# OpenAI Chat GPT3 meets Euler’s polyhedron formula.  It goes poorly.

The new OpenAI chatbot is fun to mess around with.  (You can sign up for a free account here.)  But is it smart?

I asked it an easy math question, based on Euler’s polyhedron formula.  Euler discovered that the number of edges of a polyhedron is equal to the number of faces plus the number of vertices minus 2:  E = F + V – 2.  So, for a cube, the number of faces is 6, the number of vertices or corners is 8, and the number of edges is 12, which is 8 + 6 – 2.

I asked it the following question:

If a three dimensional polygon has nine sides and nine vertices, how many edges does it have?  How do you know?

You can check that the answer is indeed E = 9 + 9 – 2 = 16 by picturing a cube with a pyramid on top and counting the edges, vertices, and faces.  Go Euler!

The first time I asked this question, I got back the following (all bold is mine):

A three-dimentional polygon with nine sides and nine vertices is called a nonagon.  A nonagon has 12 edges.

To determine the number of edges in a polygon, you can use the formula:

E = V – F + 2

Where E is the number of edges, V is the number of vertices, and F is the number of faces.

In the case of a nonagon, V = 9 and F = 9, so the formula becomes:

E = 9 – 9 + 2 = 2.

Thus, a nonagon has 2 edges.

So, it gave two different wrong answers (12 and 2) without noticing it contradicted itself, and it gave the wrong formula.  And because the chatbot has no common sense, it does not realize that it is wacky to think that a polygon with 9 faces and 9 vertices has 2 edges.

Since we’re all human, I decided to give it another chance.  Same question, different response:

A three dimensional polygon with nine sides and nine vertices is known as a polyhedron.  A polyhedron has a certain number of faces, vertices, and edges.  In this case the polyhedron has nine faces, nine vertices, and 18 edges.

To determine the number of edges, we can use Euler’s formula, which states that for a polyhedron with F faces, V vertices, and E edges, the relationship between these three quantities is given by:  E = V + F – 2.

Plugging in the values for this particular polyhedron, we get:  E = 9 + 9 – 2 = 18.

Hoo boy.  At least it found the right formula.

Third try, maybe the charm?

A three-dimensional polygon with nine sides and nine vertices is called a nonagon. A nonagon is a polyhedron, which is a three-dimensional shape with flat faces and straight edges. The number of edges in a polyhedron is equal to the sum of the number of faces and the number of vertices, minus the number of corners.

To find the number of edges in a nonagon, you would use the formula:

E = F + V – C

Where E is the number of edges, F is the number of faces, V is the number of vertices, and C is the number of corners.

In this case, we know that the nonagon has 9 faces, 9 vertices, and 9 corners.

Plugging these values into the formula, we get:

E = 9 + 9 – 9 = 9

So a nonagon has 9 edges.

The good news is that 9 + 9 – 9 does indeed equal 9.  The bad news is that corners are the same as vertices, and the formula is just wrong.

The upshot seems clear:  all you young Angry Bear readers out there, do not use chatbot to cheat on your math homework.