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alexk307
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Who is pi derived, and what exactly is pi.
NoMoreExams said:I have a feeling if people used google and wikipedia, half the questions would disappear :) Check this out: http://en.wikipedia.org/wiki/Pi
Doodle Bob said:1. It shouldn't be taken on faith that this is a well-defined concept. After all, such a constant doesn't necessarily exist in other geometries: why is it that this ratio is the same for all circles on the Euclidean plane?
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I personally like the definition of pi to simply be the area of the unit circle.
I don't really see why those are issues. Wikipedia is not a math textbook and should therefore not adhere to the same standards. Under definition, it defines pi as,Doodle Bob said:Actually, that wikipedia article leaves out some mathematically crucial aspects to the so-called "definition" of pi being the ratio of the circumference of the circle to its diameter.
1. It shouldn't be taken on faith that this is a well-defined concept. After all, such a constant doesn't necessarily exist in other geometries: why is it that this ratio is the same for all circles on the Euclidean plane?
2. Why does the same constant show up in both the circumference and area formulas for circles in the Euclidean plane? In fact, it is possible to use the formula of circumference/area to prove the formula of area/circumference.
I personally like the definition of pi to simply be the area of the unit circle.
// C example
double pi=atan(1.0) * 4.0;
Pi is a mathematical constant that represents the ratio of a circle's circumference to its diameter. It is approximately equal to 3.14.
The ancient Greek mathematician Archimedes is credited with first deriving the value of pi around 250 BC. However, the concept of pi was known to several ancient civilizations, including the Egyptians and Babylonians.
Pi is an irrational number, meaning it cannot be expressed as a simple fraction. It is typically calculated using geometric methods, such as measuring the circumference and diameter of a circle, or using infinite series formulas.
Pi is a fundamental constant in mathematics and has many important applications, particularly in geometry, trigonometry, and calculus. It is also used in various scientific and engineering fields, such as physics, engineering, and astronomy.
Pi is used in a wide range of real-world applications, including the design and construction of buildings, bridges, and other structures. It is also used in navigation, satellite technology, and computer graphics.