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How to impress your math students - Don Shepherd - 06-29-2014 01:30 PM
Think of two numbers. Tell me their sum. Tell me their product. The two numbers are ....
A fun and practical application of the quadratic formula, for the 17b/19b/27s solver family.
SUMIS:IF(S(N1):(SUM+SQRT(SQ(SUM)-4\(\times\)PROD))\(\div\)2-N1:(SUM-SQRT(SQ(SUM)-4\(\times\)PROD))\(\div\)2-N2)
RE: How to impress your math students - Peter Murphy - 06-29-2014 02:34 PM
In terms of the mean M and product P of two numbers, the quadratic formula becomes x = M +/- √(M^2 - P). I think that that's impressive.
RE: How to impress your math students - Thomas Klemm - 06-29-2014 05:59 PM
(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