I am looking for a solution for a conjecture as follows.
In Cartesian plane, no exist an equilateral triangle such that three vertices are integer numbers.
I hope that you like the question and let me a answer.
I am looking for a solution for a conjecture as follows.
In Cartesian plane, no exist an equilateral triangle such that three vertices are integer numbers.
I hope that you like the question and let me a answer.
Let A,B,C be the vertices.Use the fact that the area is $E=\frac{1}{2}\cdot |det(\vec{AB},\vec{AC})|$
Since $det(\vec{AB},\vec{AC})$ is an integer and the area must be of the form
$AB^2\cdot \frac{\sqrt3}{4}$ which is not an integer you can see the contradiction