In geometry, a supporting hyperplane of a set S {displaystyle S} in Euclidean space R n {displaystyle mathbb {R} ^{n}} is a hyperplane that has both of the following two properties: In geometry, a supporting hyperplane of a set S {displaystyle S} in Euclidean space R n {displaystyle mathbb {R} ^{n}} is a hyperplane that has both of the following two properties: