I was under the impression that there are an infinite number of "best" courses to the weather mark. The higher you sail the slower the boat goes, but it travels less distance and, if done equally well, all would get you to the top of the course in the same amount of time.

Also, I had heard or read, somewhere, that it is better to take the headed tack first, when going to weather. The belief being that less distance is traveled. Further, that belief could be demonstrated trigonometrically.

True or false?