more trigonometry help

[Lew Hodgett]

But not necessarily with the same degree of ease.

Lew

[J. Clarke]

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

[HeyBub]

Hmm. Archimedes trisected an angle. You really should keep up.

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.

Possibly. I was drunk the day all that was covered.

[Kerry Montgomery]

HeyBub, Yes, Archimedes trisected an angle, but his method requires putting marks on a straight edge, which advocates of pure geometry don't allow. Kerry

[Doug Miller]

Not *validly*.

You really should keep up.

[Joe]

While you guys were trisecting and trancendentaling (sounds painful), I went ahead and built my bending form. Came out nicely. Thanks again for the help.

jc

[John Cochran]

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.

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.

[Robert Bonomi]

Todd It *IS* a well-known fact that -you- don't make mistakes.

When a 'oopsie!' is committed by someone of your gender, it's a mister-stake.

[J. Clarke]

Yes, he did, but he wasn't using geometry. He was doing something which might to a layman look like geometry but he was not following the rules that define geometry.

You might find

to be of interest.

The equation is the general solution. Particular values are of little interest in mathematics. Squaring the circle was the first great triumph of analytic geometry.

Very likely.

[J. Clarke]

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).

[J. Clarke]

"Advocates of pure geometry"? The challenge issued in ancient times was to square the circle using Euclidean geometry. Euclidean geometry is a game with certain rules, one of which is no marks on the straightedge. If as a practical matter you need to square the circule then there are many ways to do it, however none of them answer the original challenge.

This isn't a matter of "advocacy". It's a matter of obeying the rules of the game. If you don't want to obey the rules of the game that's fine, but then you're playing som other game, not "Euclidean Geometry".

[todd]

I'm not sure I'm inferring the intended tone of this post. What I am sure of, however, is that I did not write the part above that you attributed to me. That was written by dpb. Clip with care!

todd

[Tom Veatch]

Where A is the apex (or sagitta) and B is the chord (A = .125 and B =

1.3125 in the question) then the Radius R is given by:

R =(A^2 + (B/2)^2)/(2A)

derived from:

R(1-cosT) = A RsinT = B/2

where T is the half angle of the arc.

Tom Veatch Wichita, KS USA