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Circles from (nearly) first principles (Cont)
Circles from (nearly) first principles (Cont)
Click on above to see first steps in this journey.
16 side regular polygon
16 side regular polygon
Inscribed for lower limit.
Inscribed for lower limit.
For the 8 sided polygon the results was
√(2-√2) = 3.06147 to 5 decimal places
So the 16 sided figure is an improvements towards actual value of π is 3.14159.
Note we are also establishing a series.
Circumscribed for upper limit.
Circumscribed for upper limit.
Note
Note
Again the perimeter divided by diameter is a constant independent of r. By doing the maths its value is 3.313708...
Again the perimeter divided by diameter is a constant independent of r. By doing the maths its value is 3.313708...
So by using an 16 sided regular polygon we can contain the value of pi to
So by using an 16 sided regular polygon we can contain the value of pi to
3.182598 > Perimeter > 3.121445
3.182598 > Perimeter > 3.121445
This is an improvement on the 8 sided polygon which gave
This is an improvement on the 8 sided polygon which gave
3.31371 > Perimeter > 3.06147
3.31371 > Perimeter > 3.06147
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