The Geometry of Circles. Part 1

The following is part of an  article about circles, that appeared in  Smithsonian Magazine  titled "The World is Full of Circles" by
Esri and Li Zhou
March 12, 2015 

" A perfect circle cannot exist outside the realm of mathematics. From subatomic particles to carefully built structures, nothing in the physical world passes the perfect circle test, where every point on the circumference is exactly equidistant from the circle’s center. That said, some notable natural forms and human-made buildings get pretty close. Occurring either by happenstance or designed to pay homage to the shape that the Greek scholar Proclus called "the first, simplest and most perfect form,” these sites highlight the singular symmetry and symbolism the circle embodies."

"A fascination and interest in circles predates recorded history, with many ancient cultures finding approximations for pi—the ratio of a circle's circumference to its diameter—thousands of years before mathematicians gave it that name with the tasty homophone."
A focus on circles is evident among structures built throughout history. Although the meaning of its design is still being deciphered, Gobekli Tepe, a series of stone circles in Turkey, is the oldest known temple, built 6,000 years prior to Stonehenge (another famous circle). The shape marks many more important gathering places used by diverse cultures as centers of worship, governance and even spectacle."
"In a case of modern practicality, the Large Hadron Collider underneath the Switzerland-France border takes the form of a 16.7-mile-long circular tunnel. The round shape forces particles to constantly change direction and accelerate—colliding with great enough force to shake loose new types of matter.
It seems that even thousands of years after Egyptians first approximated the value of pi, the intrigue of circles lives on."


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I will show students how to do an exercise on the white board. They will learn  by actually doing example exercises during class. I will repeat with another exercise and will explain as many times as needed until the students are ready to do the exercises by themselves. Once started, I will check their answers for accuracy and follow up with any necessary explanations. I encourage all participants to try as many exercises as possible. I follow up the class with an upload of homework with the solutions.

Course breakdown:    Note: Instructor reserves to change or modify content.

Week 1:  The Parts of the Circle. 

Week 2:  Arcs and Central Angles.

Week 3: Diameters and Chords.

Week 4: Tangent and Secants.

Week 5: Angle Measurement: Vertex on the Circle. (Inscribed angles)

Week 6: Angle Measurement: Vertex in the Interior of the Circle.

Week 7: Angle Measurement: Vertex in the Exterior of the Circle.

Week 8: Review and Summary.