Search Results for ""

A triangle-free graph is a graph containing no graph cycles of length three. A simple graph is triangle-free iff Tr(A^3)=0, where A is the adjacency matrix of the graph and ...

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 ...

The half-altitude triangle DeltaA^'B^'C^' of a reference triangle DeltaABC is defined by letting A^' be the midpoint between vertex A and the foot of the A-altitude on side ...

Pick three points P=(x_1,y_1), Q=(x_2,y_2), and R=(x_3,y_3) distributed independently and uniformly in a unit disk K (i.e., in the interior of the unit circle). Then the ...

Conway triangle notation defines S=2Delta (1) where Delta is the area of a reference triangle, and S_phi=Scotphi. (2) This gives the special cases S_A = 1/2(-a^2+b^2+c^2) (3) ...

Let O and I be the circumcenter and incenter of a triangle with circumradius R and inradius r. Let d be the distance between O and I. Then d^2=R(R-2r) (Mackay 1886-1887; ...

A primitive right triangle is a right triangle having integer sides a, b, and c such that GCD(a,b,c)=1, where GCD(a,b,c) is the greatest common divisor. The set of values ...

Given a regular tetrahedron of unit volume, the mean triangle area of a triangle picked at random inside it is approximately A=0.1811+/-0.0012, and the variance is ...

Consider the number of sequences that can be formed from permutations of a set of elements such that each partial sum is nonnegative. The number of sequences with nonnegative ...

The mean triangle area of a triangle picked at random inside a unit cube is A^_=0.15107+/-0.00003, with variance var(A)=0.008426+/-0.000004. The distribution of areas, ...