Overview and Background

Slide Rules

A slide rule or slipstick is an analog computing device. When the slider is moved, the added lengths of slide displacement and position on the body can be read from the slider. Using logarithmic scales this results by multiplication or division by well known logarithmic identities.

Tactile Markings

This tactile model can be read by touch, as the various scales are elevated. Due to the nature of the logarithmic scale, the markers get very close at high values, so the higher precision markings are left out.

Textual Description

The scales are logarithmic, so that adding lengths result in multiplications on the haptic markers. When printed, slide the tongue inside the body so that in landscape orientation the smaller markers on sides of body and tongue are both on the left top side.

Then the scale on top of the body is the A scale, then follows the B scale on top of the tongue, then the C scale is on bottom of the tongue, and the D scale is on bottom of the body. The A and B scales represent the numbers from 1 to 100, where 1 is represented by the smallest markers, 5 by middle markers and the 10 by the largest markers. Since the logarithmic scales gets denser at higher numbers the smallest scale only runs until 30, the 5er scale until 80. The C and D scales represent the numbers from 1 to 10, where the largest scale is represented by the largets markers, followed by 1/2 by middle markers and 1/10 by the smallest markers.

Usage

To multiply, shift the 1 of the tongue to the first multiplicator on the body. For example 2 on D scale, or 4 on A scale (which is the same position). If you want to multiply the 2 by 3 move your finger on the tongue to three on the C scale (or, likewise 9 on B scale), and check on which number you end on the body scale. It should be 6 on D scale, since 2*3=6, or a bit above 35 on A scale as 4*9=36.

Parametric Design

The slide rule is designed to be fully parametric using OpenSCAD.

The scales may be changed for other functions such as probability such as the Bayes Ruler or trigonometry as well.

Thanks

The design is a collaboration with Gerhard Jaworek from SZS and started from a discussion based on a German podcast on slide rulers.

Lesson Plan and Activity

Mathematics

When introducing logarithmic identities, slide rules are a very instructive application. Multiplications, divisions and many more calculations can be illustrated using this device.

Inclusion in Education

When slide rulers were common tactile versions were available as well. Right now they are not easy to find, so this model can be printed to enable blind pupils to participate on the topic as well.

Tactile Slide Rule