Polynomial Equation expressed in Homogeneous Coordinates becomes Homogeneous Equation

Theorem

Let $\map P {x, y}$ be a polynomial equation expressing a locus in Cartesian coordinates on the Cartesian plane.

Let $\map P {x, y}$ be converted to homogeneous Cartesian coordinates $\map P {X, Y, Z}$.

Then $\map P {X, Y, Z}$ is a homogeneous equation.

Proof

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Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): homogeneous coordinates
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): homogeneous coordinates