I have a line, of x length. I want to have a semicircle with that length. How can I know the max and min radius I can have with that line?
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What makes you think there is more than one possible radius? Do you not know a formula for the circumference of a (semi-)circle? And your title makes no sense to me at all. – Ted Shifrin Apr 01 '21 at 19:21
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It is nice to meet you.
Seeing as the perimeter of a semicircle=P=P(semicircle)+P(base)=$\frac{2πr}{2}+2r$:
This can be simplified down to P=πr+2r=r(π+2). Because the perimeter, or length, of the semicircle to be the same length as a line of length x, the following is needed:
P=r(π+2)=x⇔$r=\frac{x}{π+2}$.
Please correct me if I am wrong.
Here is an article found after this answer was posted: https://socratic.org/questions/what-is-the-formula-for-the-radius-of-a-semi-circle.
The max radius is the min radius in flat euclidean space, but if there was a transformation in the space, perhaps a linear transformation or a hyperbolic space was introduced, this could deform the semicircle just as a line is deformed in a line integral over another surface.
However, that is not an area of study that I am used to.
Example?: Construction of Hyperbolic Circles With a Given Radius
Тyma Gaidash
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Thanks for your answer. My question was about just the arc of the semicircle (without the base). So in this case I used just r = x/pi. – kevin parra Apr 01 '21 at 19:28
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@kevinparra . Good luck in your journey for math. I hope you have good luck in the site. I also added a bit to the answer. – Тyma Gaidash Apr 01 '21 at 19:32
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