The triangle is not right, its wrong.

The triangle is right. It's the nuts are nuts.

3-4-5 is a right triangle, not 2-3-4.

The intent was apparently to use nuts to represent edges, but he put them on points instead.

The artist's realization isn't even correct.

I believe you are responding to a joke.

I figured they remembered it was three consecutive numbers, but misremembered which three.

4-5-6 of course.

I still don't get it. The image is a 3-4-5 right triangle, which is mathematically fine. What do you mean by "nuts" and "points"?

The image in the article is of hazelnuts (I originally wrote "stones" then quickly edited it), and it's not a 3-4-5 triangle.

3-4-5 describes the length of each side - if you count the lengths of the triangle drawn in the image (the lines of chalk visible between the nuts on each side), it's only 2-3-4. To get 3-4-5 you're counting the number of nuts on each side, but those aren't lengths - those are the number of points marking the start/end of each unit length.

I see, I think you are referring to the unequal spacing of the nuts on each side, i.e. the side with 5 nuts has them closer together than the other sides.

I thought there was some point being made about the use of nuts vs. some other arbitrary item. Why does it matter they are hazelnuts and not something else?

No!

    X--X--X
    0  1  2

That diagram represents a length of 2, not a length of 3, see? Here's three:

    X--X--X--X
    0  1  2  3

It's not that the hazelnuts are somehow imperfectly laid out or are an imperfect representation. It's wrong in principle, not practice (I mean it's wrong in practice too but every representation is).

Thank you for literally explaining it to me like I was five, which apparently I am, I can’t believe I missed that.

You didn't miss it. You were focusing on the lattice edges, and PP was focusing on the lattice points. You're both right (except for PP's "No!" which should be "Yes!").

It doesn't. The entirety of my comment is that they're representing the wrong thing.

The artist meditated, he didn't realize.

(possible sarcasm detected ;)

(A 2-3-4 triangle is not a right triangle, no angle is 90º)

The triangle is right, but three nuts are left.

13 != 16

The piccie has nuts at unit lengths and the first line of the article after the very short intro is:

"The artwork references the idea of relating the lengths of the sides of a 3-4-5 right triangle ..."

How on earth did you get 2-3-4 for a right angled triangle! I blame booze, drugs, a late night or perhaps a standard issue: "off by one" (this is HN after all) ...

Whoops: "we see a 2-3-4 triangle" in the article

You can have a 2-3-4 right triangle if you can find the right axioms for it.