Why the Golden Ratio is the most irrational number
Explore the mathematical properties of the Golden Ratio through a visual demonstration of rotation. This video explains how specific fractional turns create unique patterns and why this particular ratio resists being approximated by simple fractions.
The video demonstrates the concept of irrationality by using rotations. By applying a turn of 'one over a number' between 0 and 1, Ben shows how different values affect the resulting pattern. This technique illustrates how the Golden Ratio functions within the context of fractional turns.
The demonstration also touches upon how values exceeding a single rotation, such as the square root of 2 (approximately 1.414), can be interpreted as a complete turn plus a remaining fractional component. This provides a visual framework for understanding how irrational numbers behave when applied to circular motion.
Source: The Golden Ratio (why it is so irrational) - Numberphile
