Halves can be simply found by folding a square paper. However, finding tri-sections may not be trivial.
a) Using Haga's First Fold, drag point E (pretending corner B after folding) to point M (midpoint of the opposite side of AB) to see how tri-sections can be obtained. Could you explain why?
b) Using Haga's Third Fold, drag point E along the opposite side so that point J coincides with point N (midpoint of the opposite side of BC) to see another way to obtain tri-sections. Could you explain why?
c) Using Haga's First Fold, drag point E to 1/4 portion of the opposite side of AB to see how penta-sections (1/5, 2/5, ...) can be obtained. Do you find how to obtain 1/7? Could you generalize for other fractions as well?
d) As the result of part a), how hexa-sections (multiples of 1/6) and octa-sections (multiples of 1/8) can be obtained?
e) As the result of part b), how nona-sections (multiples of 1/9) can be obtained? Do you find another way to get hexa-sections as well?