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LA SEZIONE AUREA

Calcoli sul dodecaedro

La proporzione aurea fu "scoperta" dai seguaci del filosofo e matamatico greco Pitagora.Tale rapporto venne chiamato comunemente dai Greci “sezione”. La sezione aurea, detta anhe proporzione divina o numero d'oro è un rapporto tra due dimensioni disuguali. Questo rapporto corrisponde a un numero non intero che è pari a 1,618.

I pitagorici si accorgono che il numero 1,618 presenta una particolarità: è una costante capace di esprimere universalmente il rapporto fra due lunghezze diseguali di uno stesso segmento. Tale rapporto venne chiamato dai Greci “sezione”.

uNA COSTANTE

Due segmenti sono in rapporto aureo fra di loro quando la parte di lunghezza maggiore del segmento è medio proporzionale fra quella minore e il segmento intero; a sua volta, la parte di lunghezza minore è medio proporzionale fra quella maggiore e il segmento intero. Il valore del rapporto AB:AF e AF:FB è sempre lo stesso e corrisponde al risultato dell’equazione (√5 + 1) / 2: 1,6180339887.

Definizione geometrica

Frà Luca Bartolomeo de Pacioli, religioso e matematico del Rinascimento, per la diffusione in natura e per la capacità di risultare esteticamente piacevole per l’occhio umano, definisce la sezione "divina proportione" L'aggettivo "aurea", con cui oggi la conosciamo, le viene attribuito solo nell'ottocento.

La DIVINA PROPORTIONE

LA SEZIONE IN NATURA

In alcune piante, la disposizione delle foglie o dei petali segue lo stesso rapporto della sezione aurea. Anche la forma della spirale della conchiglia del nautilus segue questa proporzione. Tra le distanze dei i pianeti del sistema solare esisterebbe una logica aurea.

La sezione nelle statue greche

Gli scultori greci utilizzano la sezione aurea per ottenere la forma perfetta del corpo umano. L' Apollo del Belvedere ne è un esempio: la distanza tra ombelico e piede è in rapporto aureo con l’altezza della statua intera.

La sezione nell’architettura greca

La facciata del Partenone, il tempio di Atene dedicato ad Atena Parthenos, è progettata in modo armonioso usando rapporti aurei. La larghezza della facciata è proporzionata alla sezione aurea, così come l'altezza complessiva della facciata rispetto all'altezza della trabeazione (architrave e timpano) rispetta il rapporto aureo.

I Greci erano consapevoli che per ottenere un edificio o una statua armoniosa ed esteticamente gradevole, mettere insieme le parti in modo proporzionato era più importante della dimesione assoluta degli elementi stessi.

L' Armoniosita' del mondo greco

1. Costruzione geometrica del rettangolo e della spirale aurea. www.tiragraffi.it 2 a sinistra. Leonardo da Vinci (attribuito), Il dodecaedro solido, tavola XXIX del De Divina Proportione di Luca Pacioli, XV secolo. Milano, Biblioteca Ambrosiana. Digital Image 2011 (c) Veneranda Biblioteca Ambrosiana/De Agostini Picture Library/Scala, Firenze 2 a destra. La costruzione del pentagramma nel pentagono. 1.bp.blogspot.com 3. Rafael Araujo, Sezione aurea. www.pecorenerd.it 4. Mauritius Cornelis Escher, Conchiglie e stelle marine, 1941. Questa composizione si basa su una simmetria rotatoria di un modulo pentagonale con al centro un triangolo aureo. i.pinimg.com 5. Pagina tratta dal De Divina Proportione di Luca Pacioli, 1509. New York, Metropolitan Museum of Art. Commons Wikimedia. 6 a sinistra. Pianta grassa che sviluppa la spirale aurea. www.scientificast.it 6 a destra. Conchiglia di nautilus che sviluppa la spirale aurea. Shutterstock/James Mattil 7. Apollo del Belvedere, copia romana di un originale greco. Città del Vaticano, Museo Pio-Clementino. Commons Wikimedia 8. Calcolo della sezione aurea sulla facciata del Partenone. it.pinterest.com 9. Ictino, Callicrate, Fidia, Partenone, 437-432 a.C. Atene. Facciata. Mauritius/CuboImages

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