7.4 A non-linear projection
In chapter 5y = x. Now we look at a special kind of projection that is non-linear. We map almost every point on the unit circle onto a line.
Here is a unit circle and the line y = −1 that sits right below it.
We can map every point on the circle except (0, 1), the north pole, to a point on the line y = −1. We simply draw a line from (0 ,1) through the point on the circle. The result is where that line intersects y = −1.
The point where it intersects the line is 
. We compute this using the slope-intercept form.
- We know two points on the line: the north pole (0, 1) and the point on the circle
. - The slope m is the difference in y values divided by the difference in x values.
- When x = 0, y = 1. The equation of the line is
y = (√2 − 1)x + 1
- To see where it...
