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- In the past, ancient geometers dedicated a significant amount of time in an effort to “square the circle.” This was a process that involved attempting to construct a square with the same area as a given circle within a finite number of steps while only using a compass and straightedge. While it is now known that this is impossible, it was not until 1880 that Ferdinand von Lindemann presented a proof that π is transcendental, which put an end to all efforts to “square the circle.” While the efforts of ancient geometers to accomplish something that is now known as impossible may now seem comical or futile, it is thanks to people like these that so many mathematical concepts are well defined today. - Source: Internet
- A circle, geometrically, is a simple closed shape. More specifically, it is a set of all points in a plane that are equidistant from a given point, called the center. It can also be defined as a curve traced by a point where the distance from a given point remains constant as the point moves. - Source: Internet
- The radius, diameter, and circumference of a circle are all related through the mathematical constant π, or pi, which is the ratio of a circle’s circumference to its diameter. The value of π is approximately 3.14159. π is an irrational number meaning that it cannot be expressed exactly as a fraction (though it is often approximated as ) and its decimal representation never ends or has a permanent repeating pattern. It is also a transcendental number, meaning that it is not the root of any non-zero polynomial that has rational coefficients. - Source: Internet
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