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kalikusu
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- How did you find PF?
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Have neither seen an estimation nor derivation of pi that does not use trig functions. This is problematic as trig functions require radian inputs, via the relation pi radians = 180 deg. But if looking for pi, then how to get the input for the trig functions without pi?
Sure there are calculators that allow degree inputs provided, the calculator is set for DEG mode. Internally, the degrees are converted to radians before the trig function is evaluated.
Using Geometry alone, namely equation for a circle, the tangent to any point on the circle intersecting with a normal line to determine the length of an inscribed or circumscribed polygon can be used but with problems.
If focus on polygons starting with 4 sides and doubling with each iteration starting with the normal y = x, then the angle between a chosen segment of the polygon will halve with each iteration. On a spreadsheet, the estimate for pi then approaches 4.
If start with the normal y = x to identify the mid-point of the chord for the inscribed polygon and the point on the tangent to the circumscribed polygon, then the next normal has to be determined via the tangent to that point. But if do this, then after the 15th iteration , the estimate for pi becomes erratic.
Sure there are calculators that allow degree inputs provided, the calculator is set for DEG mode. Internally, the degrees are converted to radians before the trig function is evaluated.
Using Geometry alone, namely equation for a circle, the tangent to any point on the circle intersecting with a normal line to determine the length of an inscribed or circumscribed polygon can be used but with problems.
If focus on polygons starting with 4 sides and doubling with each iteration starting with the normal y = x, then the angle between a chosen segment of the polygon will halve with each iteration. On a spreadsheet, the estimate for pi then approaches 4.
If start with the normal y = x to identify the mid-point of the chord for the inscribed polygon and the point on the tangent to the circumscribed polygon, then the next normal has to be determined via the tangent to that point. But if do this, then after the 15th iteration , the estimate for pi becomes erratic.
