One day I asked ChatGPT something simple: can you square the numbers from 10 to 270, going up by 10 each time? Just a casual exercise. But when I laid the results next to my BTC/USD chart, they lined up almost exactly with support/resistance zones I'd been watching for years.
Btc için destek/direnç genel olarak bu matematik ile ilerler. pic.twitter.com/SzdHWL64IQ
— ً (@ebturkcom) April 5, 2023
I later learned this overlaps with what some analysts call W.D. Gann's "square root theory" a decades-old method I'd never heard of. I'd arrived at the same place through a completely different path. This post documents that discovery and the cycle-timing system I built on top of it.
The math behind it
The method works like this: take the square root of a price, increase it by a fixed step, then square it again to get a new level.
At low prices the rungs sit close together; as price rises the gap widens, because the difference between two consecutive rungs grows by 2·root·step + step². Using BTC's actual low (15,473.78) as the base, with a step of 10, the first few rungs come out to:
This isn't a proven market law, it's a contested technical tool some traders use because the levels tend to coincide with round/psychological prices. The more interesting part is that the same logic shows up on the time axis too.
Time follows the same logic
In Gann's framework, price and time can be "squared" against each other: when the size of a move and its duration line up in certain ratios, an important turn is expected. On the time side, instead of fixed steps, day counts come from slicing a circle (360°):
On top of that, some analysts also use day counts from the Fibonacci sequence: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144… counting forward from a significant low or high. The step counts you'll see below are roughly a derivative of this same logic.
Bull market validation: 13 → 21 → 23
Using a fixed step of 10, I counted how many square-root rungs separate the low and high of each bull cycle:
| Cycle | Low | High | Steps |
|---|---|---|---|
| 2015 → 2017 | 152 | 19,665 | 13 |
| 2018 → 2021 | 3,122 | 69,000 | 21 |
| 2022 → 2025 | 15,474 | 126,219 | 23 |
13 and 21 are consecutive Fibonacci numbers, their ratio (1.615) is strikingly close to the golden ratio (1.618). If the third cycle had followed Fibonacci, it should have been 34; it came out at 23 instead. So growth slowed down which lines up with what many analysts independently call "diminishing returns": each cycle's percentage gain shrinking relative to the last.
Bear legs, counted the other way
I ran the same count from peak to trough, not as a warning, just to see whether the same math holds up in the other direction:
| Period | High | Low | Steps |
|---|---|---|---|
| 2017 → 2018 | 19,665 | 3,122 | 8 |
| 2021 → 2022 | 69,000 | 15,474 | 14 |
| 2025/26 → ? | 126,219 | 63,044* | 10.4 (ongoing) |
The first two legs ran 8 and 14 steps a gap of +6. The third leg hasn't finished yet; the starred row is an ongoing measurement that can still change once the low actually forms it's not a settled result.
If the pattern continues: a few hypotheses
Starting from the two completed bear legs (8, 14), if the pattern were to continue in some form, where might the low land? This table isn't a prediction it's just a mathematical exercise:
| Assumed total steps | Logic | Implied Low |
|---|---|---|
| 16 | repeat the +2 gap | ≈ 38,100 |
| 18 | middle scenario | ≈ 30,700 |
| 20 | repeat the +6 gap | ≈ 24,100 |
Try it yourself
Enter a starting price, a step size, and how many rungs you want the ladder calculates instantly:
Tracking this on TradingView
Rather than tracking all this by hand, I built a Pine Script indicator that draws the ladder directly on the chart and automatically updates the cycle step count: it confirms a leg once price reverses by a set percentage from a peak or trough, computes the step count, and shows a live, updating count for whichever leg is currently in progress.
This post documents a personal market-math framework (the square-root ladder and cycle step count) built from my own observations. There's no evidence that past patterns determine future outcomes; this is not investment advice it's for education and observation only.