## Interior Angles of Polygons Starting with a Triangle

Regular polygons are closed curves with a set number of sides and interior angles, each of identical value. How can one calculate the interior angles of polygons? An equilateral triangle has three equal sides and three equal interior angles. Each angle is 60° or π/3 radians, adding up to 180° or π radians total. A square has four equal sides and four equal interior angles. Each interior angle is 90° or π/2 radians, adding up to 360° or 2π radians total. Interior Angles of Polygons A short chart of additional polygons with their interior angles provides the following data: Pentagon 5 interior angles of 108° (540° or 3π radians total) Hexagon 6 interior angles of 120° (720° or 4π radians total) Heptagon 7 interior angles of about 128.57° (900° or 5π radians total)…

## Is a Circle a Polygon or Not? Implications for Calculus

[caption id="attachment_16285" align="alignright" width="380"] A 12-sided dodecagon.[/caption] What do you think? Is the circle a polygon, or not? As a result of watching a child’s video, I previously wrote a brief piece about the “corners” of a circle. The video was designed to teach children the various shapes—how many sides does a shape have, and how many corners? The video maintained a circle has no corners. I called that into question. I still do. And yet, I do not. I now think it’s all in how you look at it. Or, you might say, it’s all in the mathematical perspective. Consider. The Circle by Definition One can define the two-dimensional circle as the complete collection or “set” of points equidistant from a set point, not part of the circle. In…