If I don't remember, remind me to double-check the Sullivan text regarding the definition of arc distance. There might be a convention that you ignore multiples of 2 pi, but if so it would be inconsistent with physics and many other applications, as well as many purely mathematical issues. But it's always best to clarify.
Please pass on my congratulations to your boy. Excellent work, and a deserved reward for his effort.
Congratulations also on getting your letter published. If you're inclined append a copy to the next bit of written work you give me, or if you have an electronic copy send it. I'm not overly well-informed about the details of the situation in Ireland but of course I'm aware of the overall picture.
I got your message about the upgrade on my score. I thought for sure you were talking about a piece of a cycle when you spoke of arc length. Since theta = 15 radians and Pi * Dia was the circumference, I determined that two full revolutions where completed and the arc was the remainder, hence part of a cycle. If you are saying, which I believe you are, that the arc length is the distance between two points on a continous circle, (ie Start point 0 radian....End point 15 radians) then my understanding of the formula S= Theta * Radius was flawed. I thought this formula was integral to the Circle scribed by a given radius and theta told one the position of a point on this circle or indeed the amount of cycles which were made before it came to rest..I made the classic mistake of reading too much into a question and thus feel that you are being to generous in upgrading my test.
On a lighter note, my eldest boy passed the John Hopkins PLUS test and sored enough to receive an award in mathematics..We are thrilled with his performance, but let me tell ya he worked darn hard to get it..I got word that my letter to the editor will be published in the next issue of the Irish voice published in New York and distributed to many ex-pats here in the states. It's been an exciting weekend..
Will talk soon..