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Mathematical Modeling in Unusual Contexts: Rainbows, Halos and Glories.
 

Summary: Mathematical Modeling in Unusual Contexts:
Rainbows, Halos and Glories.
John A. Adam
Department of Mathematics and Statistics
Old Dominion University
Norfolk, VA 23529
The subject of meteorological optics is a fascinating one; it includes the study of the
above-mentioned phenomena as well as others too numerous to list here (a superb resource for all
these topics, containing many wonderful photographs, is Dr. Les Cowley's website at
http://www.sundog.clara.co.uk/atoptics/phenom.htm). Obviously there is some physics involved in
the explanation of these phenomena, but fortunately it is not necessary to go into a lot of physical
detail in order to appreciate the use of trigonometry and elementary calculus used in modeling these
beautiful arcs on the sky. This article is presented as a possible resource for high school mathematics
teachers who are looking for non-traditional contexts from which to teach some of the traditional
precalculus and calculus topics. It has been field-tested several times, within the context of a college
class that contained more advanced material, but the student excitement about and involvement with
the subject matter was quite high once students had actually noticed some rainbows, halos and
glories (and also sundogs) for themselves! [The figures have yet to be added.]
Rainbows
A thorough account of what might be called the "ray theory" for the formation of rainbows was

  

Source: Adam, John A. - Department of Mathematics and Statistics, Old Dominion University

 

Collections: Mathematics