What if angles were metric?



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Isn’t it kinda strange that there’s a thousand grams in a kilogram, a thousand millimetres in a metre, but 360 degrees in a circle? I thought so too.

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21 Comments

  1. No I never wondered why there was not a "metric" or more correctly decimal version of angles because there is one and every scientific calculator I have ever had going back over 40 years can do them. They are called Gradians, a right angle has 100 of them.

  2. First, you are wrong about the "metric" system. The "Imperial" system, which is so stubbornly used in the US (and basically nowhere else), is ALSO a "metric system", just not THAT metric system (SI) you are confusing the term "metric system" with.
    Degrees AND Gradians are NOT part of SI; radians are. And radians are scaled with SI prefixes like kilo-, milli-, nano-, etc.

    So, why does everyone use degrees instead of radians? Out of pure convenience: 360 has more factors (24), including the useful prime factors 2, 3, and 5. It's simply easier to divide circles/sectors in your head when the circle is 360 units. Meanwhile, for example, a full circle in gradians (400 gradians) has only 15 factors, and 3 is not one of them.

    And… dividing SI radians in your head is impossible, since a full circle has 2π radians, which can only be calculated to some level of approximation.

    So, radians are good for science, and degrees are good for everyday use.

  3. I don't use gradians. Or angles. I did create an Android app that'll let convert them.

    By the way, I was under the impression that the development of the Beteric system started before the Revolution. They simply recognised it as the answer to the same problem the Royal government was trying to solve, no national standards or measure.

  4. The SI system uses radians (rad), not degrees, because scientists love measuring angles by dragging their feet along the edge of a circle like a human compass. The beloved British degree (°) is technically banned from the inner SI party, but it is still allowed to hang out in the hallway because society simply refuses to give it up. Since radians are calculated by dividing meters by meters, the units cancel out, leaving you with a mathematically "dimensionless" number that has absolutely no physical substance—much like the flavor of a lukewarm British tea.

  5. @NoEngineerHere Next time you break a steel tap off in a brass or aluminium part, you can boil it in a strong solution of alum to dissolve the steel leaving the other metals alone.

  6. long story short:
    angles would become messy, with decimal(point) numbers very fast!
    360° has round numbers for basically every "daily" angle

  7. On top of that we also have radians and we use them in IT just for sake of making calculations simpler and it is SI unit … 360degrees = 400 grads = 2 * pi * radian …
    "Metric system" is common name for lenght units and lenght derived units (for example litre and gram). And it jusy happen that metric is SI unit (standard international) … in civilized countries beside metric units we also use other metric units like volts, wats, ampers … and they are not metric but they are SI.

    everyone with basic education know that (yes, schools in USA do not provide enough education to be considered basic in any european country).

  8. Actually on the whole, the metric system is fundamentally flawed. it uses base 10. That means that there are two prime factors. Consider dividing a length in half repetitively; 0.5, 0.25, 0.125, etc. Resulting preferred numbers would then be 0.5, 0.2, and 0.1. On the other hand the inch system is binary, thus 1/2, 1/4, 1/8 and so forth. essentially these are the reciprocals of 0.1, 0.01, 0.001 in binary. Base 10 was used because they didn't understand fractions. The system also messed up with the base units. The two common metric systems MKS and CGS both have base units that are not "one". In MKS we have the kilogram or 1000 grams; In CGS we have the cent-meter or 1/10 of a meter.

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