Review Suggested Edit

You can't approve or reject suggested edits because you haven't yet earned the Edit Posts ability.

Is Pythagorean theorem really valid in higher dimensional space?

I saw that someone was writing Pythagorean theorem in 3 dimensional space. The equation was :
$$c=\sqrt{x^2+y^2+z^2}$$
If it's really correct than Pythagorean should work in higher dimensional space either. So I can write that
~~$$c=\sqrt{\sum_{n=0}^nn^2}$$~~
At first I was thinking how right triangle should look like in 3 dimensional space. From my imagination, the triangle will look like a pyramid but all sides of that pyramid will be looking like right triangle that's how Pythagorean works in 3 dimension. It's impossible to imagine the shape in 4 dimension or higher dimension.
Is Pythagorean theorem really valid in higher dimensional space?

I saw that someone was writing Pythagorean theorem in 3 dimensional space. The equation was :
$$c=\sqrt{x^2+y^2+z^2}$$
If it's really correct than Pythagorean should work in higher dimensional space either. So I can write that
$$c=\sqrt{\sum_{n=0}^N x_n^2}$$
At first I was thinking how right triangle should look like in 3 dimensional space. From my imagination, the triangle will look like a pyramid but all sides of that pyramid will be looking like right triangle that's how Pythagorean works in 3 dimension. It's impossible to imagine the shape in 4 dimension or higher dimension.
Is Pythagorean theorem really valid in higher dimensional space?

pythagoras right-triangle