• Tue. May 30th, 2023

Amazing numbers you should not forget about this Pi Day


Mar 14, 2023 , , ,

Illustration shows different numbers with the pi sign the most obvious.— Pixabay
Illustration shows different numbers with the pi sign the most obvious.— Pixabay

What national day is it today in the United States? It is a mathematical one! The date of Pi Day is a key factor in determining the success of the event.

Pi is only a number in and of itself, one of countless numbers between 3 and 4. What makes it renowned is that it’s built into every circle you see — circumference = pi times diameter — not to mention a range of other, unrelated situations in nature, from the bell curve distribution to general relativity.

The real reason for Pi Day is that despite being entirely abstract, mathematics turns out to be a very accurate description of our universe. 

The most compelling proof may come from mathematical constants, those uncommon numbers like pi that stand out from the crowd by turning up so regularly and unpredictably in equations and natural occurrences that mathematicians like to elevate them with unique names and symbols.

The vertical and horizontal measures of Mona Lisa’s face fit the Golden Ratio.— The Big Bang of Numbers, Manil Suri
The vertical and horizontal measures of Mona Lisa’s face fit the Golden Ratio.— The Big Bang of Numbers, Manil Suri

What other mathematical constants merit recognition, then? Here are some ideas by Manil Suri, Professor of Mathematics and Statistics, University of Maryland, Baltimore County, for starting to fill in the rest of the calendar.

The Golden Ratio

He suggests the Golden Ratio, phi, for January. If dividing the bigger quantity by the smaller quantity yields the same result as dividing the sum of the two values by the larger quantity, then two quantities are said to be in this ratio. Since there is no January 61, we might celebrate Phi on January 6 because it equals 1.618.

This ratio, which was first calculated by Euclid, became well-known thanks to Italian mathematician Luca Pacioli, who in 1509 published a treatise extravagantly praising its artistic qualities. Some people believe Leonardo da Vinci’s decision to incorporate it into the dimensions of the Mona Lisa’s features — who is credited with creating 60 sketches for this book — is what makes her so beautiful.

Mona Lisa Golden Ratio

In researching how rabbits reproduce, another Italian named Fibonacci had the first idea that phi occurs in nature. Every couple of rabbits produces another pair every month, according to a widely held conception of reproduction.

“Start with a single rabbit pair, and successive populations will then follow the sequence 1, 2, 4, 8, 16, 32, 64, 128, 256 and so on – that is, get multiplied by a monthly “growth ratio” of 2,” Suri wrote in his blogpost for The Conversation.

“What Fibonacci observed, though, was that rabbits spent the first cycle reaching sexual maturity and only began reproducing after that. A single pair now gives the new, slower progression 1, 1, 2, 3, 5, 8, 13, 21, 34… instead.”

This famous pattern, where each population turns out to be the sum of its two predecessors, is named after Fibonacci. 

Where is Phi to be seen though? Well, as you progress, you will see that each number is nearly 1.6 times the previous one.

The constant ‘e’

Another “blockbuster constant” is February. It is called Euler’s number e and the value 2.718… You can celebrate it next February 07.

While you can study what is up with this number and how it works later, here is some history.

The development of calculus in the late 17th century revolutionised human understanding of the cosmos. Arithmetic could now analyse everything that changed, expanding its scope to include the majority of natural occurrences.

Due to its iconic role in calculus, the constant e has gained notoriety. It turns out that e is the most logical growth factor for tracking change. As a result, it appears in laws that describe a variety of natural phenomena, including radioactive decay and population expansion.

Source link

Leave a Reply