Pythagoras and other mathematicians are convinced that mathematics are the building blocks of our universe. This universal mathematical language creates patterns and harmonious structures, at both, a very large and an infinitely small scale (i.e. macrocosms and microcosms). These patterns form what is called sacred geometry.

Here is a list of some important mathematical concepts that I will explain in more details down below:

1. The Fibonacci sequence
2. Phi ratio
3. Pi

The Fibonacci Sequence

Leonardo Fibonacci of Pisa, Italy, a mathematician of the 13th century, discovered this sequence by counting and observing the growth of a population of rabbits. He was credited with this discovery, even though the Ancient Egyptians and Indians already knew this sequence.

The Fibonacci sequence is an array of numbers that represents the algorithm or formula of life. This sequence has some interesting inherent characteristics. Every number after the first one is the sum of the two preceding ones.

1,  1,  2,  3,  5,  8,  13,  21, 34,  55,  89,  144,  233,  377, … This sequence can be seen in the design of nature, for example, the number of petals on flowers generally follows this sequence. Furthermore, the Golden Mean Rectangle or Sacred Cut can be derived from this sequence and as well as the Phi Ratio which I will be discussing next.

Phi Ratio (φ)

In simple terms, the Phi Ratio exists when a line is divided into two parts and the longer part (a) divided by the smaller part (b) is equal to the sum of (a) + (b) divided by (a). which both equal 1.618034. See the example below using the Golden Mean Rectangle.

This ratio is commonly found in nature and geometry. It is often called the Divine Proportion because it creates natural compositions that are aesthetically pleasing to the eye. For this reason, this ratio is used in design, architecture, and arts. The drawing of the Vitruvian Man by Leonardo da Vinci is an excellent example of the application of this ratio to depict the ideal human body proportions.

The Phi Ratio (also known as the Golden/Divine Ratio), can also be derived from the Fibonacci sequence. This ratio is the quotient of the values derived by dividing each number in the Fibonacci sequence by the preceding number. This ratio stabilizes around 1.618034 as shown below. When the wave created by the phi ratio in the graph is converted in 3D, it reveals the pattern of the Golden Mean Spiral. This spiral appears within the Golden Mean Rectangle. The design of the spiral can be spotted easily in nature.

Pi (π)

The number Pi is a mathematical constant, the ratio of a circle’s circumference divided by its diameter. It always equals approximately to 3.14159. The digits after the decimal point in this ratio continue indefinitely and randomly (they do not seem to follow any apparent pattern). For this reason, Pi is considered an irrational number and the fraction of 22/7 is often used as an approximate for Pi. This ratio is an enigma for mathematicians because not only it appears in circles, but it tends to crop up everywhere, even when there is no connection to circles. Here are some examples:

1. the probability that any two numbers have no common factor is equal to 6/π2;
2. it appears in the physics of waves, such as ripples of light and sound (colors and music);
3. it enters in the equation known as the Heisenberg’s uncertainty principle, which defines how we can know the state of the universe;
4. it appears in the shapes of rivers (meandering ratio).

Using numerology, the Greek letter π has a value of 8 (value of 80 => 8 + 0 = 8). The number 8 is associated with matter and curiously, it also represents the infinity sign in a vertical position. If we analyze the approximation of 22/7, 22 is the master builder number, in other words, turning ideas into physical realities while number 7 is associated with spirit.

From another perspective, let’s analyze this ratio using sacred geometry. A circle represents infinity, oneness, and the immutable truth, while a straight line between two points (the diameter) represents apparent polarity, the mirror of expansion and consciousness.

From these perspectives, I conclude that Pi expresses the infinite possibilities of creation, by arranging matter in indefinite patterns (within apparent chaos, there is order). Also, it shows that polarity is at the heart of all creation and inherently connected (similar to the physical phenomenon of quantum entanglement). Finally, the circle is the immutable truth; therefore, it cannot be fully understood from our perspective since it is infinite.

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