Logarithms

Slide rule

The slide rule is a mechanical analog computer which is used primarily for multiplication and division, and for functions such as exponents, roots, logarithms, and trigonometry. It is not typically designed for addition or subtraction, which is usually performed using other methods. Maximum accuracy for standard linear slide rules is about three decimal significant digits, while scientific notation is used to keep track of the order of magnitude of results. Slide rules exist in a diverse range of styles and generally appear in a linear, circular or cylindrical form, with slide rule scales inscribed with standardized graduated markings. Slide rules manufactured for specialized fields such as aviation or finance typically feature additional scales that aid in specialized calculations particular to those fields. The slide rule is closely related to nomograms used for application-specific computations. Though similar in name and appearance to a standard ruler, the slide rule is not meant to be used for measuring length or drawing straight lines. At its simplest, each number to be multiplied is represented by a length on a pair of parallel rulers that can slide past each other. As the rulers each have a logarithmic scale, it is possible to align them to read the sum of the numbers' logarithms, and hence calculate the product of the two numbers. The English mathematician and clergyman Reverend William Oughtred and others developed the slide rule in the 17th century based on the emerging work on logarithms by John Napier. Before the advent of the electronic calculator, it was the most commonly used calculation tool in science and engineering. The slide rule's ease of use, ready availability, and low cost caused its use to continue to grow through the 1950s and 1960s, even as electronic computers were being gradually introduced. The introduction of the handheld electronic scientific calculator around 1974 made slide rules largely obsolete, and most suppliers left the business. (Wikipedia).

Slide rule
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Basic slide rule theory and use (Part 2): CI scale

The second of a series of videos explaining the basic slide rule. This video explains the CI scale and its basic uses. Basic slide rule playlist: https://www.youtube.com/playlist?list=PL_qcL_RF-ZyvJYtIr9NRXJX958d6BgdbN All my slide rule videos: https://www.youtube.com/playlist?list=PL_q

From playlist Basic slide rule theory and use

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Two operations with one slide using folded scales

This video gives a technique for computing any sequence of two multiplications/divisions, in any order, on a slide rule with a full set of folded scales (you need C/D/CI/CF/DF/CIF). This increases the accuracy of the result versus using the naive method of one setting per operation. I'm n

From playlist All Slide Rule Videos

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Basic slide rule theory and use (Part 1): C and D scales

The first of a series of videos explaining the basic slide rule. I'm not an expert -- I'm also not old enough to have learned slide rule use in school. This series of videos aims to be the set of videos I would have enjoyed while learning about the slide rule -- it assumes some mathematica

From playlist Learn the slide rule from Professor Herning

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Overview of fancier slide rules (folded scales, extended scales, LL scales)

Want to "level-up" your slide-rule ability? This video is a short introduction to the more advanced scales found on scientific slide rules. I think it's one of my best videos. It gives an overview of folded scales (e.g. CF/DF), extended scales (e.g. ST/T2), and log-log scales (LL). This v

From playlist Learn the slide rule from Professor Herning

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Basic slide rule theory and use (Part 4): Proportions -- A,B,C,D Revisited

The fourth of a series of videos explaining the basic slide rule. This video revisits the elementary scales for solving proportions. Basic slide rule playlist: https://www.youtube.com/playlist?list=PL_qcL_RF-ZyvJYtIr9NRXJX958d6BgdbN All my slide rule videos: https://www.youtube.com/play

From playlist Basic slide rule theory and use

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Practical Slide Rule 2/5: Proportion

A short series where I show how to use a slide rule by solving practical problems (mostly). Playlist: https://www.youtube.com/playlist?list=PL_qcL_RF-Zyu6ugp3E2nB9xoTSwpy1G-F For a more theoretical introduction, see my "Basic slide rule theory and use" video series:https://www.youtube.com

From playlist Learn the slide rule from Professor Herning

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Basic slide rule theory and use (Part 3): Square and Cube scales A, B, & K

The third of a series of videos explaining the basic slide rule. This video explains the A, B, and K scales and their basic uses. Basic slide rule playlist: https://www.youtube.com/playlist?list=PL_qcL_RF-ZyvJYtIr9NRXJX958d6BgdbN All my slide rule videos: https://www.youtube.com/playlis

From playlist Basic slide rule theory and use

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Trigonometry on Euro-style (Darmstadt, studio, 2/83, etc.) slide rules

This video discusses trigonometry again, this time using a slide rule with trigonometric functions on the base instead of the slide. I discuss direct reading the trig. functions, multiplying and dividing them, and the solution of various triangles. At the end is a very efficient procedure

From playlist All Slide Rule Videos

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Basic slide rule theory and use (Part 5): Chaining and S/T/L scales

The fifth (and final) of a series of videos explaining the basic slide rule. This video explains how to chain operations and how to use scales S, T, and L. Basic slide rule playlist: https://www.youtube.com/playlist?list=PL_qcL_RF-ZyvJYtIr9NRXJX958d6BgdbN All my slide rule videos: https

From playlist Basic slide rule theory and use

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Reinventing the magic log wheel: How was this missed for 400 years?

Today is about reinventing a really cool mathematical wheel and its many different slide rule incarnations, just using a rubber band. 00:00 Intro 04:40 Multiply! 06:02 Pi times e 07:15 Divide! 08:39 Sliding rules 10:53 Apollo 11:08 Star Trek 11:45 Rubber band proof 13:13 Logarithms 16:50

From playlist Recent videos

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A Tour of the Pickett Slide Rule Universe

I take a look through my Pickett slide rule collection for all of the Pickett fans out there. Note: the 902 slide rule frame is 1+1/4 inch, not 1 inch as stated.

From playlist All Slide Rule Videos

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System Wern ABC Slide Rule 1/3 -- Overview

The first part of a three part series on the System Wern ("ABC") slide rule. I introduce this unique circular slide rule which tracks the decimal point of your calculation! Correction/clarification: I list the U/V scales twice. According to the manual these are the conversion scales. They

From playlist All Slide Rule Videos

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Post 1462H / Hemmi 159 and a slide rule conspiracy!

I describe the interesting Post 1462H slide rule and its predecessor/successor. I present the theory that these slide rules inspired a certain model popular in Europe.

From playlist All Slide Rule Videos

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Soviet Slide Rules (GOST 5161)

A discussion of some Soviet slide rules that might be interesting to collectors/users! Here are links to the two videos on using the KL-1: https://youtu.be/Kuzdjy3HpWg https://youtu.be/xn6xccGmcWk

From playlist All Slide Rule Videos

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System Wern ABC Slide Rule 2/3 -- Additional Calculations

The second part of a three part series on the System Wern ("ABC") slide rule. I solve a few more problems on the rule, demonstrating the trigonometric scales and the standard slide rule scales including the log-log spiral. Carl Wern's website (history, manuals, photos, promotional materia

From playlist All Slide Rule Videos

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Circular Slide Rules: Faber Castell 8/10 + Sama & Etani Model 90

I take a look at a couple circular slide rules and discuss some pros and cons. There are a few errors: - The Gilson "binary" slide rules are thus named for having a scale of binary fractions (denominators that are powers of 2), not for have the double, caliper-style cursor. - The A and B

From playlist All Slide Rule Videos

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Practical Slide Rule 5/5: Right triangles (Trigonometry)

A short series where I show how to use a slide rule by solving practical problems (mostly). Playlist: https://www.youtube.com/playlist?list=PL_qcL_RF-Zyu6ugp3E2nB9xoTSwpy1G-F For a more theoretical introduction, see my "Basic slide rule theory and use" video series:https://www.youtube.com

From playlist Learn the slide rule from Professor Herning

Related pages

Aspect ratio | Monotonic function | Scientific notation | Right ascension | Logarithm | Nautical mile | Trigonometry | Product (mathematics) | Pythagoras | Order of magnitude | Exponential function | CORDIC | Harmonic mean | Abacus | Radian | Division (mathematics) | Multiplication | Logarithmic number system | Imperial units | Function (mathematics) | Logarithmic scale | Mechanical calculator | Pi | False precision | Otis King | Quotient | Slide rule scale | Nth root | Bygrave slide rule | Prosthaphaeresis | Declination | Nomogram | Significant figures | Natural logarithm | Square root | Hyperbolic functions | Common logarithm