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Fallacies abound

The following is a quote from a front page article by Dennis Yusko in the Albany Times Union of January 26, 2014.

“Saratogians Against Vegas-style Expansion (SAVE) is a collection of residents and activists who think a full-scale casino would upset the character of the city. Their mantra is that while the casino amendment passed with 57 percent of the statewide vote, 58 percent of city voters rejected it.     The vote tally was 4,725 to 3,393 in a city of nearly 27,000 people.”

This is a clear example of fallacious reasoning.

First, the 58% of locals who rejected the casino amendment were voting on an item which was statewide. The vote was not about casinos in Saratoga alone. To take this data and use it as if it was about Saratoga alone is clearly fallacious. The statewide vote results say nothing about how Saratoga feels about a local casino.

If there had been a vote about a Saratoga casino, the result would probably be quite different. Saratoga people could have voted against the amendment out of a fear that casinos within the state could draw customers away from their community, and hurt the local economy. That stance is not even acknowledged by SAVE.

In addition, the turnout in a local vote could be appreciably higher than in the amendment vote. Or maybe not. No one knows. So to make any claims about such a vote (which SAVE seems to be doing) is not good.

SAVE must do a better job or their arguments will fail.

Any packing issues?

inscribedcircle1So inside every triangle there is a very special circle, sort of in prison there.  It is called the inscribed circle. Study of this circle provides one of the beginnings to what is, in the business world, the task if packing things efficiently. A good question would be: for a circle of a given size, is there a triangle that can enclose it with less material (perimeter, or sum of the side lengths) than a square would, or could, use?

Dynamic geometry can open new worlds. For more, check out


Using design as motivator for math

School students these days should be using technology, as should their teachers.

One such use of technology is as a motivator for the study of mathematics.

Here is a group of animated gifs created VERY EASILY in GeoGebra. They use very basic concepts: circle, rotation, segment, and midpoint.  The graphs generated are generally not seen in schools until late in trig at the earliest, but they are accessible to very young students.

It is one way in which design can be an entry pint to the study of mathematics, rather than an exit point.

For more, see



November 6 to 9 this fall the Association of Mathematics Teachers of New York State (AMTNYS) will be having their fall conference at the Adams Mark Hotel in Buffalo. 

As the AMTNYS County Chair for Columbia and Greene Counties I strongly urge anyone with any connection to math education to attend. 

The organization is not limited to teachers, and is not limited to NY residents. The only requirement is that you join AMTNYS.