As you expand the Fibonacci series, each new value in proportion to the previous approaches the Golden Ratio.
The ratio of successive terms in the Fibonacci sequence approaches the Golden ratio as the number of terms increases.
The ratio of (distance) / (time), called "speed".The ratio of (speed) / (time), called "acceleration".The ratio of (force) / (area), called "pressure".The ratio of (force) / (acceleration), called "mass".The ratio of (mass) / (volume), called "density".The ratio of (distance) / (volume), sometimes called "fuel economy".The ratio of ( 1 ) / (time), called "frequency".The ratio of (energy) / (time), called "power".
The "golden ratio" is the limit of the ratio between consecutive terms of the Fibonacci series. That means that when you take two consecutive terms out of your Fibonacci series and divide them, the quotient is near the golden ratio, and the longer the piece of the Fibonacci series is that you use, the nearer the quotient is. The Fibonacci series has the property that it converges quickly, so even if you only look at the quotient of, say, the 9th and 10th terms, you're already going to be darn close. The exact value of the golden ratio is [1 + sqrt(5)]/2
A geometric series.
The 'golden ratio' is the limit of the ratio of two consecutive terms of the Fibonacci series, as the series becomes very long. Actually, the series converges very quickly ... after only 10 terms, the ratio of consecutive terms is already within 0.03% of the golden ratio.
As you expand the Fibonacci series, each new value in proportion to the previous approaches the Golden Ratio.
discuss objective and limitation of time series analysis
The ratio of successive terms in the Fibonacci sequence approaches the Golden ratio as the number of terms increases.
The absolute value of the common ratio is less than 1.
The ratio of (distance) / (time), called "speed".The ratio of (speed) / (time), called "acceleration".The ratio of (force) / (area), called "pressure".The ratio of (force) / (acceleration), called "mass".The ratio of (mass) / (volume), called "density".The ratio of (distance) / (volume), sometimes called "fuel economy".The ratio of ( 1 ) / (time), called "frequency".The ratio of (energy) / (time), called "power".
3.8
3.8
The "golden ratio" is the limit of the ratio between consecutive terms of the Fibonacci series. That means that when you take two consecutive terms out of your Fibonacci series and divide them, the quotient is near the golden ratio, and the longer the piece of the Fibonacci series is that you use, the nearer the quotient is. The Fibonacci series has the property that it converges quickly, so even if you only look at the quotient of, say, the 9th and 10th terms, you're already going to be darn close. The exact value of the golden ratio is [1 + sqrt(5)]/2
no it's the ratio of distance to time (ie speed)
Divide any term in the sequence by the previous term. That is the common ratio of a geometric series. If the series is defined in the form of a recurrence relationship, it is even simpler. For a geometric series with common ratio r, the recurrence relation is Un+1 = r*Un for n = 1, 2, 3, ...
The correct ratio is not 1.414 but sqrt(2), which is an irrational number.