Nature through the Lens of Number Theory
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Though we might not recognize it, mathematics is manifested in the world around us. To begin to see an example of this, we first develop the theory that links together the Fibonacci numbers, the Golden Ratio, and continued fractions to ultimately present some well-known (and some less well-known) results on the best approximation of irrational numbers by fractions. A discussion on irrationality, specifically with regard to the Golden Ratio, brings us to the conclusion that the Golden Ratio is among the most irrational numbers of the real line. Armed with this theory, we then examine the mechanics behind plant growth and discover surprising connections between mathematics and flower development. Through an in-depth understanding of the mathematical tools and number-theoretic results initially outlined, we are brought to a deeper appreciation of the Creation that surrounds us as we recognize the order and pattern that exist in the natural world.