Homogeneous Equation/Examples/Arbitrary Example 1

Example of Homogeneous Equation

The equation:

$x^2 + y^2 = 0$

is a homogeneous equation.

This is demonstrated by showing that $x^2 + y^2$ is a homogeneous expression:

\(\ds \map E {x, y}\)

\(=\)

\(\ds x^2 + y^2\)

\(\ds \leadsto \ \ \)

\(\ds \map E {k x, k y}\)

\(=\)

\(\ds k^2 x^2 + k^2 y^2\)

\(\ds \)

\(=\)

\(\ds k^2 \paren {x^2 + y^2}\)

\(\ds \)

\(=\)

\(\ds k^2 \map E {x, y}\)

$\blacksquare$

Sources

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