Spiral of Theodorus from a tape

"Theaetetus. Theodorus here was drawing some figures for us in illustration of roots, showing that squares containing three square feet and five square feet are not commensurable in length with the unit of the foot, and so, selecting each one in its turn up to the square containing seventeen square feet and at that he stopped. Now it occurred to us, since the number of roots appeared to be infinite, to try to collect them under one name,..." 

(Plato, Theaetetus 147d)

This is a very famous passage from Theaetetus (Greek: Θεαίτητος) one of Plato's dialogues concerning the nature of knowledge. Unfortunately, we do not know what the geometric construction to which Plato refers.

Even if there is no historical basis, the geometric construction is traditionally associated with a spiral composed of contiguous triangles rectangles known as Spiral of Theodorus. 

Spiral of Theodorus (source wikipedia)

In the remarkable book Spiral: Origami | Art | Design  by Tomoko Fuse is shown as a spiral of Theodorus can fold from an ordinary strip of paper!

Tomoko Fuse model

It is amazing! 

Just with a strip of paper you can get an object so interesting from a mathematical point of view. However it is not a novelty that with a strip of paper you can easily get interesting geometric objects. A very famous example in this direction is the sangaku problem of the regular pentagon.