Why are there 90 degrees in a quarter circle? Any basis for this definition? And, along these lines…
Does anyone use Grads (as opposed to Rads or Dgrs) to measure angles? Was this like a metric method since 100 grads equals 90 degrees, or more simply, 1/4 of a circle. Is this just a nice, convenient definition for a 1/4 circle?
At least, I can see that Radians as a unit of measure has some logical basis, although not very nice to work with since we’re all trained to think in degrees, IMHO! - Jinx
There are 360 degrees in a circle because some ancient geometers liked that number; it’s divisible by 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, etc. There are 400 grads in a circle because the French liked it that way (possibly another metric system innovation, although I can’t find a good cite).
Is that so in the US? As I understand it, on German road signs it rise devied by distance in percent. So 10% means 10 metres rise on 100 metres roadlength. And so 100% equals 45 dgrs = 50 grads?
Search for “sexagesimal system” in Google. One page I found claims the system came from observation of the movements of planets, specifically Jupiter and Saturn. Perhaps it’s just a coincidence that the number thereby obtained (36) has the nice property of having so many divisors.
Oh, here’s more than you probably care to know about the origin of the “grad” as a unit of measure for angles.
Gradient, as on a road sign and gradian are different things. A gradian, as the OP talks about, is 1/100 of a 90 degree angle. There are 400 gradians in a circle as opposed to 360 degrees. Gradient is the raitio of rise to horizontal distance. The conversion from gradient to gradian (or degrees for that matter) is very non-linear.
One of the nice things about good old fashioned Babylonian degrees are simple rules like the 30º-60º-90º triangle. The hypotenuese is exactly twice the length of the opposite side of the 30º corner. I don’t think there any such elegant solutions with gradians.
I’m not following you. If you have a 33.3 grad, 66.6 grad, 100 grad triangle, the same thing is true. What’s so special about measuring the angle in degrees for that?
degree (° or deg)
the standard unit of angle measure, equal to 1/360 circle, 60 minutes, 3600 seconds, or about 0.017 453 293 radian. So far as we know, this unit was introduced by the Greek geometer Hipparchus of Nicaea (ca. 180-ca. 125 BC), who developed the first trigonometric tables.
grad or grade or gon (g or grd) [1]
a unit of angle measurement equal to 1/400 circle, 0.01 right angle, 0.9°, or 54’. This unit was introduced in France, where it is called the grade, in the early years of the metric system. The grad is the English version, apparently introduced by engineers around 1900. The name gon is used for this unit in German, Swedish, and other northern European languages in which the word grad means degree. Although many calculators will display angle measurements in grads as well as degrees or radians, it is difficult to find actual applications of the grad today.
grade [2]
a measure of the steepness of a slope, such as the slope of a road or a ramp. Usually stated as a percentage, the grade is the same quantity known as the slope in mathematics: the amount of (vertical) change in elevation per unit distance horizontally (“rise over run”). Thus a 5% grade has an elevation gain of 0.05 meter for each meter of horizontal distance, or 0.05 foot for each foot of horizontal distance. The angle of inclination, in grads or grades [1], is not equal to the percentage grade in this sense: for a 5% grade the angle of inclination is about 2.86° or 3.18 grads.
