Is there some explanation for this phenomenon?

#Geometry

Note by A Former Brilliant Member
1 year ago

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Comments

If I had to guess, it involves the area of a circle and triangle... @Hamza Anushath

A=πr2A = \pi r^2 and A=A = bh2\frac{bh}{2} or A=A = 12\frac{1}{2} absinCabsinC

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I made this animation up by myself too @Yajat Shamji!

What I meant was, is there any relationship between the area of the triangle and the area of the circle?

If we assume the circle to be a unit circle and let the variable angle α\alpha here, then the height of the triangle will be sin(α)\sin{(\alpha)}.

\[\begin{align} A &= \dfrac{1}{2}bh \\ &= \dfrac{1}{2}(1)(\sin{(\alpha)})

\\ &= \boxed{\dfrac{1}{2}\sin{(\alpha)}} \end{align}\]

Mahdi Raza - 1 year ago

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Excuse me @Mahdi Raza, what do you assume as the triangle? The triangle with the right angle, or the triangle without the right angle?

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I believe it's the triangle without the right angle...

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@A Former Brilliant Member If that is so, then thanks @Mahdi Raza!

@A Former Brilliant Member Yeah, it is the other triangle. You're welcome

Mahdi Raza - 1 year ago
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