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...)