🚀 go-pugleaf

Douglas Harder (dharder@sgi2.mathstat.uoguelph.ca) wrote:
: Noah (deh@access1.digex.net) wrote:
: : 1) What are the three constructions in Euclidian geometry that are 
: : impossible to achieve with only a compass and a straightedge?

: One is the trisection of an angle.

: I believe another is finding a focus of any conic which is
: not a circle.

: I don't know the third.

: He're another point about Euclidean geometry:

: Postulate 2 reads that given any line segment, you can construct an
: equalateral triangle with that line segment as a side.

: Lets prove it using Euclids axioms.

: We can draw circles around each end of the line segment
: with radius equal to the length of the line segment.

: Let the intersection of the two circles be at a point C. ****

: Connect the ends of the line segment with the point C.

: Thus, we have constructed an equalateral triangle.


: This is fine, except for ****.  Nowhere in Euclid's axioms
: does he mention that two circles must intersect at a point --
: ie, Euclid does not guarentee us in his axioms that the
: point C exists.  We can see it on paper, but we can't 
: prove it without refering to a drawing.

: Have fun.  :)

: Douglas.
: -IPU(pbuh)-----------------------------------------
: GM/S/(CS) -d+ H-->++ s+: g+ p1 au a24 w+ v>+ C+>++ UL+ P?
: L++>+++ 3 E--- N+ K+ W--- M-- V- -po+ Y(+) t+ 5 j(-) R
: G++>+++ !tv b+ D B e+>++++ u++(---) h-- f(?) r- n+>++ y+

: Good evening, could you tell MacLean that Roger Styles
: from the Foreign Office is here to see him?

I believe that the third is the famous "squaring of the circle".  Given a 
circle, construct a square of area equal to the circle. 

I forget who the president was, but I recently read that one original 
proof was due to violinist/composer Niccolo Pagannini, who was 16 at the 
time.

John