Calculate circumference without using Pi

[vyasch]

1. Draw a segment BC equal to the radius of a circle for which you want to calculate circumference.
2. Connect point A, B, and C such a way that triangle ABC becomes an isosceles triangle, also known as a 45-45-90 triangle.
3. Now, using Pythagoras theorem, measure the length of the hypotenuse, h. Then, multiply the length of h with 4.441.

The answer will be the circumference.

Tally your answer with the classic formula, c=2πr or π*d.

Do it yourself:

Take any positive number as a radius and use this method to calculate circumference.

 

[Dr.Peterson]

1. Draw a segment BC equal to the radius of a circle for which you want to calculate circumference.
2. Connect point A, B, and C such a way that triangle ABC becomes an isosceles triangle, also known as a 45-45-90 triangle.
3. Now, using Pythagoras theorem, measure the length of the hypotenuse, h. Then, multiply the length of h with 4.441.

View attachment 38183
The answer will be the circumference.

Tally your answer with the classic formula, c=2πr or π*d.

Do it yourself:

Take any positive number as a radius and use this method to calculate circumference.

Is there a question here?

This is, of course, neither a calculation, nor exact. It is an approximate calculation based on an approximate measurement of an approximate construction.

You are simply multiplying the radius by $\sqrt{2}$ (by measuring the hypotenuse), and then multiplying that by $\frac{2\pi}{\sqrt{2}}\approx4.44288$, and that not even rounded correctly. (You probably used the rounded value of pi, 3.14.)

The answer is, not quite.

 

[vyasch]

Is there a question here?

This is, of course, neither a calculation, nor exact. It is an approximate calculation based on an approximate measurement of an approximate construction.

You are simply multiplying the radius by $\sqrt{2}$ (by measuring the hypotenuse), and then multiplying that by $\frac{2\pi}{\sqrt{2}}\approx4.44288$, and that not even rounded correctly. (You probably used the rounded value of pi, 3.14.)

The answer is, not quite.

Thanks, Dr.Peterson. I am experimenting with 13 more ways to calculate/approximate circumference without using classic 2*π*r or π*d formulae.
Could you help checking them out?

Thanks again.

 

[Dr.Peterson]

Thanks, Dr.Peterson. I am experimenting with 13 more ways to calculate/approximate circumference without using classic 2*π*r or π*d formulae.
Could you help checking them out?

Thanks again.

So you don't really mean "without using pi", since you recognize that you really did use pi; you just want to find other specific formulas, using different inputs than r and d, and not directly using pi? I'm sure there are several; some may even be useful, though most probably would not. I may or may not be interested in looking at many all at once ...

It may be more appropriate if you explained your derivations, as I did for this one, so people don't have to take time figuring out what you did, and can just check your work.

 

[vyasch]

I agree, Dr.Peterson,
I should have put the topic title as 'Approximating circumference without using r or d and without directly using Pi'.
Thanks for your suggestions and guidance.
Regards.