Fibonacci: Difference between revisions
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If you sum the squares of any series of [[Fibonacci]] numbers, they will equal the last Fibonacci number used in the series times the next Fibonacci number. This property results in the Fibonacci spiral, based on the following progression and properties of the Fibonacci series. | If you sum the squares of any series of [[Fibonacci]] numbers, they will equal the last Fibonacci number used in the series times the next Fibonacci number. This property results in the Fibonacci spiral, based on the following progression and properties of the Fibonacci series.The Fibonacci spiral gets closer and closer to a Golden Spiral as it increases in size because of the ratio of each number in the Fibonacci series to the one before it converges on [[Phi]], 1.618, as the series progresses. | ||
Beginning with Zero, then 1, then goes on with 0+1=1, 1+1=2, 2+1=3, 3+2=5, 5+3=8 and so on. The next number in the Fibonacci is derived from added together the previous number & itself, essentially going back one number each time & adding it to get the next one. | |||
Revision as of 19:15, 24 January 2016
If you sum the squares of any series of Fibonacci numbers, they will equal the last Fibonacci number used in the series times the next Fibonacci number. This property results in the Fibonacci spiral, based on the following progression and properties of the Fibonacci series.The Fibonacci spiral gets closer and closer to a Golden Spiral as it increases in size because of the ratio of each number in the Fibonacci series to the one before it converges on Phi, 1.618, as the series progresses.
Beginning with Zero, then 1, then goes on with 0+1=1, 1+1=2, 2+1=3, 3+2=5, 5+3=8 and so on. The next number in the Fibonacci is derived from added together the previous number & itself, essentially going back one number each time & adding it to get the next one.
References