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This conjecture is a generalization of A theorem for cubic-A generalization of Carnot theorem, in MSE question. I'm an electrical engineer, I am not a mathematician. I don't know how to prove this result.

Let $A_1A_2....A_n$ be a n-gons, Let $m$ points $B_{ij}$ lie on $A_iA_{i+1}$ for j=1, 2,...., m. Then $m.n$ points $B_{ij}$ for $i=1, 2, 3,...., n$ and $j=1, 2,...., m$ lie on a curve of degree $m$ if only if:

$$\prod_{i=1}^n \prod_{j=1}^m \frac{\overline{B_{ij}A_i}}{\overline{B_{ij}A_{i+1}}}=1$$

Note that: $A_{m+1}=A_1$

This conjecture is a generalization of A theorem for cubic-A generalization of Carnot theorem, in MSE question. I'm an electrical engineer, I am not a mathematician. I don't know how to prove this result.

Let $A_1A_2....A_n$ be a n-gons, Let $m$ points $B_{ij}$ lie on $A_iA_{i+1}$ for j=1, 2,...., m. Then $m.n$ points $B_{ij}$ for $i=1, 2, 3,...., n$ and $j=1, 2,...., m$ lie on a curve of degree $m$ if only if:

$$\prod_{i=1}^n \prod_{j=1}^m \frac{\overline{B_{ij}A_i}}{\overline{B_{ij}A_{i+1}}}=1$$

Note that: $A_{m+1}=A_1$

This conjecture is a generalization of A theorem for cubic-A generalization of Carnot theorem, in MSE question. I'm an electrical engineer, I am not a mathematician. I don't know how to prove this result.

Let $A_1A_2....A_n$ be a n-gons, Let $m$ points $B_{ij}$ lie on $A_iA_{i+1}$ for j=1, 2,...., m. Then $m.n$ points $B_{ij}$ for $i=1, 2, 3,...., n$ and $j=1, 2,...., m$ lie on a curve of degree $n$ if only if:

$$\prod_{i=1}^n \prod_{j=1}^m \frac{\overline{B_{ij}A_i}}{\overline{B_{ij}A_{i+1}}}=1$$

Note that: $A_{m+1}=A_1$

This conjecture is a generalization of A theorem for cubic-A generalization of Carnot theorem, in MSE question. I'm an electrical engineer, I am not a mathematician. I don't know how to prove this result.

Let $A_1A_2....A_n$ be a n-gons, Let $m$ points $B_{ij}$ lie on $A_iA_{i+1}$ for j=1, 2,...., m. Then $m.n$ points $B_{ij}$ for $i=1, 2, 3,...., n$ and $j=1, 2,...., m$ lie on a curve of degree $m$ if only if:

$$\prod_{i=1}^n \prod_{j=1}^m \frac{\overline{B_{ij}A_i}}{\overline{B_{ij}A_{i+1}}}=1$$

Note that: $A_{m+1}=A_1$

This conjecture is a generalization of A theorem for cubic-A generalization of Carnot theorem, in MSE question. I'm an electrical engineer, I am not a mathematician. I don't know how to prove this result.

Let $A_1A_2....A_n$ be a n-gons, Let $m$ points $B_{ij}$ lie on $A_iA_{i+1}$ for j=1, 2,...., m. Then $m.n$ points $B_{ij}$ for $i=1, 2, 3,...., n$ and $j=1, 2,...., m$ lie on a curve of degree $n$ if only if:

$$\prod_{i=1}^n \prod_{j=1}^m \frac{\overline{B_{ij}A_i}}{\overline{B_{ij}A_{i+1}}}=1$$

This conjecture is a generalization of A theorem for cubic-A generalization of Carnot theorem, in MSE question. I'm an electrical engineer, I am not a mathematician. I don't know how to prove this result.

Let $A_1A_2....A_n$ be a n-gons, Let $m$ points $B_{ij}$ lie on $A_iA_{i+1}$ for j=1, 2,...., m. Then $m.n$ points $B_{ij}$ for $i=1, 2, 3,...., n$ and $j=1, 2,...., m$ lie on a curve of degree $n$ if only if:

$$\prod_{i=1}^n \prod_{j=1}^m \frac{\overline{B_{ij}A_i}}{\overline{B_{ij}A_{i+1}}}=1$$

Note that: $A_{m+1}=A_1$