## Task 2 Around the Golden Ratio

• During the Renaissance artists used the Golden ratio, or the Divine Proportion, extensively in their paintings and sculptures to achieve balance and to make the art immediately aesthetically beautiful to the eye. The students learnt a basic definition of a mathematical sequence, specifically the Fibonacci sequence. They discovered the mathematical constant phi, the golden ratio, through hands-on activities using also the GeoGebra application.

Teams designed in teams presentations about golden number and its usage in nature.

Canva presentation 1 Golden ratio - LINK

Canva presentation 2 Golden ratio - LINK4

Division of a line segment into a golden section

Fibbonacci spiral - is made up of quarter-circular arcs whose radii are consecutive Fibonacci numbers. The Golden Spiral has been modeled with a series of squares that have been constructed using the first ten Fibonacci numbers. Each square has sides with lengths of Fibonacci Numbers (1x1, 2x2, 3x3, 5x5, 8x8, etc.). The large rectangle that surrounds the inner squares is a Golden Rectangle that has been divided into a Golden Section.

In Geogebra:

Construction of the regular pentagon in GeoGebra:

Enjoy the students' work in a new presentation, SWAY app.

Fibonacci Spiral - group 1

The golden number - group 2

The Golden ratio - group 3

Fibonacci Spiral - group 4