Properties of Trigonacci

Below you will find an incomplete list of general properties that characterize Trigonacci and spiral coordinates. Let’s take a look at them more carefully:

• The domain in which angles and dimensions can occur is only amongst positive real numbers. Unlike other coordinate systems, this one does not accept negative values, as it portrays an ever-expanding spiral that is portrayed often in nature.
• Similar to regular trigonometry, the functions of sine and cosine serve as building blocks for other functions or identities (coming up in the next post).
• The functions of spiral-tangent, spiral-cotangent, spiral-secant and spiral-cosecant.
• The ratio of the Fibonacci sequence is known to be the golden ratio, approximately 1.618. However, this number reveals itself more accurately as the terms get larger and larger. Since larger angles are accommodated by larger dimensions, and since the golden ratio is used in Binet’s formula, the values of the trigonacci functions become more accurate as the angles increase.
• See previous posts for a geometric proof of the Pythagorean trigonacci identity.
• Since every circle is responsible for a different set of angles, -which, if rearranged into the Fibonacci spiral get larger and larger- every circle is now called a dimension.