Homogeneous Equation/Examples/Arbitrary Example 1
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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