1.618
#The golden ratio has this inherent balance and pleasing property of being the ratio of two quantities where the ratio of one to the other is equal to the ratio of the sum of both.
The golden ratio is found by dividing a line into two parts such that the longer part divided by the smaller part is equal to the sum of the two parts divided by the longer part.
The golden ratio has geometric and aesthetic properties that are utilized by nature to optimize growth and to devine shape.
The golden ratio has been observed in natural patterns and structures, such as the spiral of the nautilus shell, the arrangement of leaves on a stem, the branching of trees, the shape of deer antlers and human fingers, and even the structure of DNA.
Scientific evidence suggests that the human heart rate may be influenced by the golden ratio. Studies have shown that the heart rate of healthy adults tends to fluctuate around a certain average value, which is typically around 70 beats per minute (bpm). When a person is at rest, their heart rate tends to be slightly lower than this average value, and when they are active, it tends to be higher. Researchers have found that the distribution of heart rates within a population follows a bell-shaped curve, with most people having heart rates within a certain range of values. The shape of this distribution is similar to the shape of the normal distribution, which is also known as the Gaussian distribution, and it is believed that this similarity may be due to the influence of the golden ratio.
The shape of the Gaussian distribution is often compared to the parabola, which is a symmetric U-shape. The golden ratio is often used to describe the symmetry of the Gaussian distribution, as the curve is asymmetric. Additionally, the idea of the golden ratio being related to the Gaussian distribution comes from the fact that the Gaussian distribution itself is derived from the exponential distribution, whose cumulative distribution function satisfies the differential equation
F(x) = e^(-λx)/λ * x^(-α)
where α = d/2 is the Golden Ratio.
There have been studies that suggest that the structure of DNA may follow a pattern that is related to the golden ratio. Scientists have discovered that the distance between the nucleotide bases in DNA follows a specific pattern called the Chargaff's rule. This pattern suggests that the base pairs in DNA are arranged in a specific order, with adenine always paired with thymine, and guanine always paired with cytosine. Some researchers have proposed that this pattern may be related to the golden ratio, as the distances between the nucleotide bases in DNA follow a pattern that is consistent with the golden ratio. However, this idea is still subject to debate and further research is needed to fully understand the relationship between DNA and the golden ratio.