In this page, the Portuguese and the Greek students presented to their partners their work on discovering the manifestation of the Golden Ratio in buildings of their city. The students were able to see the great variation that the manifestation of the Golden Ratio can take while at the same time being exposed to completely different architectural styles.
Loulé Market was inaugurated on 27th June of 1908 and designed by the architect Alfredo Campos. It occupies a whole block and was built, with halls characteristic of iron architecture, in the eclectic revivalist style with neo-Arab inspiration, itself part of the Art Nouveau style.
Searching the golden number and the golden ratio in the original project of Loulé Market:
Making geometric constructions using the golden rectangle:
Golden number φ - Fibonacci sequence- Golden spiral
In mathematics, two quantities are in the golden ratio if the ratio is the same as the ratio of their sum to the larger of the two quantities.
So, for two quantities a and b with a>b>0:
Where the Greek lettet phi (φ or Φ ) represents the golden ratio and its value is φ=1,6180339887........ . The golden ratio is also called the golden number. The letter phi (φ) is the first letter of the name Phidia (Φειδία). Phidias was an Ancient Greek scultor, painter and architect, who made the Parthenon statues that seem to embody the golden ratio.
Fibonacci sequence
The Fibonacci sequence is the integer sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,....... and is characterized by the fact that every number after the first two is the sum of the two preceding ones.
Fibonacci sequence and Golden ratio
The ratios of two succesive numbers of the Fibonacci sequence after the first one is:
.
We see that the ratio of succesive Fibonacci numbers converges to the golden ratio φ.
An orthogonal rectangle whose side lengths are 13 and 8, is the golden orthogonal rectangle because the numbers 13 and 8 are succesive numbers from the Fibonacci sequence which converges to the golden nymber φ.
The spiral which is inscribed to the golden rectangle is a golden spiral and the Fibonacci spiral approximates the golden. The Fibonacci spiral is inscribed to the rectangle whose side lengths are 13 and 8. In the picture below we can see the golden spiral :
We create the golden spiral with using the geogebra
Golden spiral and nature
Approximate golden spirals can occur in the nature, for example: the Nautilus
which resembles the pattern of the Ionian column
