Blogging Community Archimedes Discovery of Pi - Technologies In Industry 4.0

Archimedes Discovery of Pi

Introduction

Greek Mathematician Archimedes’s discovery of Pi is the largest fraction known to humans. The number π (spelled as “pi”) is a mathematical constant – approximately equal to 3.14159.

It is defined as the ratio of a circle’s circumference to its diameter & is also called Archimedes constant.

The π cannot be expressed as a common fraction & its decimal representation has not been found by supercomputers & goes on into trillions of numbers after 3.14 & never ends.

Ancient civilizations including Egyptians & Babylonians required fairly accurate approximations of π for practical computations. In 250 BC Greek mathematician, Archimedes created an algorithm to approximate π with reasonable accuracy to 7 digits.

In this article, we will discuss the history and importance of Pi. Also, describe the Deep learning prediction of the digits of Pi.

Archimedes Discovery of Pi

Description

Archimedes (287-212 BCE) was a pioneer in the fields of mathematician and mechanical engineering. He is greatest recognized for formulating Archimedes’ Principle. That is well-known as the law of buoyancy. Similarly, he observed a lot of other laws of physics. He logged his observations as mathematical theorems.

Archimedes reaches the logical decision that the ratio of a circle’s circumference to its diameter is greater than 3 1/7 but less than 3 10/71. This is a very good estimate in his work on the measurement of the Circle. That is known as the mathematical constant we today call “pi” (π).

History of Pi (π)

  • Pi (π) has been recognized for almost 4000 years.
  • The prehistoric Babylonians calculated the area of a circle by taking 3 times the square of its radius that presented a value of pi = 3.
  • One Babylonian tablet shows a value of 3.125 for π that is a nearer approximation.
  • The Egyptians considered the area of a circle by a formula that provided the estimated value of 3.1605 for π.
  • The first calculation of π was completed by Archimedes of Syracuse.
  • Archimedes approached the area of a circle by using the Pythagorean Theorem.
  • That was used to discover the areas of two regular polygons.
  • The polygon carved inside the circle and the polygon in which the circle was circumscribed.
  • In the meantime, the definite area of the circle lies between the areas of the inscribed and circumscribed polygons.
  • The areas of the polygons provided upper and lower bounds to the area of the circle.
  • Archimedes distinguished that he had not found the value of π then only an estimate inside those limits.
  • Archimedes presented that π is between 3 1/7 and 3 10/71 like this.

Importance of Pi

  • The number Pi or π is one of the most significant numbers in our universe. Discover humankind’s journey—efforts all over the ages that really transcend cultures—to calculate, imprecise, and realize this mysterious number.
  • It is an essential concept that seems in all features of mathematics.
  • Pi is a vital concept that benefits from knowing the universal truths and some mathematical concepts.
  • Generally, pi values are used in concepts such as trigonometry, geometry, and advanced concepts like probability, statistics, and complex numbers.
  • Pi is a well-identified mathematical constant used all over the world.
  • In early times it is used as a top-secret code for certain confidential works.
  • Later, a circle containing 3600 and π is used to denote the 3600 of a circle.
  • It is mentioned as a circular constant.

Deep learning prediction of the digits of Pi

  • An adequately big neural network can easily mimic one of the several algorithms for producing the digits of π.
  • It’ll require to be big enough to put up the necessary logic and memory for variables.
  • Though, there’s nothing essentially unpredictable about those digits.
  • They are without a glitch computable, with really pretty short computer programs.
  • There’s no motive to attempt this, actually.
  • There’s no aim to imagine any deep revelation from a neural network that learned to compute the digits of π.
  • It can be exciting from the viewpoint of studying the easy-to-read power of Neural Networks, and the quantity of information required to train for a short algorithm.
  • Neural Networks aren’t a fit algorithmic paradigm for this kind of computation.
  • However, there’s no object to suppose this to be aware or valuable from a mathematical perspective.