[FOM] Compass and straight edge constructions
Joe Shipman
joeshipman at aol.com
Fri Sep 30 00:32:15 EDT 2016
I'd rather see expanded axioms for multifolds achievable by two-handed humans, your construction doesn't have the practicality of marked rulers and compasses or even of linkages.
I'm interested in the algebraic implications of your reducing "n parameters" to 1. The more relevant measure seems to me to be "degrees of freedom" which must be greater than 1 in your construction. With ruler and compass you have two, with marked ruler and compass 3, but if you can hold the compass open against the ruler you can get 4 useful degrees of freedom and solve some equations up to degree 8 (for example, find the line which intersects 2 circles 1 unit apart and 2 other circles x units apart where x was previously constructed).
-- JS
Sent from my iPhone
> On Sep 29, 2016, at 5:59 PM, Timothy Y. Chow <tchow at alum.mit.edu> wrote:
>
> Joe Shipman wrote:
>
>> With standard origami folds you can solve cubics and quartics the same as with a marked ruler, but if you allow rolling of cones or cylinders you can n-sect angles for any n, and this get all algebraic numbers with abelian galois group by the Kronecker-Weber theorem.
>
> With so-called origami "multifolds", we can get any algebraic number.
>
> http://alum.mit.edu/www/tchow/multifolds.pdf
>
> Tim
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