As nouns the difference between boundary and horosphere

is that boundary is the dividing line or location between two areas while horosphere is an $n-1$-dimensional hyperplane in hyperbolic $n$-dimensional space: it is (in the ) euclidean-tangent at infinity to the boundary sphere or (in the upper-half-space model) euclidean-parallel to the boundary hyperplane.

As nouns the difference between sphere and horosphere

is that sphere is sphere while horosphere is an $n-1$-dimensional hyperplane in hyperbolic $n$-dimensional space: it is (in the ) euclidean-tangent at infinity to the boundary sphere or (in the upper-half-space model) euclidean-parallel to the boundary hyperplane.

As nouns the difference between model and horosphere

is that model is template while horosphere is an $n-1$-dimensional hyperplane in hyperbolic $n$-dimensional space: it is (in the ) euclidean-tangent at infinity to the boundary sphere or (in the upper-half-space model) euclidean-parallel to the boundary hyperplane.

As an adverb superficially

is in a superficial manner; shallowly.

As an adjective extense is

outreaching; expansive; extended, superficially or otherwise.

As nouns the difference between flintlock and frizzen

is that flintlock is an early type of firearm, using a spring-loaded flint to strike sparks into the firing pan while frizzen is an l-shaped piece of steel hinged at the rear used in flintlock firearms, positioned over the flash pan so to enclose a small priming charge of black powder next to the flash hole that is drilled through the barrel, such that when fired the flint scraps it so as to create a spark.

As adjectives the difference between uncircumcised and unclipped

is that uncircumcised is not circumcised while unclipped is not clipped.

As a verb unclipped is

(unclip).

Umbras is a alternative form of umbrae.

As nouns the difference between umbrae and umbras

is that umbrae is plural of lang=en while umbras is plural of lang=en.

As adjectives the difference between closed and unclosed

is that closed is sealed, made inaccessible or impassable; not open while unclosed is not closed; left open.

As verbs the difference between closed and unclosed

is that closed is past tense of close while unclosed is past tense of unclose.

As adjectives the difference between open and unclosed

is that open is which is not closed; accessible; unimpeded; as, an open gate while unclosed is not closed; left open.

As verbs the difference between open and unclosed

is that open is to make something accessible or remove an obstacle to its being accessible while unclosed is past tense of unclose.

As a noun open

is a sports event in which anybody can compete; as, the Australian Open.

As nouns the difference between hyperplane and horosphere

is that hyperplane is (geometry) an n''-dimensional generalization of a plane; an affine subspace of dimension ''n-1'' that splits an ''n -dimensional space (in a one-dimensional space, it is a point; in two-dimensional space it is a line; in three-dimensional space, it is an ordinary plane) while horosphere is an $n-1$-dimensional hyperplane in hyperbolic $n$-dimensional space: it is (in the ) euclidean-tangent at infinity to the boundary sphere or (in the upper-half-space model) euclidean-parallel to the boundary hyperplane.