“Espresso.West” will tell you everything you need to know regarding this number, which is one of the most famous in mathematics.
What the article is regarding:
- What is Pi;
- The history of Pi: how scientists around the world have been searching for it for centuries;
- Why the number Pi is special and even considered mystical;
- Competition to memorize the number Pi, or piphilology.
What is the number Pi?
Pi is a mathematical constant used to describe a circle and circles. Its value is defined as the ratio of the length of the circle to its diameter. In other words, if you divide the length of any circle by its diameter, you will always get the same number, which is called Pi.
Pi is an irrational and infinite number. As everyone knows from school, its decimal system starts with 3.14, but then it also has a series of numbers that scientists around the world have been trying to figure out for years. By the way, this number got its name only in the 18th century, and before that it had many names. The notation for Pi was not chosen by chance. This is the Greek letter from which the Greek word “circle” begins.
The history of the number Pi, as scientists around the world have been searching for it for centuries
Photo: Wikipedia
The history of the study of Pi goes back several millennia. After all, this number was already known in ancient Egypt, Babylonia and India, but only as an approximate value. Ancient mathematicians used various methods to approximate this number, such as measuring the length of a circle and calculating its diameter. In ancient Egypt, it was believed that the number Pi is equal to 25/8, that is, approximately 3.125. By contrast, Babylon has 256/81, which is approximately 3.160. But the most accurate were the ancient Indians who wrote regarding this number as 339/108, i.e. 3.139.
But the first who actually tried to calculate the number Pi with the highest accuracy were the ancient Greek mathematicians. Archimedes was one of the first to approach the correct value of Pi, setting it between 3 1/7 and 3 10/71. He proposed a mathematical method for calculating the number Pi. For this, he inscribed in a circle and described regular polygons near it. Taking the diameter of the circle as a unit.
Astronomer and mathematician Ptolemy in his Almagest gives an even more accurate value of the number – 3.141. Subsequently, the Chinese mathematicians Liu Hui and Tsu Chongzhi improved the calculations and wrote more accurate numbers of Pi – 3.1415.
During the Middle Ages, the number Pi was calculated with an accuracy of no more than 10 digits. However, with the development of mathematical science during the Renaissance, it was possible to overcome this limit. For example, the 15th century Persian mathematician Jamshid al-Kashi calculated it to 16 decimal places. The first major European contribution since Archimedes in the 16th century was made by the German mathematician Ludolf van Zeilen, who spent ten years calculating a number with 20 decimal places.
At the beginning of the 18th century, the British John Machin was the first to calculate 100 decimal digits of a number. And in the 19th century, the Englishman William Shanks, following 15 years of work, calculated 707 signs. Johann Lambert was the first to prove that the number Pi is irrational, that is, infinite.
The famous physicist Isaac Newton also studied the number Pi, he once said:
“I am ashamed to say how many times I have done these calculations, doing nothing else all this time.”
Indeed, before the creation of the computer, calculations related to finding more and more accurate digits of Pi were a very slow and difficult task. Although in reality, physicists only need 39 digits of Pi to calculate the volume of the universe with precision to the size of a hydrogen atom. And mathematicians have even less – regarding 15 digits.
That is, finding more and more numbers of Pi has no practical significance for science, so it has become more of a hobby and mathematical competitions.
The world’s first programmable computer ENIAC took 70 hours in 1949 to calculate the 2037 digits of Pi. The computer was able to overcome the milestone of a million digits already in 1973. In 1995, 6.5 billion Pi numbers were obtained. At the beginning of the 21st century, computers have established a trillion numbers of Pi. One of the latest records was set in August 2021, when Swiss scientists calculated 62.8 trillion decimal places of this number using a supercomputer in 108 days and 9 hours.
As for the future, it is hard to imagine whether the complete number Pi will ever be found. After all, this is an irrational number, infinite, so finding all its digits is rather from the science fiction category, that the supercomputers of the future will be able to calculate all possible digits of Pi. But the further from the comma, the less practical value the additional signs of Pi have, so it does not make sense and is only a matter of sporting interest.
Why is the number Pi special and considered even mystical
Photo: Wikipedia
The number Pi has an iconic status due to its uniqueness and importance in mathematics, science and engineering. After all, it is a constant, like the speed of light, which is present at all levels of the universe, starting from atoms and ending with giant stars and the entire infinite universe. Therefore, Pi is also regarding the beauty of proportions created by nature, and man managed to see and solve it.
Here are a few reasons why this number is so important to science:
Circle geometry: Pi is defined as the ratio of the length of a circle to its diameter. This means that any formula or calculation involving circles or circles will involve the number Pi.
Analytical geometry: Pi appears in formulas describing geometric objects in space. For example, in the formulas for the volume of a sphere, the volume of a cylinder, as well as in various integrals and derivatives that model geometric objects.
Mathematical analysis: Pi is found in numerous formulas used to calculate limits, integrals, and derivatives, which in turn are important for analyzing functions and modeling various physical processes.
Physics: The number Pi is used in many physical equations, such as those for calculating the volume of a sphere, the area of a circle, and in formulas describing waves, electric and magnetic fields, atoms, and more.
Engineering: In many engineering disciplines, such as construction, mechanics, electrical engineering, and others, the Pi number is used to calculate various parameters and properties of objects.
Quantum physics and cosmology: In more modern scientific studies, such as quantum physics and cosmology, the number Pi also plays an important role, appearing in various equations describing the physical laws and properties of the universe.
On a cultural level, Pi is also somewhat of a magical, even mystical number. After all, first of all, it is infinite and irregular. Which already seems strange and mysterious. And, secondly, because of its direct relation to the circle, it has a symbolic connection with cyclicity, which evokes associations with the spiritual concepts of wholeness and repetition, which are present in all spiritual practices.
But the most interesting thing is that the number Pi is found in natural phenomena, such as the formation of waves in the ocean, the ratio between the volume of the body and its surface, as well as in various physical processes that can be talked regarding for a long time. These connections can create an impression of deep harmony in nature and even be mystical for someone who is prone to philosophical thoughts and likes to look for a “theory of everything”.
Photo: a frame from the 1997 movie “Pi”.
Probably the most famous example of popularization of the peculiarity of the number Pi is the feature film of the same name directed by Darren Aronofsky, which tells the story of a genius mathematician who tries to reveal the secrets of the number of this number. The film has an arthouse style and is known for its symbolic and philosophical aspects, including quotes.
“If we are made of spirals and live in a giant spiral, then everything we touch has a spiral,” says the main character of the tape, alluding to the number Pi.
By the way, an interesting fact is that Pi Day, March 13, coincides with the birthday of the famous scientist Albert Einstein.
Competition to memorize the number Pi, or piphilology
Because of its popularity and uniqueness, the idea of memorizing as many digits of Pi as possible has become popular among many people. This is called piphilology – the creation and use of mnemonic techniques to remember the many digits of the mathematical constant Pi.
As already mentioned, for mathematical calculations it is enough to know 10-15 decimal places of Pi — 3.141592653589793, so there is no practical use of this method. However, for mnemonists (people who remember a lot of things) who master the techniques of memorizing numbers, the number Pi is one of the training tasks for memory training.
There are special clubs in the world, the members of which compete to remember the greatest number of signs following the comma. On the Internet, you can find information that the Japanese mathematician Akiri Haraguchi allegedly reproduced 100,000 symbols of the number Pi. However, there is no official confirmation of this record. Instead, on the official website, which is engaged in the registration of such records specifiedthat the record belongs to the Indian Suresh Kumar Sharma, who in 2015 was able to reach the mark of 70,030 digits in 17 hours and 14 minutes.
So how do they do it? There are many different mnemonics. The simplest example is in the form of poems. When memorizing poems, each word of which has such a number of letters that reflect the next number Pi. But this is impractical when it comes to very large numbers.
Another popular method was developed in ancient times, which is called the “memory palace”. This is a method of association where you associate numbers with something you already know very well. For example, with your house. You know exactly where everything is and can walk through your home in your head, so this mnemonic teaches you to put numbers (which you associate with associations) in your memory in your house, in the “memory palace”. Then, relatively speaking, the books on the shelf have one number, the TV in the corner – another, and the color of the floor – yet another. That is, the essence of this method is that it is easier for people to remember not abstract things, but concrete things from life, when you associatively intertwine them and thus you can remember important things for you for a very long period of time.
For example, in order to remember the 100 signs of the number Pi, it is necessary to break the numerical series into two-digit numbers and translate them into word-images of the alphanumeric code, which are easy for you to remember personally, and have a special meaning for you thanks to some invented stories. And then place them in your “memory palace” where it is convenient for you to “walk” with your thoughts in order to reproduce a complete picture of 100 numbers.
