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 (6):

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 Game.