Understanding Why C/d = pi is a Constant

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The discussion centers on why the ratio of the circumference (C) to the diameter (d) of a circle is a constant, represented by π (approximately 3.14). The proof involves geometric principles, particularly similar triangles, which demonstrate that this ratio holds true in Euclidean geometry. However, it is noted that this relationship does not apply in spherical geometry, where the ratio can vary. The conversation highlights the foundational role of Euclidean assumptions in establishing the constancy of C/d. Understanding these geometric principles is essential for grasping why π remains a constant in flat geometrical contexts.
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Lets say that "d" is diametr of a circly,and C is the perimetr(length).
Why C/d = pi (3.14) is a constant?? I know the proof of archimides with poligons,from which found the value of pi,but how we know that C/d is always equal with a constant that we named as π=3.14;

Thanks !
 
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I found it guys. The proof use similar triangles etc...
Thanks for your time !
 
Hepic said:
I found it guys. The proof use similar triangles etc...
Thanks for your time !

This also requires assumptions of Euclidean geometry. In spherical geometry it is not constant.
 
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