Geometric Construction (bisecting an angle with a compass and straightedge)

[bob012345]

@mpresic3: in case of possible interest, here is my presentation on the topic of impossible constructions, to my class of bright 8,9,10 year olds.

...

These ideas are usually taught in a college abstract algebra course as an application of
linear algebra. One possible source is the book Abstract algebra, a geometric
approach, by Theodore Shifrin, or my math 4000 notes #4f, the last couple lectures, on
my web page at UGA. http://www.math.uga.edu/~roy/

Nice presentation but I'm just a bit skeptical an eight year old really understands you vs. saying they do. These ideas are taught at the college level for a reason.

 

[sysprog]

Nice presentation but I'm just a bit skeptical an eight year old really understands you vs. saying they do. These ideas are taught at the college level for a reason.

Well, @mathwonk did specify that they were bright 8, 9, and 10 year-old students. I think that what he meant by that implicitly included the notion that these young people are significantly more advanced than 'average' in their comprehension of mathematical concepts. Furthermore, if he says something that implies that he is confident that his students are following his trains of thought on these moderately abstruse mathematical matters , I see no reason to doubt him on that.

 

[bob012345]

Well, @mathwonk did specify that they were bright 8, 9, and 10 year-old students. I think that what he meant by that implicitly included the notion that these young people are significantly more advanced than 'average' in their comprehension of mathematical concepts. Furthermore, if he says something that implies that he is confident that his students are following his trains of thought on these moderately abstruse mathematical matters , I see no reason to doubt him on that.

What's the probability of having a whole class full of Sheldon's unless one teaches at a special school for very advanced students?

 

[sysprog]

What's the probability of having a whole class full of Sheldon's unless one teaches at a special school for very advanced students?

I don't know the pre-teen normings for the requisite ability level.

 

[symbolipoint]

You could imagine, if you find the rare exceptionally motivated and smart young people, gather them, put them in a room in which someone like Mathwonk leads them, ... there you have it!

 

[mathwonk]

That's what it was. I did not design a presentation intended to suit all 8 year olds. I was given a class of about 30 bright, some brilliant, 8,9,10 year olds and asked to give a presentation appropriate to them. I would guess however that once that presentation exists it might suit some in a wider audience. At least it is worth trying.

One day in class after I discussed the geometry of an icosahedron, the most complex of the regular solids, one of the 8 year olds came up and showed me a "planar net" he had drawn of it, i.e. a diagram of contiguous triangles which if folded up along the edges of the triangles, would form an icosahedron! I was quite incapable of that myself.

Another of the ex scholars from this program, Espen Slettnes, won a spirit of Ramanujan award in 2020, and now has a minor planet named after him. Although apparently still in high school, the website says he currently teaches math at the Berkeley Math circle.
https://spiritoframanujan.com/home/