How to write equilateral function ?

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Hamza 2023-2-12

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https://ww2.mathworks.cn/matlabcentral/answers/1911305-how-to-write-equilateral-function

评论： ghania gigi 2023-2-14

Write the function in Matlab equilateral, which takes two different points x,y ∈ R N, N > 1, and returns one point z ∈ R N such that (x,y,z) are the vertices of an equilateral triangle, that is, the point z must satisfy ||x−z|| = ||y−z|| = ||x−y||

thanks in advance

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John D'Errico 2023-2-13

@ghania gigi If we give you the code when you are perfectly capable of doing it yourself, then we are doing what is clearly a homework assignment for you.

@Walter Roberson - Given only two points, it is not possible to find a UNIQUE equliateral triangle in more than 2 dimensions, so your comment is not correct here. Said differently, there would be infinitely many such equilateral triangles. And that is clearly not the question at hand, so you can assume the 2-d case.

But again for @ghania gigi, What is the height of the triangle? You are almost there. I'll recap what you have done so far. Given two points, x and y, the midpoint is:

midpoint = (x + y) / 2;

That formula works for vectors too.

The length of one of the sides is the distance between those points. abs(x-y) does not quite work, since x and y are vectors that live in a 2-dimensional space. But this does work:

edgelength = norm(x-y);

I'll give you that much.

But now I'll repeat my question. If the edge has length 1, then what would the height be? This is basic geometry. The Pythagorean theorem would suffice. Or basic trig will do it too. But you need to make some effort!