🚀 go-pugleaf

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?