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LFCFAN
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Homework Statement
How to find area of an n-dimensional triangle using vectors?
First, what do you mean by the area of such an object? Do you mean its n-dimensional volume?LFCFAN said:Homework Statement
How to find area of an n-dimensional triangle using vectors?
Homework Equations
The Attempt at a Solution
LFCFAN said:Find the area of the triangle with sides
A = (a1 ... an)
B = (b1 ... bn)
and A-B = (a1-b1 ... an-bn)
I don't even know where to start. I know how to do it in 3D with the cross product, but that obviously won't work for higher dimensions.
So I need help generalizing for Rn.
LFCFAN said:I've literally typed out the question as it has been given.
I think take it as a standard triangle in n-dim space
LFCFAN said:A = {2,1,2,4}
B = {4,1,6,2}
angle = arccos( (A.B)/(norm(A)*norm(B)) )
area = (1/2)A.B sin(angle)
Is this correct? if yes, it is easy to generalize for Rn.
An n-dimensional triangle is a geometric shape that exists in n-dimensional space. In simpler terms, it is a triangle that exists in a space with more than three dimensions, such as four-dimensional or five-dimensional space.
The formula for calculating the area of an n-dimensional triangle is (n-1)/n * base * height. The base and height are measured in the same unit as the dimension of the space (e.g. meters for a three-dimensional triangle).
No, the area of an n-dimensional triangle cannot be negative. It represents the amount of space within the triangle, and space cannot have a negative value.
No, an n-dimensional triangle can exist with sides of varying lengths. However, in certain dimensions, such as two or three dimensions, an equilateral triangle (all sides equal) is the only possible shape.
Yes, n-dimensional triangles have applications in fields such as computer graphics, physics, and mathematics. They are used to model and understand complex systems and phenomena that exist in higher dimensions.