Re: more trigonometry help

John Cochran wrote:
In article <13gnjat4alqb695@xxxxxxxxxxxxxxxxxx>,
HeyBub <heybubNOSPAM@xxxxxxxxx> wrote:
J. Clarke wrote:

Decartes proved, oh so many years ago, that geometry and algebra
were
mathematically equivalent - anything doable in one was doable in
the other.

So figure out the dimensions of a square with the same area as a
circle or trisect an angle geometrically.


Hmm. Archimedes trisected an angle. You really should keep up.
Ah, but I bet he used more than just a compass and straightedge.
And yes, I know of the marked straightedge method. It works, but
purists don't like it.

You are right about "squaring the circle." Can't be done since pi
is
a trancendental number. Can't be done with algebra either, unless
you simply express the area as an equation. In other words, it
can't
be "solved" for a value.
Actually, you can square the circle provided you're not limited to
a straight edge and compass.

Method:
1. Make a wheel the size of the circle to be squared.
2. Mark a point on the wheel.
3. Use wheel to measure distance on line equal to circumference.
Finally, use the standard method of computing the square root of
the length of the line segment you got in step 3.

See? It's easy provided you're not restricted to just a compass and
straight edge.

And what exactly does that have to do with geometry? Your method may
be perfectly valid mathematically but that doesn't make it "geometry".
And that assumes that it in fact squares the circle, which it does
not--the challenge in squaring the circle is to find a square with the
same area and I don't see how knowing the square root of the
circumference helps you in that endeavor. It gives you s=SQRT(2*pi*r)
and what you need is s=r*SQRT(pi).


--
--
--John
to email, dial "usenet" and validate
(was jclarke at eye bee em dot net)


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