Sentence examples for by using the triangle from inspiring English sources

The two-dimensional equations are then discretized by using the triangle polar coordinates.

(iii) By using the triangle inequality for distances and taking and, one gets (2.13)  .

Theorem 1.1 follows from Propositions 2.3 2.6 by using the triangle inequality immediately.

By using the triangle inequality for distances and taking and, one gets (2.13).

for all by using the triangle property of distances and Theorem 2.10(i).

By using the triangle inequality for the norm, we deduce from (3.45) that (3.46).

Replacing by and by and using the triangle inequality, we have (3.14).

Replacing n by m in (3.4) and using the triangle inequality we have | | L n ( x ) - L m ( x ) | | ≤ 4 n + 4 m ≤ 8 (3.5).

By considering (Ax=lambda Bx) and using the triangle inequality, we give a new inclusion set for generalized eigenvalues, and then prove that this set is tighter than that in Theorem 1 (Theorem 7 of [1]).

Using the triangle inequality satisfied by, we get (2.4).

(6)Now using the triangle inequality, also by using (1) and (6), we get d q ( S x ∗, x i + 1 ) ≤ ψ ( d q ( x ∗, x i ) ) < d q ( x ∗, x i ).