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JamesU
Gold Member
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Pi is said to be discovered by ancients, but if even we don't know the EXACT number of pi, how could they, or was theirs just a close estimate of pi?
If you accept a definition of similarity in terms of scaling :Manchot said:How would one prove precisely (using geometry) that all circles are similar? The only way that I can think of is to imagine a circle as a regular polygon with an infinite number of sides. Since it's easy to prove that any two n-sided regular polygons are similar, it should therefore extend to circles. However, this isn't very rigorous. Anyone know of a way to prove it rigorously using classical geometry?
Pi is a mathematical constant that represents the ratio of a circle's circumference to its diameter. It is approximately equal to 3.14159 and is used in many mathematical and scientific calculations involving circles and spheres.
The concept of Pi has been studied and used by many ancient civilizations, including the Egyptians, Babylonians, and Chinese. However, the first known calculation of Pi as 3.1416 was done by the ancient Greek mathematician Archimedes around 250 BC.
The ancients discovered Pi through various methods, including measuring the circumference and diameter of circles, inscribing polygons inside circles, and using geometric constructions. They also used approximations and ratios to calculate Pi.
The accuracy of the ancients' calculations of Pi varied depending on the method and tools they used. The ancient Egyptians were able to calculate Pi with an accuracy of up to 3.16, while the ancient Chinese had an accuracy of up to 3.125. The most accurate calculation of Pi by the ancients was done by Archimedes, who was able to approximate it to 3.1416, which is accurate to four decimal places.
Pi is used in many modern scientific and technological applications, including engineering, physics, and astronomy. It is also used in computer science for calculations involving circles and spheres. Pi has also been used to test the accuracy of supercomputers and to break records for calculating the most digits of Pi.