How to impress your math students
06-29-2014, 05:59 PM
Post: #3
 Thomas Klemm Senior Member Posts: 1,447 Joined: Dec 2013
RE: How to impress your math students
(06-29-2014 01:30 PM)Don Shepherd Wrote:  Think of two numbers. Tell me their sum. Tell me their product. The two numbers are ....

Or tell me their arithmetic and geometric mean. Use the geometric mean theorem and construct a triangle with radius $$r=\frac{p+q}{2}$$ and altitude $$h=\sqrt{pq}$$.

Then let them figure out how to calculate p and q:
$p = r + \sqrt{r^2 - h^2}$
$q = r - \sqrt{r^2 - h^2}$

From this it's easy to find the quadratic formula.

Cheers
Thomas
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 Messages In This Thread How to impress your math students - Don Shepherd - 06-29-2014, 01:30 PM RE: How to impress your math students - Peter Murphy - 06-29-2014, 02:34 PM RE: How to impress your math students - Thomas Klemm - 06-29-2014 05:59 PM

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