# PI THE MATHEMATICAL CONSTANT

9 de Feb de 2021
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### PI THE MATHEMATICAL CONSTANT

• 1. INTRO TO π  Pi (π) is the 16th letter of the Greek alphabet, and is used to represent the most widely known mathematical constant.  Pi is the ratio of the circumference of a circle to its diameter. In other words, pi equals the circumference divided by the diameter (π = c/d). Conversely, the
• 2. 𝐶𝐼𝑅𝐶𝑈𝑀𝐹𝐸𝑅𝐸𝑁𝐶𝐸 𝐷𝐼𝐴𝑀𝐸𝑇𝐸𝑅 π =  π is commonly defined as the ratio of a circle’s circumference C to its diameter D. The ratio C/D is constant ,regardless of the circle’s size. For example, if a circle has
• 3. WHAT TYPE OF A NUMBER π IS?  π is an irritational number, meaning that it can not be written as the ratio of two integers such as 22/7 or other fractions that are commonly used to approximate.  When starting off in math, students are introduced to pi as a value of 3.14 or
• 4. The notation of π The first to use the symbol of pi (π) with its current meaning was William Jones in 1706.  Leonhard Euler adopted the symbol of pi (π) in 1737 and it soon became a standard .It is widely believed that the great Swiss-born mathematician Leonhard Euler (1707-83) introduced the symbol π into common use. WILLIAM JONES LEONHARD EULER
• 5. How was π developed The ancient Babylonians calculated the area of a circle by taking 3 times the square of its radius, which gave a value of pi = 3.14 .  The first calculation of π was done by Archimedes of Syracuse (287–212 BC), one of the greatest mathematicians of the ancient world.  Around 250 BC the Greek mathematician Archimedes created an algorithm to approximate π with arbitrary accuracy.
• 6. Archimedes method to find an approximation ofπ  Archimedes' method finds an approximation of pi by determining the length of the perimeter of a polygon inscribed within a circle and the perimeter of a polygon circumscribed outside a circle .  By doubling the number of sides of the hexagon to a 12-sided polygon, then a 24-sided polygon, and finally 48- and 96-sided polygons, Archimedes was able to MONTE CARLO
• 7.  Archimedes found that if they drew circles in polygons and calculated the inner and outer polygon’s perimeters and calculated the value that estimates that the pi was 3.1419… econd major advancement in understanding pi came with the develop calculus .
• 8. Newton’s approximation of π In 1665, English mathematician and physicist Isaac Newton used infinite series to compute pi to 15 digits using calculus he and German mathematician Gottfried Wilhelm discovered. ISAAC NEWTON GOTTFRIEDWILHEM
• 9. PI WAS DEVELOPED NOT made !  In 1704 John Machin developed a converging series that calculated up to 100 decimal places. By the year 1949 digital computers were invented and could calculate 100’s of decimal places of pi in hours. In 1949 John Von Nuemann calculated 2037 digits of pi
• 10. pi (π) in the professions  Agricultural professionals may use π to determine the area covered by a pivot irrigation system or storage facility . They would use the formula of- 𝐴𝑟𝑒𝑎 = 𝜋𝑟2 Architect and construction works would both use the formula for the area extensively. The also use the formula of the volume extensively to fill columns of concrete and to know the space a building would take up. They would use the formula of- 𝑉𝑜𝑙𝑢𝑚𝑒 = π𝑟2 h
• 11. Uses of pi (π)  Electrical engineers use it for solving problems of electrical applications .  Statisticians use it to track population dynamics.  Clock designers use it when designing pendulums for the clocks .  Aircraft designers use it to calculate areas of the skin of the aircraft .  Medicine benefits from it when studying the structure of our eyes.  Bio chemists see it when trying to
• 12. π fun facts The current Guinness world record is held by Lu Chao of China in 2005 who recited 67,890 digits of π in 70 hours.  July 22 is π approximation day also known as casual pi day ,the day is dedicated to the mathematical constant π.