Dissections

The aim is to cut a shape into pieces to form another shape (of course using all pieces...) as here two squares into one larger square.
Dissect a Pythagorean triple in only 4 pieces.
5² → 3² and 4² etc... Solution    Details (square to two squares)

Training...
Dissect a rectangle into just 3 pieces to build a square. Solution
Specific case : 9×16 rectangle into square using just 2 pieces. Solution

One square into 3 equal squares
Dissect a square into 3 equal squares. Solution
Bonus : into 3 squares of areas in ratio 2:3:4

A rotated square
Dissect a square in just 5 pieces to make the same square, rotated by 45°, but without rotating nor flipping the parts, just translations are allowed.
Solution

Details (rectangle to square and square to several squares, or turned).

A triangle into a square
Dissect an equilateral triangle in 4 pieces to build a square. Solution

Details (triangle to square).
Bonus : Any triangle into a square, a triangle into another triangle.

An hexagon into a triangle
Dissect a regular hexagon in just 5 pieces to build an equilateral triangle. Solution

A pentagon into a square
Dissect a regular pentagon in 6 pieces to build a square Solution

Details (regular polygons).
Bonus : regular polygons to other regular polygons.
General methods : P-strips, tiling etc.

Crosses and stars
Dissect a greek cross or a latin cross into a square.
Dissect an hexagram (star hexagon) into a square.

Details (crosses and stars).
Bonus : other crosses, n-gon and n-gram cross-dissections.

Miscellaneous shapes

Details (misc. shapes).

Curved shapes
Of course not squaring the circle !
But dissect into a square :
The crescent is made of two equal circle arcs.
(hence connected by a straight segment !)
The urn is made of circle arcs with same radius.

Details (curved shapes).
Bonus : crescent to greek cross, curved shapes to curved shapes.
For instance the classical round table into two oval tables.
... in 6 parts only !

And the dissection of a flower into a circle.
(the hardest part is to find the exact shape of the flower, so the dissection is possible...)

 

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