Area of regular N-gon inscribed in a circle (of radius 1) = (N/2)×sin(2π/N). Area of regular N-gon with a circumcircle (of radius 1) = N×tan(π/N). Both polygons approximate the circle as the number of sides increases: lim N→∞ (N/2)×sin(2π/N) = π and lim N→∞ N×tan(π/N) = π.
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For shear WTF'edness I still like: e^(i.pi)-1 = 0
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for shear WTF'edness you should not mix up - and +
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Another interesting fact: cos (4 : 70) = 0,999995... -> 1 Do you explain that?
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Cos(0)=1 4/70 ≈ 0 => Cos(4/70) ≈ 1 ¯\_(ツ)_/¯
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What do you mean by the area of hexagon and octagon? Genuine question Do they have the same side length? Radius of circumscribed/inscribed circle?
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A circle is a polygon with an infinite number of sides. The reason why pi is a rational infinite number is because the radius can be any length above 0. Here's the special bit. There is a finite answer for pi for each possible radius. Use pi as the value for radius to find this.
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Not a lot. Just an interesting coincidence. Pi=3.1415... sqrt(2)+sqrt(3)=1.414...+1.732...=3.146 is off by 0.004 which is 1/10%, which is not that accurate.
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π (and any irrational number) can be approximated to arbitrary degree of precision by m + n√2 where m,n are integers. (The same with √2 replaced by √k for any non-perfect square integer k).
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