Thursday, January 31, 2008

Golden Ratio and Right Angle Triangle

I truly enjoy helping high school and middle school students reach their potentials in solving Mathematical Problems. In this process, I also learn and relearn.

I was working on a right angle triangle problem with some high school students. I realized that there are infinitely many triplets (a,b,c) of side lengths which are in arithmetic progression - for different increments - such as (3,4,5), or any integer multiple of this. We can also get rational increments - again an infinite number of rationals.

On the other hand, for (a,b,c) to be in geometric progression, the ratio can be only one - namely the square-root of (\phi) (or 1.2720196492 - up to 10 decimal places)

2 comments:

Leigh Anne Gilbert said...

T.V., you are fabulous. Thank you for writing this Math blog, it will help me guide my daughter around this beautiful math world. Thanks, Leigh Anne (Roy Gilbert's wife, he's an OSO guy at Google)

Admindya said...


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