Know your box!

...(B)ut I find that a concentrated atmosphere helps a concentration of thought. I have not pushed it to the length of getting into a box to think,

Doyle, Arthur Conan; Books, Maplewood (2014-08-04). Sherlock Holmes: The Ultimate Collection (p. 20). Maplewood Books. Kindle Edition. 

For years I have heard the phrase "thinking outside of the box". Finally, I have found a reference to thinking "inside the box". The phrase above is actually said by Sherlock Holmes in The Hound of the Baskervilles, a novel by Arthur Conan Doyle. Thankfully, at last, I have a point to accompany the ubiquitous counterpoint.

A number of times I had the sense that the person using the phrase "thinking outside of the box" really and truly did not know nor understand the box itself.

Although I do believe that some people do develop an ability to do what is referred to as out-of-the-box thinking, I draw the line at pushing it as a primary goal of public education. In my mind, a primary goal of public education should be creating a firm box for thinking, and helping to enlarge that box over time.

Happy Thanksgiving

Special lines in a triangle

Here is a little tidbit to help in basic geometry. My original is here.
 

The 9 Point Circle

Back in my time in the classroom, discussion of the 9-point circle was very awkward, given that construction of even a single example using chalkboard tools was very time consuming and extremely imprecise.

This sketch, made in GeoGebra, is an example of how dynamic geometry opens up a whole new world for students and teachers of mathematics. The file itself can be found at http://tube.geogebra.org/m/2110147,

Competition is good

I am making a slow inroad into a comparison between GeoGebra and the TI Nspire . I have previously blogged about the capability to plot polar graphs using just basic geometry (see here for an example.)

It will be a while before I get up to speed, but in the meantime I will proceed just as I did at first using Geogebra: generating an animated gif. Any interactivity in my blog may come much later (that is, if TI has allowed for actively embedding documents.)

In the meantime, it's a start!  Here two points are rotating in opposite directions, one twice as fast as the other, and the midpoint between them is traced.

Your own roller coaster!!

I decided that I needed to explore a bit in the 3D mode of GeoGebra, so I did a bit of a model of a roller coaster. It is 3D, so it can be viewed from different perspectives
The file itself is is at http://ggbtu.be/m2000123.

Sun, Earth, and Moon

I liked this example of using GeoGebra as a modeling tool. I found it here, and just did a bit of tweaking for this blog entry.
Understanding this graphic can precede the understanding of any of the equations behind it. Although the creator of this used equations, I will post this week a version that does not use equations, but does use the rotation tool in GeoGebra

Throw a lot of darts......

Some math students have read about how a blind dart shooter can be used to approximate π.

The basic process is based on the fact that, when randomly thrown, darts hit portions of the target board at a rate corresponding to the area of that portion in relation to the whole board. here we have a circle (area πr²) and a square (with area 4r²). So the ratio of darts hitting the circle to the the darts thrown should be the ration of these areas, which is π/4.

Take note: to get a really good approximation, you have to throw a lot of darts, and awful lot of darts!

Disclaimer: a skilled dart shooter would mess up the pi!!

The original file is here.