1 radian is the angle where the arc length equals its radiuspic.twitter.com/76mIudvdSg
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Is there a similar notion of "radian" for a sphere? .. Indeed!
Circle: We define the angle θ as the arc length over R
Sphere: We define the 𝒔𝒐𝒍𝒊𝒅 𝒂𝒏𝒈𝒍𝒆 Ω as the surface area of a patch on the sphere over R²
Solid angle Ω is measured in 𝒔𝒕𝒆𝒓𝒂𝒅𝒊𝒂𝒏𝒔pic.twitter.com/9ebVMZ8adY
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What about a triangular or circular area on the surface, aren't there multiple angles involved in any case?
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Doesn't matter here. The solid angle describes the fraction of the surface, like the angle describes the fraction of the circumference.
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So, I've always wondered that if u were to plot a point on a sphere for every degree, minute, second and then change the diameter, is that steradian or some other maths?
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Es momento de extender esto a n-dimensiones.
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Is this not well-known? Isn't solid angles part of high school curriculum? Heck, you can't even define candela without it.
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