When we discuss angles in mathematics we consider anticlockwise angles as the positive direction of rotation.

 

In particular this is carried through to phasor theory in electrical engineering and many other fields.

 

But when mathematicians and physicists discuss rotational symmetry the clockwise rotational direction is chosen as positive.

 

eg

 

http://www.mathsisfun.com/geometry/symmetry-rotational.html

 

Is this anomaly not potentially confusing for young minds?

Edited August 5, 201411 yr by studiot

In the link it didn't matter which way you rotated.

 

In the link it didn't matter which way you rotated.

 

 

I don't understand the comment.

 

The moving demonstrations clearly rotate clockwise.

He's simply pointing out that the direction of rotation doesn't matter, i.e. an object with rotational symmetry has the same symmetry rotating clockwise as it has rotating counterclockwise.

 

At least in Euclidean geometry, the direction certainly doesn't matter. I suppose there may be other contexts in which rotational symmetry does depend on "direction" in some sense, but by the time a student gets that far, he should be past the point of being confused by minor details like this.

 

Perhaps my professors have been abnormal, though, because in all the real discussions I recall having regarding rotational symmetry (specifically, in geometry and algebra), we used the counterclockwise convention anyway, or at least specified which direction we meant in a particular instance.

Edited August 5, 201411 yr by John

Thank you , John, for your reply.

 

I fully appreciate that mathematically the direction of rotation is a matter of convention and perhaps choice.

 

But the question I asked was about teaching the subject to youngsters.

 

You may have been lucky with your professors or older or both but this question was prompted because I looked at the teaching material supplied to some 9/10 years olds about rotational symmetry., ie in primary school.

 

They are being taught that the 'natural' direction of rotation is clockwise, having not long been taught about clocks.

 

They will also be taught about bearings in Geography, which are also measured clockwise.

 

I have seen much confusion arise in secondary schools when the maths teacher attempts to teach anticlockwise angles.

 

So my question still stands for discussion.

Edited August 6, 201411 yr by studiot