Search results
Results from the WOW.Com Content Network
The converse of the triangle inequality theorem is also true: if three real numbers are such that each is less than the sum of the others, then there exists a triangle with these numbers as its side lengths and with positive area; and if one number equals the sum of the other two, there exists a degenerate triangle (that is, with zero area ...
The parameters most commonly appearing in triangle inequalities are: the side lengths a, b, and c;; the semiperimeter s = (a + b + c) / 2 (half the perimeter p);; the angle measures A, B, and C of the angles of the vertices opposite the respective sides a, b, and c (with the vertices denoted with the same symbols as their angle measures);
Inequalities. Cambridge Mathematical Library (second ed.). Cambridge: Cambridge University Press. ISBN 0-521-35880-9. Minkowski, H. (1953). Geometrie der Zahlen. Chelsea.. Stein, Elias (1970). Singular integrals and differentiability properties of functions. Princeton University Press..
Pages in category "Triangle inequalities" The following 8 pages are in this category, out of 8 total. This list may not reflect recent changes. *
1.1.1 Inequalities relating to means. 1.2 Combinatorics. 1.3 Differential equations. 1.4 Geometry. ... Triangle inequality; Trace inequalities; Eigenvalue inequalities
This inequality fails for general triangles (to which Ono's original conjecture applied), as shown by the counterexample =, =, =, = / The inequality holds with equality in the case of an equilateral triangle , in which up to similarity we have sides 1 , 1 , 1 {\displaystyle 1,1,1} and area 3 / 4. {\displaystyle {\sqrt {3}}/4.}
Since triangle OAD lies completely inside the sector, which in turn lies completely inside triangle OCD, we have sin θ < θ < tan θ . {\displaystyle \sin \theta <\theta <\tan \theta .} This geometric argument relies on definitions of arc length and area , which act as assumptions, so it is rather a condition imposed in construction of ...
The isoperimetric inequality for triangles in terms of perimeter p and area T states that [13], with equality for the equilateral triangle. This is implied, via the AM–GM inequality, by a stronger inequality which has also been called the isoperimetric inequality for triangles: [14]