Chapter 1: Triangles and Circles

• $\mathbf{\text{Angles and Triangles}}$
• $\mathbf{\text{Similar Triangles}}$
• $\mathbf{\text{Circles}}$

Circles and triangles are the simplest geometric figures. A circle is the simplest sort of curve, and a triangle is the simplest polygon -- the one with the fewest sides. Each has properties that makes it useful in many fields of endeavor. A triangle is the most stable of polygons, because once its sides are fixed in length, its angles cannot change. A triangular truss bridge is a stable structure. A three-legged stool will not wobble.

A circle encloses more area then any other figure of the same length, or perimeter, and a sphere encloses more space. A geodesic dome is a portion of a sphere constructed with triangles. It has been called "the strongest, lightest and most efficient means of enclosing space known to man.”

Geodesic domes may also help us learn how to live on another planet. In 2017, the United Arab Emirates began construction on Mars Science City, a series of interconnecting geodesic domes designed to be a realistic model for living on Mars. The city will cover 1.9 million square feet, and its walls will be 3D-printed using sand from the desert.