English
English Golden Ratio
Golden Ratio is obtained, when a line is divided into the long part A and the short part B. The division has to be done in a way that A plus B divided by A is equal to A divided by B. Golden Ratio is indicated by the Greek letter phi φ and has the approximate value 1,618. An interesting feature of the Golden Ratio is its definition: φ = 1 + 1 / φ.
Furthermore, it is believed that the Golden Ratio is related to the Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21... Each number in the Fibonacci sequence is the sum of the previous two numbers (for instance, 21 = 8 + 13). If you divide the last number of the Fibonacci sequence by the previous one, we obtain approximately φ (for instance, 21 / 13 = 1.61...).
In arts and architecture, it is considered that a rectangle with edges 1 and φ has an aesthetic shape (pleasing to the eye). The Golden Ratio appears in nature for example in the spiral shells, sunflowers, pinecones, spiral galaxies or hurricanes. Hence, it is a cross-cutting phenomenon that covers many different fields.

#### Challenges

Urbanization: Currently more than half of population lives in the cities. it is expected that urbanization will continue in near future. Architects are exposed to the challenge of designing our future urban environment.
Education: In many European countries we see a shortage of mathematics teachers. There is insufficient interest of students for mathematics, since it is often considered as a boring topic.
Product Design: The success of many products depends on whether their design is perceived as pleasing in appearance. Hence, the proportion of objects plays a crucial role in product design.

#### Keywords

Golden Ratio, Fibonacci sequence, Golden Angle, Golden Ratio in Nature, Golden Ratio in Art and Architecture