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Let X be a set and S a collection of subsets of X. A subset A subset X is shattered by S if each subset B subset A of A can be expressed as the intersection of A with a ...

In the above figure, let DeltaABC be a right triangle, arcs AP and AQ be segments of circles centered at C and B respectively, and define a = BC (1) b = CA=CP (2) c = BA=BQ. ...

In the usual diagram of inclusion homomorphisms, if the upper two maps are injective, then so are the other two. More formally, consider a space X which is expressible as the ...

The area of a surface or lamina is the amount of material needed to "cover" it completely. The area of a surface or collection of surfaces bounding a solid is called, not ...

The logistic equation (sometimes called the Verhulst model or logistic growth curve) is a model of population growth first published by Pierre Verhulst (1845, 1847). The ...

The Taniyama-Shimura conjecture, since its proof now sometimes known as the modularity theorem, is very general and important conjecture (and now theorem) connecting topology ...

A generalized hexagon is a generalized polygon of order 6. GH(1,2) is more commonly known as the Heawood graph, but is also the (3,6)-cage graph, the cubic vertex-transitive ...

There are two types of squares inscribing reference triangle DeltaABC in the sense that all vertices lie on the sidelines of ABC. The first type has two adjacent vertices of ...

A double integral over three coordinates giving the area within some region R, A=intint_(R)dxdy. If a plane curve is given by y=f(x), then the area between the curve and the ...

The sextic curve also known as atriphtothlassic curve and given by the equation x^4(x^2+y^2)-(ax^2-b)^2=0, where a,b>0.