Polar Bear Math

The Polar Bear's Map

This polar bear is really smart. He knows where the Prime Meridian (zero degree line of longitude) is and can measure angles to find any other meridian. You can tell him where things are by telling him how far to travel from the North Pole along which meridian. Every point that you can name using direction coordinates in your home town can be located in the polar bear's world by distance and angle coordinates.

Here's Triangle Park located on the polar bear's map. All the streets really go all the way to the North Pole, but they get too close together to show on the map.

Graph showing triangle in polar coordinates

The Polar Bear's Map
A = 2 blocks at 150, B = 3 blocks at 75, C = 4 blocks at 315

Mathematically these are called polar coordinates and they are written as \(r\angle\theta\) where \(r\) is the distance and \(\theta\) (Greek letter theta) is the angle. The corners of Triangle Park are 2\(\angle\)150, 3\(\angle\)75, and 4\(\angle\)315. (The regular kind of coordinates are called rectangular, or less commonly, Cartesian coordinates.)

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