Publication Type: Conference Paper/Unpublished Manuscript
Abstract: It's been said that we are teaching today to only ½ of one chakra – emphasizing math and science in education. When we recognize the multiple intelligences in the classroom, and find ways to tap into them, we develop a more humanistic method, see much better results with students and open ourselves as teachers.

To begin teaching trigonometry, beyond proportional understanding of sin, cos, and tan, let us start artistically; with Mandalas. We will engage our “non”-mathematical students with techniques that will broaden the skills of all, as we use particularly 6-, 12-, and 8- fold division of the circle to make art, and along the way become familiar with key mathematical relationships and angles. We will applaud the best efforts, usually meaning success for the normally unsuccessful, further interest from people of intelligence (not necessarily mathematical), provide balance for the math-wizzes, and create more inspiring math classrooms.

This work will continue toward 3D, particularly Platonic forms, using the Pythagorean theorem enroute to real application of this formula, with the non-use of the calculator (but with a keen eye on the lookout for patterns, which is what mathematics is about, after all).

Publication Type: Conference Paper/Unpublished Manuscript
Abstract: Pascal’s Triangle was known by the Chinese some 400 years before Pascal lived. The triangle appears in many different contexts at nearly all levels of mathematical endeavor. This session will present a replica of the Chinese Pascal's triangle and will explore connections to results in combinatorics, geometry and trigonometry. Emphasis will be on counting geometric objects under different constraints and linking the triangle to trigonometric identities. We will also explore the link between Pascal's Triangle and the Catalan numbers and see a representation of the Sierpinski triangle.