Help on 3D Pythagorean Theorem

Ok so I know how to use a 3d pythaergous therom in shapes but in ina graph it makes no sense. Please help

What do you mean? It makes sense everywhere because it’s a proven mathematical theorem.

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…do you mean Pythagoras’ theorem?

Most people are familiar with the traditional 2D Pythagorean theorem, which states that for any right triangle where a and b represent the legs and c represents the hypotenuse, the equivalence a² + b² = c² holds true. This allows us to determine any of the triangle’s side lengths if the other two are known.

The 2D Pythagorean theorem can be applied twice to calculate the longest diagonal inside a rectangular prism. If the base of the prism has dimensions x and y, and the diagonal along the base is represented by c, then x² + y² = c². The longest diagonal in the solid, s, is the hypotenuse of the triangle formed by the sides c and the height of the solid, z. So we know that, c² + z² = s². From this you can see that it is possible to find the longest diagonal inside a rectangular prism using the 2D version of the theorem alone, but we can skip a step by using a slightly different equation.

There is a 3D analog to the Pythagorean Theorem that is both intuitive and useful. If we are attempting to calculate the longest diagonal that can fit inside a rectangular prism or cube we use the 3D Pythagorean Theorem. If the side lengths of the rectangular prism are x, y, and z, and the diagonal line connecting opposite corners of the rectangular prism is s, then the equivalence holds where x² + y² + z² = s²


Yes thats the part i get in 3d but I dot get how to use it in a graph

yes thats what i mean but in 3d

What you’re looking for is space-diagonals, the question is; why would anyone use it in graphs…? :thinking:

I mean 2d graphs have length and height. If you want to apply space-diagonals, you require another axis, which is depth.

For ‘3d’ graphs
It is quite simple, simply draw out points and add vectors with directions. I used a site named calcPlot3D to make this image

The basic idea to Pythagoras theorem is to find the hypotenuse from the magnitude of vectors. The general usage of it in graphs is to draw a line between two set points.
However, when using space diagonals in a 3D graph, you are playing with three points. If you understand the idea of space-diagonals, you most likely know how to apply it in graphs because as I previously stated. If it is a three-dimensional graph, it has three axis, thus in future calculations, just take depth into account and you’ll be fine.

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In a graph, just get the distance between two points to get the length of a side. For example, in @jody7777 's example, to get s, you could just get the distance between the endpoints of it.