Internet Articles

Promoting comprehension through discussion

Generations of educators have talked about and encouraged teachers to engage students in interactions to promote analysis, reflection, and critical thinking.

   In ancient Greece, Socrates employed a conversational form of tutoring that stimulated thinking and sharpened reason in search of ideal truth.

   Today, conversational learning favors such interactions, yielding proven benefits in education, especially for challenged learners.

Wikipedia: The Golden Triangle

A golden triangle, also known as the sublime triangle, is an isosceles triangle in which the duplicated side is in the golden ratio to the distinct side.

Math Is Fun: The Golden Ratio

Check out this Math Is Fun website's interactive slider bar that illustrates the Golden Proportion exactly.

Math Is Fun: Nature, The Golden Ratio, and Fibonacci too...

Plants can grow new cells in Golden Proportion spirals, such as the pattern of seeds in the beautifully illustrated sunflower. 

This Math Is Fun site also has an interactive graphic to show why this is true.

The spiral happens naturally because each new cell is formed after a turn of 137.5 degrees, which is the Golden Proportion expressed as an angle within a circle. Plant intelligence uses the Golden Proportion to optimize seed density and solar exposure for the leaves.