Golden Ratio | Golden Number

The Golden Ratio, also known as the Golden Mean or Golden Section, is a mathematical concept that has been recognized as aesthetically pleasing and has been used in art, architecture, and design for centuries.

The Golden Ratio is an irrational number that is approximately equal to 1.6180339887... (the digits go on infinitely without repeating). It is represented by the Greek letter phi (φ).

The Golden Ratio can be expressed as a simple algebraic equation: φ = (1 + √5) / 2

This equation states that the ratio of the whole to the larger part is the same as the ratio of the larger part to the smaller part. In other words, if a line is divided into two parts such that the ratio of the longer part to the shorter part is equal to the ratio of the whole line to the longer part, then the ratio of the longer part to the shorter part is the Golden Ratio.

The Golden Ratio is found in many aspects of nature, including the proportions of the human body, the structure of DNA, the shape of galaxies, and the spirals of shells and pinecones. It is also used in art and design, such as in the layout of books, the design of logos, and the composition of paintings.

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AI Technical Trustability Update

While working on an update to my RF Cafe Espresso Engineering Workbook project to add a couple calculators about FM sidebands (available soon). The good news is that AI provided excellent VBA code to generate a set of Bessel function plots. The bad news is when I asked for a table showing at which modulation indices sidebands 0 (carrier) through 5 vanish, none of the agents got it right. Some were really bad. The AI agents typically explain their reason and method correctly, then go on to produces bad results. Even after pointing out errors, subsequent results are still wrong. I do a lot of AI work and see this often, even with subscribing to professional versions. I ultimately generated the table myself. There is going to be a lot of inaccurate information out there based on unverified AI queries, so beware.

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