Concept

At first glance, fluctuations of price and time in financial markets might appear chaotic and random. However, various regularities, such as price-to-time ratios, geometric structures, and periodicity, can be found within market data.

As seen in the research of W.D. Gann and Larry Pesavento, concepts such as mathematics, geometry, ratios, and cycles have been utilized as a perspective to study charts.

METRIX is analysis and research software designed to handle these mathematical and geometric concepts on charts.

That is not to say that mathematics, geometry, or cycle theory can completely predict future price movements. What METRIX provides is the functionality to visualize price-time relationships, geometric ratios, and cyclical structures on charts based on historical market data, thereby supporting users' own chart research, analysis, and learning.

The Pythagorean Theorem

In his book "The Secret of the Universe" (Mysterium Cosmographicum), the astronomer Johannes Kepler wrote, "Geometry has two great treasures: one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio (Golden Ratio)."

Renaissance greats like Leonardo da Vinci, Michelangelo, and Albrecht Dürer viewed themselves not just as artists, but as architects, engineers, mathematicians, and geometers.

The Pythagorean Theorem is one of the most famous theorems in the history of mathematics. From its origins in surveying to architecture, civil engineering, manufacturing, IT/game development, and seismic analysis, it appears and is utilized in almost every field. It can be called the most universal and foundational pattern in mathematical history for quantifying spatial/geometric structures.

In a right-angled triangle, if the length of the hypotenuse is c, and the lengths of the other two sides are a and b, the following relationship holds:

The essence of this theorem lies in the conservation of area: the sum of the areas of the two squares on the legs (sides a and b) equals the area of the square on the hypotenuse (side c).

• Top Figure: A right-angled triangle formed on a number line with a base of length 1 and a perpendicular leg of length 1. The Pythagorean Theorem determines the hypotenuse length to be √2.
• Left Figure (Square): A right-isosceles triangle formed by drawing a diagonal inside a square with side length 1. The length of the diagonal is √2.
• Center Figure (Spiral): Part of the "Spiral of Theodorus" demonstrating how to construct consecutive irrational numbers geometrically.
• Right Figure (Rectangle): A right-angled triangle formed by drawing a diagonal across a rectangle of width 1 and height 2. The diagonal length is √5.

■ Application to Chart Research: The horizontal axis of a chart represents "Time," while the vertical axis represents "Price," intersecting at 90 degrees. Applying the Pythagorean Theorem to chart analysis means that the two independent axial components of "Time variance (dt)" and "Price variance ( dp)" are synthesized and visually organized/quantified as a diagonal "vector indicating the trend direction" (hypotenuse).

Freemasonry Symbols and Geometry

The symbolic system of Freemasonry features many emblems related to geometry, including the square, compasses, the letter "G", Euclid’s 47th Proposition (Pythagorean Theorem), and the Eye of Providence.
Regarding this connection, the Museum of Freemasonry in London explains the letter "G" in Masonic symbolism as representing "Geometry."
The square and compasses, the iconic symbols of Freemasonry, were tools actually used by stonemasons. The square was used to verify right angles in stone, and the compasses were used to draw circles and arcs.
Thus, geometry in Freemasonry is not merely a later "mystical interpretation" but has a tradition directly linked to the practical trade of stonemasonry and architecture.

• Square: A tool to verify and construct right angles
• Compasses: A tool to draw circles and arcs, and to transfer distances

According to the Museum of Freemasonry, the square represents acting with morality and fairness, while the compasses symbolize the boundaries of one's actions, teaching not to exceed those limits. For this reason, the square and compasses embody both practical stonemasonry techniques and Masonic moral allegories.

The "G" placed at the center of the square and compasses is especially significant. In Freemasonry across many countries, it is officially defined as standing for "Geometry"—one of the oldest symbols of the craft—though interpretations relating it to "God" also exist.

A prominent example of Freemasonry's tie to Euclidean geometry is "Euclid's 47th Proposition" (the Pythagorean Theorem), which is integrated into Masonic ritual and symbolism, as verified by historical documents.

The Golden Ratio, Fibonacci Numbers & Sacred Proportion

The Fibonacci sequence is formed by adding the two preceding numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233…
As the sequence progresses, the ratio between adjacent numbers converges to the Golden Ratio φ ≈ 1.618 (or its reciprocal 0.618).

The Golden Ratio appears in natural growth patterns such as the logarithmic spiral of the nautilus shell or sunflower seeds because it is the unique ratio that allows scale expansion without losing self-similarity (fractal structure).

■ Application to Chart Research: Chart analysis using the Golden Ratio and Fibonacci numbers is a technical method that applies these ratios (approx. 1:1.618) and sequence ratios to analyze chart "Price" and "Time cycles". It is widely used to visualize grids and lines as benchmarks to organize price-time ratio structures, facilitating chart research.

Vesica Piscis

This is a fundamental symbol of sacred geometry formed by the intersection of two circles with the same radius, where the center of each circle lies on the circumference of the other.
The ratio of the vertical axis to the horizontal axis of the lens shape (vesica) formed in the intersection is precisely 1 : √3 (√3 ≈ 1.73205…).

In ancient geometry, this figure was regarded as the "gate of creation," from which polarities emerge from unity (one circle to two) and generate irrational numbers (√2, √3, √5) as well as equilateral triangles and regular hexagons. The shape is historically linked to harmony and creation, used in Christian art, medieval architecture, and stonemasonry ornaments such as the west facade of Chartres Cathedral.

In Christian traditions, the fish symbol represents Christ and Christian faith.

■ Application to Chart Research: Taking two reference points (pivots) as the centers of the two circles, the √3 ratio generated by the intersection is utilized to visualize geometric symmetry relationships and intersections on the chart, serving as reference lines for chart research.

The Diagram & Semi-Diagonals: Harmony of Geometric Symmetry

To construct the Diagram using a square, you draw eight "Semi-Diagonals" from the four corners to the midpoints of the opposite sides.
If half the side length of the square is 1, the ratio between this half-side (1) and the semi-diagonal length is 1 : √5 (√5 ≈ 2.23606…) by the Pythagorean Theorem.

This √5 is the geometric constant that underlies the calculation of the Golden Ratio φ = (1 + √5) / 2. The intersection of the eight semi-diagonals creates a beautiful symmetric "star cut" in the center, dividing the space into perfectly harmonious proportions (integer and Golden Ratio relationships) without using external scales or measurements.

■ Application to Chart Research: The grid formed by the intersection of these eight semi-diagonals and the main diagonals visualizes the geometric ratio relationships of a single square formed by time and price. These geometric split points (star cut intersections) serve as references for drawing angle lines or grid lines that show specific harmonic price/time relationships.

■ Relation to W.D. Gann Theory (Gann Box / Gann Square): The specifications of this diagram share a common foundation with W.D. Gann's squaring theories (such as the "Gann Box" and "Gann Square of 144") regarding the proportional integration of time and price.
・Based on squaring theory, it draws key research auxiliary lines representing geometric price-time structures, such as the main diagonal (1x1 angle = 45 degrees) or double-square diagonals (1x2 angle, √5).

References

• 『The Magic Word』 W.D. Gann (1950)
• 『Astro-Cycles: The Trader’s Viewpoint』 Larry Pesavento (1987)
• 『Harmonic Vibrations: A Metamorphosis from Traditional Cycle Theory to Astro-Harmonics』 Larry Pesavento (1996)
• 『Fibonacci Ratios with Pattern Recognition』 Larry Pesavento (1997)
• 『Complete Stock Market Trading and Forecasting Course』 Michael S. Jenkins (1999)
• 『Basic Day Trading Techniques』 Michael S. Jenkins (2007)
• 『Integrated Pitchfork Analysis: Basic to Intermediate Level』 Mircea Dologa (2009)
• 『Day Trading For 50 Years: The Michael S. Jenkins Methods』 Michael S. Jenkins (2022)
• "Beautiful Geometry" Eli Maor & Eugen Jost (Japanese translation published by Maruzen Publishing, 2015)
• "The Secret Code: The Mysterious Formula That Rules Art, Nature, and Science" Priya Hemenway
• "The Mystical Power of The Diagram" Adam Tetlow (2023)
• "Sacred Geometry" Miranda Lundy (2011)
• "Ruler and Compass: Practical Geometric Constructions" Andrew Sutton (2012)