View Full Version : Gradian Measure

peter eldergill

2005-Sep-29, 02:13 AM

Hey all

I've a Master's degree in math and have never once used gradian measure.

For those who don't know, a right angle can be divided into 90 degrees, pi/2 radians or 100 gradians (which gives a circle 400 grad, instread ot 360 deg or 2pi rad)

I didn't even know the definition until a couple of years ago when I taught grade 11 math. There is one question about it in the book.

Has anyone ever used this measure. If so, why?

Pete

Charlie in Dayton

2005-Sep-29, 02:42 AM

I have had it used on me, by a physics instructor. I'm guessing it was done strictly to give the undergrads another dose of insecurity at midterms time.

CalabashCorolla

2005-Oct-01, 05:23 AM

It always seemed to me that some of the units we learned in physics (measuring pressure in Torr, for instance, when 99% of the rest of the free world uses millibars, inches of Hg, psi, atmospheres, or some sort of Pascals) were thrust upon us lowly undergrads solely for the purpose of converting them into something else, and throwing us off on the exam equation sheets. The only time I have ever seen "gradians" is on my graphing calculator, and only because our teacher told us not to use them.

Quite frankly, I'm surprised that not more units have gone the way of cubits and spans in the last century or so. It's almost as if the various niche groups in the scientific community have their pet units that they use, that they swear are better than the units that the other scientists use. It's kind of like the "I'd rather push (my truck) than drive a (crappy truck) or (equally crappy truck)" people. Or like the two countries in the world that don't officially use metric...

01101001

2005-Oct-01, 06:50 AM

Suddenly, metric doesn't seem so cool.

Wikipedia: Gon (http://en.wikipedia.org/wiki/Gon)

The unit originated in France as the grade, as part of the all metric system. Due to confusion with existing grad(e) units of northern Europe, the name gon was adopted.

[...] the unit was really only adopted in some countries and for specialized areas, like land measurement. The French artillery has used the gon for decades.

hhEb09'1

2005-Oct-01, 11:15 AM

Quite frankly, I'm surprised that not more units have gone the way of cubits and spans in the last century or so. It's almost as if the various niche groups in the scientific community have their pet units that they use, that they swear are better than the units that the other scientists use. It's kind of like the "I'd rather push (my truck) than drive a (crappy truck) or (equally crappy truck)" people. Or like the two countries in the world that don't officially use metric...But...but...grads are metric! :)

Taks

2005-Oct-01, 11:19 PM

gradian is regularly used in the mountains, though not as the unit grad, but a % number for the grade of a slope (same difference i think). however, i can't guarantee they aren't simply dividing the rise over the run to get the number, as opposed to each grad being an equal spacing. hmmm...

EEs live by radians, particularly if you're into signal processing/comm. i think it actually makes more sense to use it in our arena anyway.

taks

01101001

2005-Oct-02, 06:40 AM

gradian is regularly used in the mountains, though not as the unit grad, but a % number for the grade of a slope (same difference i think). however, i can't guarantee they aren't simply dividing the rise over the run to get the number, as opposed to each grad being an equal spacing. hmmm...

The only percent measurement of grade that I've experienced is indeed rise/run * 100%. If a road drops 1 km over 10 km horizontal distance, that is a (steep for driving) 10% grade.

That is not the same as 10 gradians (or grads or gons), which would be 1/10 of 90 degrees, or 9 degrees.

By my calculation, a 10% grade would have an angle down of arctan(1/10) or about 5.71 degrees.

100% grade is 45 degrees. 45 degrees is 50 grad.

Mosheh Thezion

2005-Oct-02, 06:47 AM

I think that is awesome.. thanks for sharing it...

yes.. not 360.. 400 4 equal parts divisible by 100.... Pi/2 fascinating..

I might be able to use it in my quatification effort of my Unifying field theory.

it fits anyway...

thanks again.

-MT

HenrikOlsen

2005-Oct-03, 10:41 AM

Please don't, you'll be accused of deliberately using obscure units to confuse people.

gradian isn't metric, it's one of the units the french went overboard with after the revolutions when they had a fetish for the number 10, like when they redefined the week to be 10 days.

Metric isn't about something being in 10's, it's about keeping the 1, as in 1 gram pushed by 1 newton is accelerated by 1m/s2 and applying 1 newton over 1 meter has expended 1 joule of work.

To get rid of of pushing 1 pound with a force of 1 kilopond to get an acceleration of 2.2g.

Fram

2005-Oct-03, 10:53 AM

I've never used it (400° grad) either. At first it looks cool (a straight corner is 100° grad!), but then you come to other things (an equilateral (?) triangle has three corners of 66.666... °grad), and those aren't as useful anymore... 360 is simply more useful, as it can be divided by 2, 3, 4, 5, 6, 8, 9, and 10 (and many more), while 400 can be divided by 2, 4, 5, 8, and 10.

Oh, and Mosheh, it's just a different notation. If your theory works in 360° grades, it will work in 400° grad, and vice versa. Of course it fits, but it doesn't solve any problems.

peter eldergill

2005-Oct-03, 03:52 PM

Soo...no one has ever actually used this measure....

Why is it on the calculators? rad/deg is confusing enough for my students, so why don't they just omit it?

Anyhow, in terms of Calculus (and hence about every science), radian measure is the only correct measure, especially in the Taylor expansions for sin/cos. Also, the derivatives of sin/cos etc are valid only for radian measure. You'd have to make a change of variable from deg to rad if you want to use it properly.

Pete

hhEb09'1

2005-Oct-03, 05:52 PM

gradian isn't metric, it's one of the units the french went overboard with after the revolutions when they had a fetish for the number 10, like when they redefined the week to be 10 days.obviously, how far they went overboard is a subjective judgement :)

Metric isn't about something being in 10's,But that is just revisionism. Every site I've googled emphsizes its decimal nature.

it's about keeping the 1, as in 1 gram pushed by 1 newton is accelerated by 1m/s2 and applying 1 newton over 1 meter has expended 1 joule of work.Those would be the derived units, which all systems have.

To get rid of of pushing 1 pound with a force of 1 kilopond to get an acceleration of 2.2g.That "g" in 2.2g is a reference to gravity. How do you avoid that in the metric system? (a kilopond is a metric derived unit anyway, right?) Similarly, 2pi is involved in converting from angular velocity to rotational frequency.

It used to be that the simple complexity of the units system acted as an early filter for the sciences. Now, we have all sorts of softer acumen entering the field. The famous Hubble incident where different systems were mixed together is a case in point. :)

Mosheh Thezion

2005-Oct-04, 06:55 AM

I understand, and i don't plan on spouting stupidity.. i mean't.. in my own studies. as part of my efforts for the quanification of a dimensional progression...

it is possible to relate the 4 90 angles as 100's... thus simplifying any progressions which i might wish to pursue...

I am in no ways prepared to present any formulas at this time.

and yet, the idea may serve some use in the future, and if it were not for the sharing of it.. something wonderful might not happen... i.e.. in case it does, thanks.

snarkophilus

2005-Oct-04, 05:29 PM

Soo...no one has ever actually used this measure....

Why is it on the calculators? rad/deg is confusing enough for my students, so why don't they just omit it?

I have seen it used in a couple of old engineering texts. I think one was about civil engineering, but it's been a while since I last saw it. I've also been told that forestry people use them, too.

The only relation between the two I can see is surveying, so I'm going to go out on a limb and assume that that's the major application.

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