With a simple tile

How to build different panels with copies of the same tile?

Area of a rectangle

How to obtain the area of a rectangle?

Area of a parallelogram

How to obtain the area of a parallelogram?

Area of a triangle

How is the area of a triangle related with the area of a rectangle?

Area of a triangle

How to obtain a parallelogram by duplicating a triangle?

Area of a trapezium

How to transform a trapezium in an equivalent parallelogram with half the height?

Area of a trapezium

How to transform a trapezium in a parallelogram with double the area and the same height?

Area of a kite

How to transform a kite in a rectangle with the same area?

Area of regular polygons

How to determine the area of a regular polygon?

Area of a circle

How to obtain the area of a circle?

The Calculus of Pi

How to calculate the value of pi approximating it by regular polygons?

Cavalieri’s principle

If a line cuts two polygons creating segments with the same lenght in each one, do the polygons have the same area?

Cavalieri’s principle

If a plane cuts two solids creating polygons with the same area in each one, do the solids have the same volume?