# Seven Circles III

##### This Seven Circles III activity & project also includes:

A basic set-up leads to a surprisingly complex analysis in this variation on the question of surrounding a central circle with a ring of touching circles. Useful for putting trigonometric functions in a physical context, as well as linking the trig of triangles with that of circles. A great bridge into the higher-level thinking that upper-level mathematics requires of motivated young scholars.

CCSS: Designed

##### Instructional Ideas

• A variety of geometric manipulatives or modeling programs are available to demonstrate the outer circles surrounding the central circle
• Use to introduce double- and half-angle formulas
• Consider the spacing and quantity of outside spheres needed on a central spere in 3-D
##### Classroom Considerations

• If not used in sequence with Seven Circles I or II the class might need some help setting up the triangles and ratios needed for the calculations
• Use as a refresher lesson on triangle trigonometry before introducing unit circle trigonometry, to help strengthen links between the two
##### Pros

• Clear set-up and step-by-step answer key leads the class through analysis
• Diagrams provided throughout add key information and insight
• General application of answers emphasized, rather than specific values
##### Cons

• Teaching notes and answer key not clearly separated from the class activity part