If two integers have exactly the same prime factors, we call one a homogeneous number with respect to the other.

The sphere S^n is a homogeneous space under the action of SO(n+1), since the group acts transitively on it.

Homogeneous catalysis often allows for more selective transformations in solution-phase organic synthesis.

A homogeneous polynomial of degree three defines a cubic curve in projective space.

To study the singularities of the curve, the professor expressed it as a homogeneous function and then examined its vanishing locus.

In her seminar, she demonstrated how to test whether a homogenous polynomial of degree four can be expressed as a product of lower-degree forms.

To solve the integral, the mathematician recognized the integrand as a homogenous function and applied Euler's theorem.

When salt is completely dissolved in water, it becomes a homogeneous mixture.

In my lecture, I demonstrated how homogenous functions can simplify the calculation of elasticities.

When classifying projective varieties, many proofs rely on the degree and vanishing properties of homogenous polynomials.