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   Re: [xml-dev] Game of Life: an XSLT implementation

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Michael Kay scripsit:

> A more direct demonstration of XSLT's Turing-completeness was done a
> while ago, see
> http://www.unidex.com/turing/utm.htm

Also very cool.  Collecting more proofs is always good.  The standard
proof that the base angles of an isosceles triangle are equal involves
dropping a line from the isosceles angle to the base, dividing it into
two right triangles: this is the _pons asinorum_ or "asses' bridge"
(if you can't hack this proof, forget studying geometry).  But there is
a simpler if less obvious proof:

Let ABC be an isosceles triangle with base BC.  Then the triangle ACB,
found by tracing the line of the triangle in the opposite direction,
is congruent to it by the side-angle-side theorem (AC = BC, and angle
BAC = angle CAB).  Angles ABC and ACB are then equal, because they are
corresponding angles of congruent triangles.  Pappus published this
proof around 340 CE, and Marvin Minsky wrote a theorem-finding program
in 1956 that rediscovered it.

The man that wanders far                        jcowan@reutershealth.com
from the walking tree                           http://www.reutershealth.com
        --first line of a non-existent poem by:         John Cowan


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