## IterationHere we have our two intervals on our single, purple line ‘permanently’ end-to-end
linked by conscious construction. They are “daisy-chained”.
And we at once find that we have a new perspectivity, centered on M, making
the interval PS
equivalent to the black interval and, thereby, identical to the red and blue
intervals, too! |
We see that we can join N to S, and get a new equivalent black
interval, and from P form a new perspectivity on it, to get a new, green
interval. We see we can repeat this process, indefinitely, and develop a set of intervals in one line, all identical with a single interval (PS),
and so get our projective ruler.
There are exactly two places on the purple
line, called “invariants”, beyond which
this, “back-and-forth, up-and-down”, process of interval
replication cannot go.
In fact, they “end” the entire ruler.
Can you find them?here.You can explore all this ruler's manifestations |