II8 Squares. Triangles. Various ......................................................................................... 50
Square with half the area of another one. Isosceles right-angled
triangle from a square. Equilateral triangle from a square: Equal
sides of triangle and square, or maximum equilateral triangle (
solutions). Equilateral triangle: from a rectangle; envelope. Stel-
late triangle. Square / Set square. Another curiosity.
8.2.8 Singular points in triangles .......................................................................................... 59
Orthocenter. Circumcenter. Baricenter. Incenter.
8.2.8.5 Rumpled and flattened origami.................................................................................... 61
8.2.8.6 Incenter and hyperbola................................................................................................. 6 3
8.2.8.7 Flattening of a quadrilateral ......................................................................................... 65
8.3 Various......................................................................................................................... 67
Homotomic figures. Area of a triangle. Pythagorean theorem.
8.3.4 Pythagorean units......................................................................................................... 70
8.3.5 Unit squares (Jean Johnson) ........................................................................................ 73
9 Division in equal parts ................................................................................................. 75
Of a perigon. A square in two parts of equal area. Trisection of the
angle of a square. A square in three equal parts (exact and ap-
proximate solutions). A square in three equal parts after Haga ́s
theorem.
9.7 Trisection ..................................................................................................................... 80
Of a square (Corollary P). Of a square by trisection of its diago-
nals. Of any angle. Idem after H. Huzita.
9.11 Division of a square in five equal parts ....................................................................... 84
Other inexact form of division.
9.13 Thales ́ theorem: division of a rectangle in n equal parts ............................................ 85
9.14 Division of a square in 7 equal parts........................................................................... 86
Two approximate solutions.
9.15 Division of a square in 9 equal parts........................................................................... 88
Inexact and exact solutions.
9.16 Division in n parts after Corollary P ............................................................................ 89
9.17 Division of a paper strip (Fujimoto ́s method) ............................................................ 94
In 3 and 5 equal parts.