Can /sci solve this tusk. We have cube and 4 points in edjes.

>>9001299
Get a bucket full of water, dunk green part of cube, measure spilled water, ???, profit

You can calculate a triple integral.

>>9001300
Good, but solution must be based on mathematics.

>>9001307
Can you get any example?

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>>9001308

>>9001304

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bump

>>9001307
Get a bucket full of water and set said bucket on top of math book, dunk green part of cube, measure spilled water, ???, profit

>>9001299

Use the volume formula, divide the result by three.

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(l*w*h)/2

>>9001299
>Volume of green area
Trick question

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Tusk too difficult. Four points have no common plane.

>>9001299
Just integrate 1 over the volume three times

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>>9001509
you are right

>>9001529
min one point always in top min one always in bottom? wtf does this mean?

>>9001509
You can alway take the convex hull. Nobody said that the green shape has 6 sides rather than 7.

>>9001509
>>9001529
No one said the sectional cut is planar.

>>9001535
One point in top corner of cube another in bottom corner of cube, other always in edges but height might be different.

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apply to 3d

>>9001299

Can we take it that the 3 lower points form a horizontal triangular plane, and that this connects to a second triangular plane made by the top corner and the 2 closer points?

Are the lower points at unspecified heights, or are they halfway up?

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>>9001299
I'm assuming [math]d\leq c\leq b\leq a\leq 1[/math]
I started working on a formula for volume in terms of a,b,c and d but it's really really fucking tedious and I can't be arsed. There are multiple formulae which depend on how many variables are equal to each other.

It's more straightforward to calculate the volumes of four tetrahedra and then subtract the overlaps (intersections).

>>9003035
That's got to be a harder way to do this... Actually there isn't.

>>9001299
0, you only shaded the faces of the cube :^)

>>9001299
7

>>9003035
good job, tnx

>>9003035
this is wrong though

Your question isn't clear enough since it is impossible to deduce your actual indication by the term "green area" led by your artistic implication of a cube. I assume that the 4 points are co-planar, and if I am correct, then the valoume should be (a2x) m3 where a is the length of a side of the cube and x is the height from base to the plane held by the 4 assumed co-planar points you "tried" to indicate.

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>>9003597
X is actually the height of the plane from top. Now# the third point is not on a plane rather it is on a vertex keeping rest three points oon a plane, then I "think" that the volume would be half of ax2+a quarter of ax2. I wouldn't insist that I am correct and hence I welcome any counter propositions.

>>9003120
>>9003543
>>9003569
i'm coming back to retract my "add up the tetrahedra" approach

there's a region in the middle of the cube that's clearly inside the region of interest but not inside any of the tetrahedra
it should have been obvious when i was drawing the diagram, but i am an idiot

>>9004089
Is my approach even borderline "correct"?
>>9003641
*Pretentious use of words doesn't give me the feeling of being correct. It just feels to me dude :)*

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>>9003143
/thread