find "a" so that pink and purple have the same area | Mathematics | Page 1

exotic flower Sep 16, 2024, 11:44 PM

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assume radius is 1, conjured up this problem while cutting a slice of pizza, i haven't gotten too close to solving it

oblique deltaBOT Sep 16, 2024, 11:44 PM

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south crater Sep 17, 2024, 12:01 AM

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exotic flower assume radius is 1, conjured up this problem while cutting a slice of pizza, i h...

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You can compute the purple area by computing the red area of my picture as well as the section of the disk that's purple + triangle (which is just some fraction of π)

exotic flower Sep 17, 2024, 12:10 AM

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my issue then is how to find that section of the circle without knowing the angle measure is.
you'd have to work out where that point is which has been weirdly challenging

ashen mauve Sep 17, 2024, 3:51 AM

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What exactly is a in this case?

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Like the x value?

ashen mauve Sep 17, 2024, 4:57 AM

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Btw the total area is
pi/4-(1/2)arcsin(1/2)

ashen mauve Sep 17, 2024, 5:58 AM

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After many eons I think I finally fixed all my mistakes.

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Also if you want a value more exact than 1 trillionth of a percent you can set the bottom 2 values equal

ashen mauve Sep 17, 2024, 2:02 PM

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ashen mauve Btw the total area is pi/4-(1/2)arcsin(1/2)

This is equal to pi/6
And the last line in the picture is equal to pi/12

ashen mauve Sep 17, 2024, 3:48 PM

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Since you might not know calculus I simplified it to this

exotic flower Sep 18, 2024, 1:50 AM

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dude, where did this come from, curious
this is some cleo shit

ashen mauve Sep 18, 2024, 4:26 AM

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Its kinda a pain to explain what I did but I used calculus

#find "a" so that pink and purple have the same area