Protractors scaled in Radians

We have a few forum members with an interest in mathematical curiosities, so I think these may be of interest: **LINK**

https://www.proradian.net

They are also available from: **LINK**

https://www.tarquingroup.com/radian-protractors-pi-24.html

[ who sell quite a range of teaching aids ]

MichaelG.

We had a Wyler precision square at work that could be set to display in milliradians but the process on the drawings had a small angle in degrees as the target. For a long time we used it to set up large fabrications to level using jacking and shims. The milliradians were useful because for small angles a milliradian was an adjustment of 1mm per metre. The fabrications had machined locations on them and the idea was to get the fabrication back into the machining set-up when on an uneven concrete floor.

I got the set-up process changed when I pointed out to the design department that the small angles of 5 minutes of arc they wanted us to achieve were close to one milliradian and that since some of the pads were 3m apart a milliradian over that distance was 3mm. By using a dumpy level (basic optical theodolite used by builders) and a few rules on magnetic bases we could achieve better levelling in a shorter time.

They thought a small angle in minutes gave good results because none of them had an understanding of radians or, more specifically, milliradians, and their relative size to a degree and the mm/m ratio.

Martin C

Edited By Martin Connelly on 26/08/2021 08:47:55

Perfect justification of the lady’s mission, Martin

MichaelG.

The right angle, and its common multiples and divisions, is critically important in most practical geometries.

In radians it doesn't have an integer value, greatly complicating much arithmetic that is simple mental work in degrees.

We have largely superseded Imperial measures in most fields for the specific purpose of simplifying everyday mental arithmetic.

As Martin's pointed out above, there are clear applications where radians have their place, but across-the-board adoption would be IMO a retrograde step.

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Clearly true, but I don’t think anyone is suggesting that.

MichaelG.

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Ref. https://www.proradian.net/proradian-protractor-story/

Edited By Michael Gilligan on 26/08/2021 10:51:14

Degs, hegs, kegs and megs?

pgk

I'm bemused. I have to work in degrees for measuring things but usually in radians in electronics. It's horses for courses, have to be fluent in both (to mix metaphors!).

Military compasses are now graduated in mils, which are butchered miliradians. When you include Grads, people are now messing with 4 UoM systems for angular measurement. I didn't think this was supposed to be the result of developing International Standards.

Horses for courses:

• Radians for electrical engineering, computers and sums, because degrees are a pain
• Degrees for practical work, because fractions help express and visualise common angles
• Mils for snipers, because the system does basic range-finding
• Hexacontades for stirring up controversy on websites.

Dave

I've never understood why Excel does trig functions in radians making for an extra calculation instead of providing a straight-up degree option. It must waste millions of man-hours per year around the world.

Well, I suspect the answer is that most of the people designing software in the early days were mathematicians, and so it made sense to make your software that does mathematics do it in a mathematical way. Or, probably more likely, those functions were imported in from a Fortran library, long, long ago and now can't be updated, or everything would break. As an aside, trig functions are calculated in radians, so if you enter anything else it must be converted under the hood anyway.

This may be egg-sucking territory, but Excel has a "named range" functionality, where you can give a grid of cells a name. This grid can be 1x1, and it functions like a programming variable. It is useful for constants like this: you can name a cell "to_radians", say, and then enter your formula as =SIN(90*to_radians).

Sine and cosine can be calculated from a mathematical series but the input value used is in radians. The conversion from and to degrees is an extra calculation in the software. When computers were slow and memory capacity was small this extra step was best avoided. The calculation method means you do not need a look up table for the values of sine, cosine and tangent (which is calculated from sine divided by cosine gives tangent).

The sine series formula

Martin C

Edited By Martin Connelly on 26/08/2021 19:35:29

Thanks for the extra Calum.
Given the ever expanding set of unused features in Word I would have expected them to add eg "sinD() " that just takes the argument in degrees.

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… and these particular protractors

• designed to help students also visualise angles in Radians, so that they are more comfortable when the need to use them arises.

MichaelG.

You could use them to draw Pi charts.

Neil

So freely available in Wigan then? (the land of pies}

Easy enough with degrees and minutes. When I was into target rifle we generally used the approximation that 1 minute ~ an inch per 100 yards. I can remember shooting in a 19-minute wind at 1000 yards on Stickledown at Bisley - IIRC the bore line would've been pointing between the next target and next-but-one. Also way above of course, for trajectory.

Military binoculars had graticules with lines 1/2 degree apart and 1/4, 1/2 and 1 degree high. Naturally you had to know the height or width of the object/target to be able to estimate range, but it's the same case with mils or any other UoM.

Well … my enthusiasm seems not to be widely shared

Never mind … I bought the ‘Pro’ version of the protractor, and am pleased with it.

To continue my belated education; I have just spent the princely sum of 89p with Apple

This App is astonishing: **LINK**

https://apps.apple.com/gb/app/a-little-calculus/id631866056

… if only things like this had been available when I was at school !

MichaelG.