IINDEX
1 Origami resources to deal with points, straight lines and surfaces ............................. 1
Symmetry. Transportation. Folding. Perpendicular bisector. Bi-
sectrix. Perpendicularity. Parallelism. Euler characteristic applied
to the plane. Interaction of straight lines and surfaces. The right
angle. Vertical angles. Sum of the angles of a triangle.
2 Haga ́s theorem ............................................................................................................ 8
Demonstration, applications.
5 Corollary P ................................................................................................................... 11
Demonstration, applications.
6 Obtention of parallelograms ........................................................................................ 12
Square from a rectangle or from other square. Rhomb from rec-
tangles or squares. Rhomboid from a paper strip. Rectangles with
their sides in various proportions. DIN A from any other rectangle
or from any other DIN A. Argentic and auric rectangles.
6.7 Dynamic rectangles. Square roots................................................................................ 20
6.8 A rectangle from an irregular piece of paper ............................................................... 22
6.9 Stellate rectangle ......................................................................................................... 22
7 Geometry in the plane. Cartesian plane. Algebra ....................................................... 24
The area of a rectangle. Binomial product. Squares difference.
Area of the other parallelograms and trapezium. Problems in the
cartesian plane. Maxima and minimums.
7.7 Resolution of a quadratic equation ............................................................................. 29
Square root of a number. Square of a number. Parabola associated
to the folding of a quadratic equation.
7.11 Complete equation of 3rd degree: Its resolution (J. Justin) .......................................... 33
Idem equation of 4th degree. Parabolas associated to the folding
of a complete equation of 3rd degree.
7.14 Fundament of orthogonal billiards game (H. Huzita) ................................................. 37
Squares and square roots. Cubes y cubic roots. The orthogonal
spiral of powers. Resolution of a quadratic equation (H.H). Reso-
lution of the complete equation of 3rd degree (H.H).
7.15 Arithmetic and geometric progressions ...................................................................... 46