Mathematical ideas like angle bisection
, perpendicular bisector, congruence of shapes and segments, properties of right triangles, similar triangles, reflection, and rotation become more tangible and vivid in the context of paper folding.
Anyone interested in pursuing further aspects of paper folding could investigate folding ellipses and hyperbolae by using circular paper (Yates, 1943) or turning to any of: Hilton and Pedersen (1983), (1993); Polster (2004); Froemke and Grossman (1988); to investigate a technique that allows the approximation of any rational angle with simple sequences of angle bisections
. These sketches show convergence to 60[degrees] (180[degrees]/3) from an initial estimate: