An extended version of the Fibonacci ratio, about the Tribonacci ratio
Fibonacci Ratios are used in many trading methods, but Trilobonacci Ratios have not yet been established in trading methods.
This time, I would like to explain the extended version of Fibonacci ratios, the Trilobonacci ratios.
【What are Fibonacci Ratios?】
To understand Trilobo-nacci ratios, you first need to understand what Fibonacci ratios are in the first place.
The numbers used as Fibonacci ratios are ①23.6% ②38.2% ③61.8% ④78.6%. How are these ratios calculated in the first place?
If you list Fibonacci numbers explicitly, they are “1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, …”.
Take four consecutive Fibonacci numbers and denote them from smallest to largest as a, b, c, d. Using these four numbers, you can calculate Fibonacci ratios.
①23.6%: a / d
②38.2%: a / c
③61.8%: a / b
④78.6%: square root of 0.618
We will calculate by taking four consecutive Fibonacci numbers.
(a) 144 (b) 233 (c) 377 (d) 610
①23.6%: 144 / 610 = 0.23606…
②38.2%: 144 / 377 = 0.38196…
③61.8%: 144 / 233 = 0.61802…
④78.6%: square root of 0.618
We were able to find numbers close to Fibonacci ratios.
The larger the values of the four consecutive numbers, the more they converge to Fibonacci ratios.
【What are Trilobonacci Ratios?】
Now, let's calculate the Trilobonacci ratios.
The Trilobonacci sequence is defined as “a sequence where the first two terms are set to 1, and each term is the sum of the previous three terms.”
If we list the Trilobonacci numbers concretely, they are “1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 504, 927, 1705, 3136, 5768, 10609, 19513, 35890, 66012…”
Take four consecutive Trilobonacci numbers and denote them from smallest to largest as a, b, c, d.
Using these four numbers, you can calculate Trilobonacci ratios.
①16.0%: a / d
②29.5%: a / c
③54.3%: a / b
④73.6%: square root of 0.543
We will calculate by taking four consecutive Trilobonacci numbers.
(a) 927 (b) 1705 (c) 3136 (d) 5768
①16.0%: 927 / 5768 = 0.16071…
②29.5%: 927 / 3136 = 0.29559…
③54.3%: 927 / 1705 = 0.54369…
④73.6%: square root of 0.543
We have obtained the Trilobonacci ratios.
Also, the ratio of adjacent two terms in the Trilobonacci sequence converges to the Trilobonacci constant (1.839286…).
This Trilobonacci ratios ①16.0% ②29.5% ③54.3% ④73.6% and the Trilobonacci constant’s ⑤83.9% are used to develop and operate EAs and indicators.
I hope you have gained a deeper understanding of the extended version of Fibonacci ratios, the Trilobonacci ratios.
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