Mainstream "math" education is misguided and causes life-long misunderstanding & learning trauma.
The term "diameter" in Greek, διάμετρος (diámetros), essentially means "through measure," which is a very intuitive way to describe the function of the diameter in a circle.
By measuring the distance across the circle through its center, the diameter becomes a key element in determining the circle's properties. Specifically, when you compare the circumference (c) of a circle to its diameter (d), the ratio of the two gives the mathematical constant π (Pi).
This ratio, denoted as c/d = π, is a fundamental property of all circles, regardless of size. The value of π is approximately 3.14159, but it is an irrational number, meaning it cannot be expressed as a simple fraction and its decimal expansion never repeats.
So, the diameter is not only a geometric concept but also directly tied to one of the most important constants in mathematics!
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https://www.academia.edu/126646580/Le...
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Learn about the Gabriel Polynomial (GP) which is a very advanced concept not possible using mainstream derivative or integral definitions. The GP is always a closed form polynomial and has no Error term:
https://www.academia.edu/45229087/The...
Discover closed -form trigonometric functions never realised before:
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