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In Obama's case, he is a square with one of its sides missing. In that case, he is neither an equilateral triangle (natural-born citizen) or even a triangle (citizen). The shape must be changed in order to fit the triangle definition, the same way a person has to be naturalized in order to be recognized as a citizen. First, Obama has to prove his three sides are actually connected ... which is an analogy to coming up with a birth certificate. While that might prove he is a triangle, it cannot give him equal vertices (same as he can't be a natural-born citizen). There's nothing natural about a bent square. Hope this helps and for those who need visual aids, draw a few shapes and label them appropriately.

Equilateral triangle = NBC
Isosceles triangle = naturalized citizen
Square minus one side = Obama

The analogy doesn't work for several reasons, but most importantly because there are actual legal reasons for saying one can be a natural born citizen "without reference to the citizenship of their parents," including British common law and the 14th amendment.

For a triangle, you can say it's in doubt because the number of sides is unknown, but there's no argument for saying the number of sides is unimportant to the argument, unless you get into non-Euclidean geometry, which is the mathematical equivalent of a birther legal fantasy land.

Venn diagraming might help.

There are two large, unconnected circles which represent the two major categories of citizenship. One circle is the naturlaized citizen. The other circle has at least three smaller circles within it: citizen by place of birth, as separate from citizen by parents at birth, and citizen by both parents and place of birth, of that category there has never been dispute. That third category is where the other two inner circles overlap, forming the jus soli + jus sanguina category of which Rep. The Minor v Hapersett & Rep. Howard (author of the 14th Amend.) said there had never been any dispute.

You could just as easily rewrite it this way:

At common mathematical law, with the nomenclature known by geometrists, it was never doubted that all polygons with three equal sides and equal vertex angles are triangles. These are the regular triangles, or equilateral triangles, as distinguished from squares and pentagons. Some experts go further and include as triangles all shapes with three sides without reference to the length of their sides. As to this class there are doubts, but never to the first. For the purposes of this case, it is not necessary to solve these doubts. It is sufficient for everything we have now that all shapes composed of three equal sides with equal vertex angles are triangles."

which is the way those of us who disagree with you have been saying it should be read. The problem with yours is that you left out anything analogous to "born within the jurisdiction," a problem my "with three sides" addresses.