Fibonacci extension in Elliott waves: check all three anchors
Calculate a three-point projection and show why changing the third anchor moves the result.
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Different projection tools may use different conventions. State the formula and anchors instead of comparing only the ratio label. This synthetic exercise uses the arithmetic length of the first movement projected from the end of the following correction.
Write the convention explicitly
Let A be 100, B be 120 and C be 110. For this exercise, the projected level is C plus the difference between B and A multiplied by the chosen ratio. The measured first movement is therefore 20.
Calculate one projection
Using 1.618 gives 110 plus 20 times 1.618, or 142.36. Record A, B, C, their timestamps and the scale with the number. A tool displaying 1.618 without those conditions does not provide a complete calculation record.
Change only the third anchor
With C changed to 113 and the other conditions retained, the result becomes 145.36. The projection moved by 3 because its starting anchor moved by 3. The ratio did not change. Compare anchor conventions before diagnosing two projection results as inconsistent.
Keep projection and confirmation separate
A reference level is not proof of a completed wave or a command to trade. Check the proposed structural relationship independently, and verify that the movements compared belong to the intended level. The linked Fibonacci lesson supplies the broader context for anchor selection.
Does the common label 1.618 guarantee identical projected prices on two charts?
No. The measured movement, projection anchor, scale and tool convention also need to match.
A three-anchor extension on a linear chart
Fix invented anchors A=100 at t=0, B=120 at t=10 and C=110 at t=20. Measure B−A=20, then project from C: T(r)=110+20r. Ratios 0.618,1 and 1.618 give 122.36,130 and 142.36. The diagram’s horizontal lines represent those calculations, not observed future turning points.
Record all three anchors, their times and the calculation scale before comparing results. Moving only C to 113 moves the 1.618 projection to 145.36. A ratio label alone is therefore insufficient. The chart scale and a drawing’s logarithmic-level option can be separate settings; these numbers use a stated linear convention, without confirming an Elliott pattern.
| Item | Calculation or value |
|---|---|
| r=.618 | 110+20×.618=122.36 |
| r=1 | 110+20=130 |
| r=1.618 | 110+20×1.618=142.36 |
| C=113 | 113+20×1.618=145.36 |
Two charts show 1.618 but different prices. What should be checked first?
Compare all three anchors, direction and calculation method. Here changing C from 110 to 113 explains a 3-unit shift without changing the ratio.
A Fibonacci cluster needs a declared tolerance
This original exercise combines two separately specified calculations. A 61.8% retracement of 100→180 is 180−80×0.618=130.56. A projection of 90→115 from 105 at r=1 gives 105+25=130. Choose the closeness allowance 0.6 before inspecting the result. Their separation is 0.56, so they form the chosen zone [130,130.56] under that rule.
Record the anchor roles, scale, tolerance and both formulas. Two arithmetic results are not independent empirical signals, a reversal probability or proof of a valid count. Do not multiply identical measurements into apparent confirmation. If the projection anchor changes from 105 to 108, its result becomes 133, outside the old zone; the earlier cluster must be reassessed.
| Item | Calculation or value |
|---|---|
| R(.618) | 180−80×.618=130.56 |
| T(1) | 105+25=130 |
| Δ | 130.56−130=.56≤.6 |
| C:105→108 | 108+25=133 |
Can the tolerance be widened after seeing 133 so the old cluster still appears to work?
That changes the protocol after the outcome. Preserve the original 0.6 rule and report the changed calculation separately.
Thirteen coefficients: origins and explicit projections
Keep the existing linear anchors P1=100, P2=120, P3=110: T(r)=110+20r. The table uses exactly the displayed decimal constants, not hidden exact golden-ratio values. Let φ=(1+√5)/2. Its powers and inverse powers motivate several references, while 0.5 is a halfway comparison, 1 equality and 2 a chosen double-length comparison. None is a compulsory length for a named wave.
The square-root family motivates conventions near 0.786 and 0.886. In particular √0.786≈0.886566; adopted 0.886 is neither that exact root nor its nearest three-decimal rounding. Likewise 1.272≈√φ and 1.382≈1+φ⁻² are different references. Freeze the ratio, anchors, scale, rounding and tolerance before viewing outcomes. A coefficient is not an Elliott invalidation boundary or proof of completion; its availability in a drawing tool does not establish a wave count. These are calculations, with no measured market probabilities.
| r | Mathematical reference / chosen comparison | T=110+20r |
|---|---|---|
| 0.236 | φ⁻³≈0.236068 | 114.72 |
| 0.382 | φ⁻²≈0.381966 | 117.64 |
| 0.5 | halfway comparison | 120 |
| 0.618 | φ⁻¹≈0.618034 | 122.36 |
| 0.786 | √(φ⁻¹)≈0.786151 | 125.72 |
| 0.886 | adopted root-family constant; √0.786≈0.886566 | 127.72 |
| 1.0 | equality | 130 |
| 1.272 | √φ≈1.272020 | 135.44 |
| 1.382 | 1+φ⁻²≈1.381966 | 137.64 |
| 1.618 | φ≈1.618034 | 142.36 |
| 2.0 | double-length comparison | 150 |
| 2.618 | φ²≈2.618034 | 162.36 |
| 4.236 | φ³≈4.236068 | 194.72 |
Do 1.272 and 1.382 give the same projection? Is 0.5 a limiting adjacent Fibonacci ratio?
No. The projections are 135.44 and 137.64, a difference of 2.20. The value 0.5 marks half the selected length; the adjacent-term limiting ratio is approximately 0.618.