The Globe

Some interesting things about a sphere, like the Earth (approximately¹)

• The "Hairy Ball"² theorem tells us that for something that can be modeled as a continuous³ vector⁴ field, like the wind, there must be a point on the globe where the value of that field is zero. Which is to say: somewhere, at this moment, there is no wind.

• For a scalar⁵ field on a globe, like temperature, there must be two antipodal⁶ points with the same value. So somewhere, two points on direct opposite sides of the earth have the same temperature.
• For any five points on the globe, there is some view of the globe that shows four of them.

¹ The Earth is a slightly "squashed" sphere, and not perfectly smooth, but close enough.
² Great name, right? Think of a ball densely covered with hair all over, no matter how you comb it, at some point it's sticking straight up.
³ Continuous meaning no "jumps" from one geometric point to another. Note that these points are infinitely close together, so you can still get some very dramatic changes from place to place. It's reasonable to assume the wind is continuous.
⁴ A vector is a magnitude and a direction at a point. Like, "At this spot the wind is blowing 10 mph south-west."
⁵ A scalar is a name for something that just has a magnitude and no direction at a point, as opposed to a vector.
⁶ Antipodal, points on a sphere across the center from one another.