Post History
#2: Post edited
by
zavier
·
2021-12-22T05:38:12Z (about 3 years ago)
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?
#1: Initial revision
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?