# On the General Shape of Scales on Slide Rules

## TL;DR

This paper provides a comprehensive analysis of the properties of various slide rule scales based on different mathematical functions, aiding future scale design and understanding historical scales.

## Contribution

It offers a detailed explanation of the general properties of scales derived from all possible mathematical functions, including numerous examples.

## Key findings

- Analysis of properties of scales from various functions
- Guidelines for designing custom slide rule scales
- Enhanced understanding of historical and modern scales

## Abstract

We give a thoroughful explanation of the general properties of different, general scales, corresponding to different (all possible) mathematical functions f(x), we mention and analyse many examples. These observations and statements might help us to plan and realize any specific scale we need in the future, or to understand better any interesting or miserable properties of old scales.

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Source: https://tomesphere.com/paper/1706.03286