Understanding Why C/d = pi is a Constant

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SUMMARY

The ratio of the circumference (C) to the diameter (d) of a circle is always equal to the constant π (approximately 3.14) due to the properties of Euclidean geometry. This relationship holds true regardless of the circle's size and is proven through methods such as Archimedes' polygon approximation and the use of similar triangles. However, it is important to note that this ratio does not remain constant in non-Euclidean geometries, such as spherical geometry.

PREREQUISITES
  • Understanding of Euclidean geometry principles
  • Familiarity with the concept of circumference and diameter
  • Knowledge of Archimedes' polygon approximation method
  • Basic grasp of similar triangles and their properties
NEXT STEPS
  • Study the proof of Archimedes' approximation of π using polygons
  • Explore the properties of similar triangles in geometry
  • Investigate the differences between Euclidean and non-Euclidean geometries
  • Learn about the applications of π in various mathematical contexts
USEFUL FOR

Mathematicians, geometry students, educators, and anyone interested in the foundational concepts of circles and the significance of π in mathematics.

Hepic
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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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