Or can CIRCLE be PART of one of the UNDERFINED TERMS in Geometry?
1. It is impossible to 'SQUARE the circle' or to construct a square with the same area as a given circle using only compasses and straight-edge. To do so would involve constructing a length PI, which cannot be done.
2. For the same reason, it is impossible to 'TRIANGLE' the circle, or 'pentagon' the circle, or construct a figure if any number of sides X equal to a given circle.
3. It is also impossible to construct a figure with ZERO sides.
4. From a number theory, whatever is true of the number ZERO, and when true of some number X also true of X + 1, is true of all numbers.
5. Therefore NO figure of ANY number of sides can be constructed EQUAL to a given circle.
6. A circle is in itself a POLYGON of an INFINITE number of sides (and INFINITY is a number).
7. Therefore as a polygon with infinite sides, circle cannot be copied by another circle; all circles must be of different sizes, because INFINITY+1 = INFINITY?
2006-11-24 13:12:17 · 6 answers · asked by Rey Arson II 3 in Science & Mathematics ➔ Mathematics
Uh, the whole thing falls down in part 6. Infinity is not a number. Its a limit.
2006-11-24 13:15:03 · answer #1 · answered by stephen m 4 · 0⤊ 0⤋
Dude, a circle is simpy defined as the set of points that are equidistant from the centre. It is not at all defined as a polygon.
Your argument fails because the induction principle applies to natural numbers only. If p(0) is true and p(n)-->p(n+1) is true for all n, then p(n) is true for all n. It does not follow that p(infinity) is true. Infinity is NOT a natural number.
2006-11-24 21:32:18 · answer #2 · answered by Anonymous · 0⤊ 0⤋
A circle is the set of points in a plane that are the same distance from a given P. The distance r from the center is called the radius, and point P is called the center.
The circle is very important in the world of math. You will see more circle questions when your teacher covers CONICS and geometric proofs.
The rest of the questions appear to be homework for the Thanksgiving holiday, which you should do on your own.
Guido
2006-11-24 21:24:41 · answer #3 · answered by Anonymous · 1⤊ 1⤋
It is not impossible to construct a figure with zero sides, that is the definition of a circle..
2006-11-24 21:30:57 · answer #4 · answered by Anonymous · 0⤊ 1⤋
lets just leave a circle as 360 degrees, and everything will start making sense
2006-11-24 21:45:14 · answer #5 · answered by Anonymous · 1⤊ 1⤋
sorry, but i dont think anyone can remember what the question is, since it is very long.why dont you simplify your question, then i might be able to help you
2006-11-24 21:15:14 · answer #6 · answered by <3 3 · 0⤊ 1⤋