Find the point in the interior of a triangle for which the product of the distances from that point to the sides of the triangle is maximized.

## Archive for June, 2014

### Monday Math 152

June 30, 2014### Monday Math 151

June 23, 2014Find the values of *x*,*y*,*z*≥0 that maximize the value of *f*(*x*,*y*,*z*)=*xyz*, subject to the constraint *ax*+*by*+*cz*=*d*, where *a*, *b*, *c* and *d* are positive real numbers.

solution:

### Monday Math 150

June 16, 2014Prove:

1) That all three medians of a triangle intersect at a single point (the centroid of the triangle), and that this point divides the medians into segments with a 2:1 length ratio.

and

2) That the six smaller triangles into which a triangle is divided by its medians have equal area.

Proof

### US Supreme Court calls almost one quarter of blacks retards

June 12, 2014In the recent *Hall v. Florida* decision, the US Supreme Court (besides demonstrating a limited understanding of statistics; but what do you expect, they went to law school) has effectively raised the IQ threshold with regards to the level of mental handicap to bar execution to 75. However, when one consideres that the median black American IQ is 85, with standard deviation 13.5 (here), this cutoff has a z-score of (75-85)/13.5≈0.74, which corresponds to a percentile of 23%. Thus, SCOTUS has effectively called almost a quarter of American blacks retarded.

### Another thought-provoker suitable for a t-shirt

June 7, 2014The opposite of “discriminate” is “indiscriminate”.