Why do we define our axes to be perpendicular to each other?

Geometry Level 2

What could have happened if we redefined planar coordinate geometry with our axes to be inclined at an angle other than \(\frac{\pi}{2}\)?

This problem is inspired by megh choksi

We'd have a new kind of geometry with new sorts of theorems. It would not be a consistent idea because the points on the plane would not have unique coordinates. Nothing at all. We just define it to be \(\frac{\pi}{2}\) to keep things simple. The axes would have projections on each other and would not be independent.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 5 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.