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You can't just baldly assert that radians are just as easy to understand as degrees - clearly they require more effort to understand, from an intuitive point of
by jameshart 11y ago
You can't just baldly assert that radians are just as easy to understand as degrees - clearly they require more effort to understand, from an intuitive point of view.
It seems obvious to me why degrees are easier to handle than radians: 180 is an easier number to understand than pi.
People don't instinctively understand why on earth they would use a measurement unit where '1' of the unit has no obvious purpose. What can you do with a 1 radian angle? It's a bit less than the angle in an equilateral triangle. It's too big for usefully measuring things - most angles you come across will be somewhere between 0 and 3 radians, which is just weird.
What's that, you don't use radians like that? You use 'fractions of pi' radians? But my calculator can only approximate pi to 9 decimal places, so how does that help me?
It's incredibly easy for people to intuit that a ninety degree angle is the same as a 30 degree angle plus a 60 degree angle. But it takes deeper intuition about fractions to figure out that a pi/2 radian angle is the same as a pi/6 radian angle plus a pi/3 radian angle. People are not used to units of measure that are typically denominated with rational fractions of irrational numbers.
- jeffwass 11y agoEvery argument on radians you presented applies equally well to Tau as Pi. My original point is that IMHO, mainstream radian educational materials should NOT use the lesser-known and niche 'tau' in lieu of the globally understood 'pi' (other than a possible footnote or sidebar). Ie - it can cause more confusion to the student, especially when connecting it back to the greater scope of their studies.
- jameshart 11y agoI wasn't addressing your tau/pi issue, but rather your assertion that if you understand '90 degrees' that you should be able to understand radians. That seems like a case of 'well I find it simple, why doesn't everyone else?'