Razão áurea: história e suas aplicações matemáticas - Lima, José Antonio Ferreira de (2015)
The objective of this work is to show a part of mathematics that is fascinating, surrounded by mysteries and could be included in the school curriculum: The Golden Ratio. Surveys were conducted around the subject from ancient civilizations to the present day. Taking into account the historical and social aspects, several companies were studied: Egyptian, Babylonian, Greek, Roman, among others. Is addressed also times when people sought renowned aspirations to display their art in the ideal formula of this proportion in his works. Pythagoras, a great philosopher and mathematician, demonstrated a remarkable property of many pentagrams, that looking at the line segments in order of increasing length, can be proved easily by elementary geometry, each segment is larger than its predecessor by a factor which is exactly equal to the Golden Number. Fibonacci, was known for his work Liber Abaci (Book of Abacus) written in 1202, created a sequence that has become known by his name and was expressed as a problem involving rabbits in which the expression was denoted by a formula. This research has also shown how this reasoning is applied in mathematical formulas involving primary and secondary level operations to get the number of Gold.