As a child, I remember being mystified how a circle could hold any great secrets. After all circles are so easy to construct and they look the same from all directions.

How wrong I was!

In studying circles, as with investigating anything of importance, one question leads to another, and insights gained in other areas of mathematics prove to be relevant to our study and reveal yet more hidden patterns. Entire books have been written about the geometry of circles, and even more books about π, the ratio between a circle’s circumference (perimeter) and diameter.

I remember being astounded when I learned that the size of the angle at the centre of a circle (the yellow angle in this image) is always exactly twice the size of ANY blue angle on the circumference! The ratio was always two, and the conclusion was that it did not matter where on the circumference you placed the angle, it would *always* be the same size … if it was standing on the same arc. Such amazing simplicity! And so, my adventure with circles began.

As you will see, there is so very much more to discover …

Gone to a lot of sites and watched a lot of math lessons on the internet, but your lessons seem to sink in my mind better than others, perhaps you explain each step in a way that is meaningful to me…anyway, i think you are an excellent instructor, thanks for your help.

Maggie J (on a CCM YouTube video about How to Graph Type 2 Rational Functions)

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