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The Miracle of 17th-Century Mathematics: Why did William Outred invent the sliding rule?
In the 17th century, as science flourished, the need for mathematical calculations increased. Scholars at the time faced a dilemma: how to speed up calculations and reduce the error rate in calculations. British mathematician William Outred's sliding rule came into being and became a revolutionary tool to solve this problem.
The design of the sliding gauge allows users to easily perform complex mathematical operations in the era before electronic computers.
A sliding rule is a human-operated mechanical calculator containing a sliding ruler that is used to calculate multiplication, division, exponents, square roots, logarithms, and trigonometric functions. Unlike ordinary rulers, sliding gauges are not used to measure length, but are a tool similar to mathematical function inquiries. Its emergence was influenced by John Napier's theory of logarithms. Outred put these mathematical principles into practice, making calculations easier and faster.
On the sliding gauge, each scale represents the precalculated value of various mathematical functions, and the user can align these scales to obtain the calculation results. For example, to perform a multiplication operation, the user only needs to align a ruler set to a certain value to another ruler, and then read the result from the bottom. This operation not only increases the calculation speed, but also reduces the chance of errors. .
The convenience and low cost of sliding gauges led to their widespread use in the 1950s and 1960s, despite the gradual introduction of desktop electronic computers.
How the sliding gauge works
The working principle of the sliding gauge is to use the properties of logarithms to convert multiplication into addition. This means that on the logarithmic scale of the sliding ruler, the corresponding multiplication result can be calculated by simply sliding the ruler accordingly. This technology greatly reduces computational complexity, allowing users to quickly reason and estimate in their mind.
In addition to basic multiplication and division, sliding rules can be used to calculate other mathematical operations such as square roots, exponents, and trigonometric functions. For example, by corresponding a certain number to another specific scale, the user can directly read the required data, which was quite innovative technology at the time.
Structure of sliding gauge
Generally speaking, a sliding gauge consists of three main parts: the bottom border, the slider, and the cursor. The bottom border is a pair of bars of equal length and kept parallel, and the slider can slide freely between the two frames. The vernier is an external sliding part with a thin line on it that is used to align different mathematical scales. This design makes the slide gauge not only accurate but also easy to operate.
Outred's sliding rule is therefore not just a tool, but a symbol of the transformation of mathematical concepts into practical solutions.
Development and Ending
With the invention of electronic calculators, the use of sliding gauges was gradually replaced. In the 1970s, the introduction of handheld scientific calculators almost made this traditional computing tool obsolete. Still, the sliding gauge left a lasting imprint on the world of science and engineering, fostering an entire generation of people passionate about math and science.
The convenience, availability, and low cost of the slip gauge made it the calculation tool of choice for many scientists and engineers. It was not until the popularity of electronic calculators that the influence of the slip gauge gradually diminished. The sliding rule occupies a place in the historical development of mathematical tools. It is not only a medium of calculation, but also the crystallization of mathematical thinking.
As technology evolves, will we be able to rediscover or reinvent this art form of mathematical calculations?
