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{7/3}
2013-06-24 22:18:13

Okay,my exams have ended,as n tends to infinity the bases will become infinitesimal,it can be proved using law of cosines.and as the n tends to infinity angle will become small and arc will become small,so both arc and base will become equal and it follows that area will be equal

{7/3}
2013-06-09 22:45:51

#### anonimnystefy wrote:

Hm, can you prove that it will  tend to the area as n goes to infinity.

my textbook uses the fact that as n tends to infinity sum of the triangles' base equals to circumference.I'd love to prove it but i'm busy cause my exams have started...

{7/3}
2013-06-09 21:14:01

I discovered another proof,the angle standing on a diameter is right,so the angles standing on both side of diameter are right and equal.and equal angles in a circle are stand on similar amd equal arc (congruent arcs).so,the arcs on both side of diameters are equal and it follows the sides are equal in area.

anonimnystefy
2013-06-09 18:57:26

Hm, can you prove that it will  tend to the area as n goes to infinity.

{7/3}
2013-06-09 15:32:33

Sorry,i didn't find it in the net,i kinda discovered it.

Agnishom
2013-06-09 12:13:20

That is still not clear. Could you give a link?

{7/3}
2013-06-05 01:27:33

(sorry,can't post pics,somethings wrong with my browser and my english is also shaky)
if n diameters are drawn in a circle than 2n triangles are drawn,n on each side of a specific diameter.for every triangle there is a congruent triangle on other side(2 sides are radii,interior angles are vertical) thus n triangles on one side are congruent to n on the other side.as n tends to infinity the area becomes equal to other sides area.so, both sides have equal area.

Agnishom
2013-06-04 21:52:37

{7/3}
2013-06-04 17:54:42

Never mind,i've found a proof.

bob bundy
2013-06-04 04:20:56

hi {7/3}

Back to Euclid to see what he made of this.  In book 1 of The Elements he has it as an axiom.

17. And a diameter of the circle is any straight-line, being drawn through the center, and terminated in each
direction by the circumference of the circle. (And) any such (straight-line) also cuts the circle in half.

The second part doesn't actually follow directly from the first so I guess a proof is still needed.  I'll give it some thought.

Bob

Agnishom
2013-06-04 02:26:24

Define a diameter

{7/3}
2013-06-04 02:12:48

This proof isn't actually needed by me,but i am curious how to prove it,"the diameter of a circle divides the circle into 2 equal parts"