Chart Patterns

Forty-one days that fall from 110 to 90 and climb back. Fitting y = a·x² + b·x + k gives a = 0.05 (positive, so a U) with the turn at day 20, the middle of the window. Measured from the rim: 110 + (110 − 90) = 130. Many traders use a smaller target; the full depth is the optimistic version.

• It takes weeks or months to form, and the right side looks like any rebound until the rim is reached.
• A quadratic fits any dip that recovers; the fit says the shape is round, not that the rise will continue.
• Few formal studies test it; the evidence is mostly practitioner counts.

y = df['close'].iloc[-41:].values
x = np.arange(len(y))
a, b, k = np.polyfit(x, y, 2)                         # y ≈ a·x² + b·x + k
vertex = -b / (2 * a)                                 # where the curve turns
is_round = a > 0 and 0.3 < vertex / len(x) < 0.7     # a U, bottoming near the middle
rim, bottom = max(y[0], y[-1]), y.min()
target = rim + (rim - bottom)

Assumes import numpy as np, import pandas as pd, and a DataFrame df with columns open, high, low and close for the data above.