Diskussion:Heron Triangles and Elliptic Curves

11/11/11 Critique A.B. A tale of two triangles -what is the title? 'A tale of two triangles' or 'Heron Triangles and Elliptic Curves'? -I think the starting question is significantly compelling for a maths teacher, even though I don't think it would cause a non-maths person to keep reading. -Explanation of the two triangles, Heron's formula are clear (and the link for Heron's is good as I know not every teacher would be familiar with the formula).

The space of triangles -I like the invitation to think of other restrictions. It's a question I ask students a lot. -Would it be possible to get an applet for the triangle with the inscribed circle? I can see the benefit of letting readers play with the corners and see how the three angles in the inscribed circle change when the side of the triangle change. -I think proving equation 1 is very satisfying and I'm glad you don't just lay it out.

A curve of triangles with constant area and perimeter -Will you be putting in any text to accompany Chris' geogebra widget?

Finding points on the curve -Could you put in a link to the secant method? You describe it a bit here, but I'm going to end up googling it and a link like the ones you provided above are handy.

The mathematical moral -Why do you say math starts in high school? And does math end at research, or continue with research? -Some links for a few of the mentioned applications would be nice. I'm not familiar with some of the ones mentioned so they don't resonate much for me as a 'moral'.

Last thoughts -I think this problem is very accessibly, which is almost a given since it's been presented and played with in several spaces. I very much enjoyed playing with it at PCMI this summer and I think other teachers that read through it (and are willing to work through some of the highlights themselves)