Entire number continuum is equivalent to any finite segment: Courant and Robbins Book I am reading What is Mathematics? by Richard Courant and Herbert Robbins.
They discuss about the fact the $\Bbb{R}$ is not countable and after they say 

«it is easy to show that the entire number continuum is equivalent to any finite segment, say the segment from 0 to 1 with the endpoints excluded. The desired biunique correspondence may be obtained by bending the segment at $1/3$ and $2/3$ and projecting from a point »

Here is the figure is the book:

Unfortunately I don't understand the construction. Not sure what "projecting from a point" mean here and how can I get the bijection.
Can someone explain how to construct it?

Imagine that the dot at the center is a light bulb. Then every point on the cup-shaped part of the figure has a shadow point on the line. (That's what "projection" means in this context.)
The points on the cup shaped figure correspond to the points on the unit interval using the "bending" Courant and Robbins describe.
