The golden section

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1. THE GOLDEN SECTION b y Prof. Boni and Biasini

2. Let's see a video together …….. https://youtu.be/D5n6iT2AqrI

3. Let’s take a credit card or the badge of our school If we measure the length of the sides, then divide the two measures, THE LARGEST BY THE SMALLER WE GET 1.6 ....

4. Let’s consider the Temple of Concord in Agrigento (Sicily) If we divide again the base by the height (THE LARGEST DIVIDED BY THE SMALLER) WE GET 1.6 ....

5. Let’s consider the cathedral of Notre Dame of Paris We can identify particular rectangles, whose measures divided among them GIVE 1.6 ....

6. Let’s consider the portal of Castel del Monte (Apulia)

7. Portal of Castel del Monte COINS OF 1 CENT OF € you can find the same proportions that GIVE 1.6 ....

8. Let’s consider the Parthenon of Athens We recognize some golden rectangles, just like the Temple of Concord in Agrigento

9. Gustav Theodor Fechner  ( Dr. Mises ) (1801 – 1887) In 1875 the German psychologist Fechner submitted to the judgment of several people a set of rectangles, with different side lenghts. Then he asked to indicate which rectangle inspired them a greater sense of harmony. He observed that the choices of the respondents were almost the same: they chose a particular rectangle, the one built on the basis of golden ratio. AC : AG = 1,6180339887 AC : AG = AG : BC CE : CB = CB : DE … .

10. The body proportions E verything that seems harmonious and pleasing to the eye, hides in itself the golden ratios

11. Let's see a video together …….. https://youtu.be/bGO_TlC9Vvs The construction of the golden rectangle

12. In simboli: A few calculations .... where does the number 1.6 come from? In Math two unequal lengths are in the GOLDEN RATIO only if: (a + b) : a = a : b it’s an irrational and algebric number

13. The golden ratio is also called the DIVINE PROPORTION or GOLDEN SECTION (Latin: sectio aurea ) or CONSTANT NUMBER OF PHIDIAS (φ is the initial of Phidias, a Greek architect and sculptor, active around 500 BC, who worked very hard for the construction of the Parthenon). Its geometric and mathematical properties and the fact that this number is often found in numerous natural and cultural contexts (apparently not connected to each other) have led man to think that there could be a relationship between God and man, universe and nature: a relationship between the whole and the part, between the largest and the smallest part that is repeated endlessly through infinite subdivisions. Different philosophers and artists have caught through times an ideal of beauty and harmony, searching for it and, in some cases, recreating it in the anthropic environment as a canon of beauty. Its name has recently assumed the appellations of golden and divine. THE GOLDEN RATIO 𝛗

14. JAKE GARN an American photographer "..... and we want to build a composition in which the main points are placed on lines used by nature in different ways, followed by the Golden Section. Of course, I am not recommending to take a team and start measuring …….. but what I am recommending is to start seeing the world in the same way that Mother Nature does, IN A PROPORTION THAT IS ABSOLUTELY ELEGANT IN ITS MATHEMATICAL BEAUTY . If you can do it, the images would start to be more attractive and appealing. "

15. Some examples ……..

16. NOW IT'S YOUR TURN LET’S TRY TO FIND THE GOLDEN PROPORTIONS IN THE IMAGES THAT WE PROPOSE YOU Thanks for the attention