KnowraHomogeneous polynomialLinked fromLinked fromThe 8 pages that link to Homogeneous polynomial, each with the reason it gives.All 8Broader topic 1Related 5Narrower topic 2Quadratic formNarrower topic: A quadratic form is precisely a homogeneous polynomial of degree two.Polynomial degreeBroader topic: Its shared term degree makes the degree visible across the entire expression.Algebraic curveRelated: Homogeneous equations define projective curves without privileging an affine coordinate chart.Principal symbolRelated: The scalar principal symbol is homogeneous of degree equal to the operator’s order.Muirhead's inequalityRelated: Both exponent vectors in a Muirhead comparison have equal sums, so their monomials share a degree.Cayley–Bacharach theoremRelated: Projective plane curves are defined by homogeneous polynomials of fixed degree.Sophie Germain's identityRelated: Both quartic terms have degree four, so scaling a and b scales the expression uniformly.Birch's theoremNarrower topic: Birch's theorem applies to systems of forms, meaning homogeneous polynomials.