add each number to the number before it to get the next number
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55
and so on
The sequence is used to express that which is pleasing to the eye. when displayed in squares it creates a spiral form. The ratios of any subsequent numbers divided by each other will get you 2.666 repeating or .66666 repeating. 2/3 basically. That ratio is found in nature, attractive peoples faces, etc. Basically anything pleasing to human senses is found to have this ratio. Tool uses it in a lot of their music, and a video on YouTube can be found about it. So it really is everywhere. As far as the mathematical proofs and equations, I do not know them.
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he did math
When he was in India with his father
Fibonacci was a mathematician who travelled and studied under other mathematicians. He received a salary from the Republic of Pisa for his work in math and science.
He discovered the Fibonacci Sequence (although long after an Indian named Pingala did), and he brought the current Arabic number system into popularity through his publication of "Liber Abbaci".
he did not have college back in the middle ages so when he was travling with his fatherr is when was learning about math