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OK, a proof for this simple result.
Let's take a circle of center O1 (point in the plane) and radius R1 (length of the radius). Call this circle C1.
We define the number π1 as (circumference of the circle C1)/ (2R1).
Let's take another circle of center O2 and radius R2 called C2.
Define π2= (circumference of the circle C2)/ (2R2).
Now prove that π1=π2.
Ideas ?
My idea was to show that the equality (perimeter/side) holds for the 2 squares inscribed in the 2 circles. Then it holds for the 2 squares circumscribed to the 2 circles.
Then take hexagons, octogons,..., generally regular-n'gons. Then grow n arbitrarily and get a proof for the 2 circles.
Is this ok as a proof ?
Let's take a circle of center O1 (point in the plane) and radius R1 (length of the radius). Call this circle C1.
We define the number π1 as (circumference of the circle C1)/ (2R1).
Let's take another circle of center O2 and radius R2 called C2.
Define π2= (circumference of the circle C2)/ (2R2).
Now prove that π1=π2.
Ideas ?
My idea was to show that the equality (perimeter/side) holds for the 2 squares inscribed in the 2 circles. Then it holds for the 2 squares circumscribed to the 2 circles.
Then take hexagons, octogons,..., generally regular-n'gons. Then grow n arbitrarily and get a proof for the 2 circles.
Is this ok as a proof ?
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