# Copy of Shortest Path Between 2 Points on a Sphere

- Author:
- mark vasicek, Tim Brzezinski

In the context of a

**SPHERE**, A**GREAT CIRCLE**is defined to be a**CIRCLE**that lies on the**SURFACE OF THE SPHERE**and**LIES ON A PLANE that PASSES THROUGH THE CIRCLE's CENTER.**In essence, the center of a**GREAT CIRCLE**and the center of the**sphere**are the same. Consequently, a**GREAT CIRCLE**also the largest possible circle one can draw on a**sphere**. In the applet below, the**pink arc**and**blue arc**make up a**GREAT CIRCLE.**## 1.

Note that the **black arc** and **yellow arc** (put together) DO NOT make a great circle. Why is this?

## See below this applet for directions.

**Directions:**Move the

**2 WHITE POINTS**anywhere you'd like on the

**sphere**. The

**PINK ARC**is part of a

**GREAT CIRCLE**of this

**SPHERE**. You can move the

**YELLOW POINT**anywhere you'd like as well. Again, note that the

**YELLOW ARC**is

**NOT PART**of a great circle. Slide the slider slowly and carefully observe what happens.

## 2.

How would you describe the SHORTEST DISTANCE between 2 POINTS along a **SPHERE**? Explain.