion in the hands of specialists. This book presents an approach to the problem which can hopefully be understood by anyone with reasonable knowledge of high school Algebra. A number of the techniques described were investigated using programs written and run on a microcomputer. The text may be of interest to students of Mathematics, Computer Science, Engineering, and perhaps Physics. However, I hope that anyone who enjoys playing around with numbers will find the contents appealing and be persuaded to have a go.

SOME THOUGHTS ON BIG SCIENCE

There are many example of experiments in modern science which are so large and expensive that no single govenment can afford to pursue them. The international collaborations which have developed over the years have brought with them issues of national prestige. The experiments themselves have therefore taken on a "Life of their own" so to speak.

The total sums spent on science will always be trivial compared to the cost of wars, or even some financial scandals. Nevertheless, the issue of whether the research is being carried out in the most cost effective manner give pause for thought .

PATENTLEASE

The patentlease principle is a means by which intellectual property can be adopted by any company worldwide without the need for expensive and time consuming negotiations with the owner of the intellectual property. The intention is for both parties to benefit while new technology is made available worldwide, rapidly and cheaply.

DISPLACERLESS ENGINES

Displacerless engines are a form of heat engine which have attracted atention from enthusiasts, partly because they do not appear to conform to any of the well known thermodynamic cycles. This document contains commentary on the engine construction and proposes certain improvements which may be possible.

THE BROTHERS STIRLING

Experiments based on a hearth constructed in accordance with the description shown in the Stirling Brother's patent of 1816 gave disappointing results. This led the experimenter to conclude that the engine probably never existed. The conclusion seems slightly excessive. This response presents an alternative view.

TURNING STEEL INTO HAPPINESS

The essential feature defining an activity as recreational seems to be the element of choice exercised by the individual. For as long as an actiity is optional to the person doing it, the activity is recreational. Usually, the satisfaction obtained from the activity cannot be measured in the banal terms of financial remuneration. It would seem that most recreational activities are fiscally worthless, and represent a drain on the resources of the person involved. In fact, it can be argued that when a tangible reward becomes associated with a recreation, the satisfaction is displaced to a greater or lesser extent by competitive ambition, a degree of anxiety from obligation, and disappointment if the reward is not achieved.

SCALE MODELLING AT 12" TO THE Ft.

Over the years, I have manufactured some very small precision components. The smaller the item, the more closely the tolerances have to be controlled. Errors which would be of no consequence on a large item can be glaringly obvious and even ruinous to a small component. It is therefore with some admiration that I regard the products of those who construct operational models of the most intricate detail at a fraction of the size of their prototype counterparts. Accepting the limitations of my abilities, I decided that the scale most appropriate for my model making activities could not really be anything less than 12" to the Ft.