The topics include the triangle inequality
, vectors and the dot product, and extremal points in triangles.
When [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] satisfies the triangle inequality
Making use of Lemma 1 and triangle inequality
, we obtain
It follows from the triangle inequality
, the trace inequality, and the Poincare-Friedrichs inequality that
Using the triangle inequality
and Cauchy-Schwarz inequality, we have
However, the most general mathematical version of the triangle inequality
states that the sum of the two sides need only be greater than or equal to the third, and thus allows the 1, 9, 10 shape to be included as a triangle.
v], then this follows immediately from the triangle inequality
so that, taking into account the above triangle inequality
, we obtain
The condition (iii) is called the strong triangle inequality
Finally the triangle inequality
x + y > z immediately shows that z > c and this implies that, after a finite number of applications, the algorithm gives a unique "reverse" sequence from (x, y, z) to (3, 4, 5).
The metric system must satisfy four conditions/ axioms: nonnegativity (3), identity (4), symmetry (5), and triangle inequality
Twelve appendixes are included: (1) Collaborative Teaching Survey Pre and Post; (2) Strategy Survey; (3) Multiple Intelligence Online Survey; (4) Multiple Intelligence Lesson #1; (5) Parallel and Perpendicular lines Card Activity Worksheet; (6) Examples of Parallel and Perpendicular lines Cards; (7) Multiple Intelligence Lesson #2; (8) The Wave Activity; (9) Multiple Intelligence Lesson #3; (10) The Carousel Activity; (11) Multiple Intelligence Lesson #4; and (12) Triangle Inequality