In the second post in this series commemorating Mathematics and Statistics Awareness month, we explore our relationship with numbers and the beauty behind some of our favorites…
Pick a number, any number.
This exercise is usually the precursor to magic tricks or parlor games, but it can also provide an interesting insight into our relationship with numbers. Many people who are instructed to select a number often choose their favorite or ‘lucky’ digit.
A recent global survey from Brazilian mathematician Alex Bellos claimed ‘7’ is the world’s favorite number, based on responses from more than 30,000 people.
But would you get the same result if you asked mathematicians for their favorite number? Probably not. In fact, they are likely to choose from a multitude of numbers that could be considered ugly to the untrained eye, yet hold specific mathematical significance. For example, pi (π) and the Golden Ratio (Φ) are irrational numbers, but both are frequently cited for their beauty. Other popular choices could include Kaprekar’s constant (6174) the Hardy-Ramanujan number (1729) or 3654345456545434563, which is currently acknowledged as the largest palindromic triangular number with a palindromic index.
These numbers all possess unique quirks and properties that may make them beautiful to a mathematician. Moreover, numbers are just one of many mathematical building blocks. It is perhaps easier to understand the natural beauty in mathematics once the scope is widened to include more complex mathematical concepts.
The Golden Ratio: The epitome of beauty?
Fibonacci numbers are also linked to arguably the most well-known example of mathematical beauty - the Golden Ratio. Represented by the Greek letter Phi (Φ), the Golden Ratio was first described by mathematician Euclid in his treatise ‘Elements’ and has become famous for its supposed aesthetic value. The ratios of successive Fibonacci number pairs eventually converge on Phi (1.618 …), with the ratio frequently used in art, music and architecture.
Golden rectangles - rectangles that have side lengths corresponding with the Golden Ratio - have been used to map physical beauty in human faces and bodily proportions for centuries.
Traditionally, experts believed people who are perceived as naturally beautiful have facial features that are more consistent with Phi than those whose features do not fit the ratio. This theory remains an area of contention between mathematicians and scientists, with some still confident of its validity and others claiming it has been debunked. University of Toronto researchers have even proposed a new Golden Ratio for female beauty. Whether or not Phi truly corresponds with aesthetic beauty is uncertain, but the ratio has still influenced thousands of years’ worth of artistic creations. The fact that mathematicians, historians and other researchers continue to debate the existence of the Golden Ratio in both natural and man-made phenomena lends credibility to its status as one of mathematics’ most beautiful numbers.
Famous examples of the Golden Ratio
Advocates of the Golden Ratio’s beauty have argued it was used in the creation of numerous historical masterpieces over time, ranging from the Great Pyramid of Giza and the Parthenon to the music of Mozart and Leonardo da Vinci’s Vitruvian Man. Some of these claims have more substance than others; nevertheless, there is strong evidence that the ratio is present in many popular pieces of art, music and architecture.
The above is an excerpt from a dedicated free eBook: The Beauty of Numbers. Download your copy here.