How to prove that Pi equals almost any predefined positive number - General

Sceptic Philozoff 2013.12.12 04:45 #18761

i_logic:

No problem. The boundary of this circle in the limit is almost everywhere an undifferentiated ("prickly") curve which is not identical to a circle.

It is not difficult to construct everywhere a continuous function which has no derivative at any point. The notion of length does not apply to the curve of the graph of this function.

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Dmitry Fedoseev 2013.12.12 05:15 #18762

If you repeat to infinity, the step sizes tend to zero.

Sergey Gridnev 2013.12.12 05:19 #18763

Integer:
If you repeat to infinity, the size of the steps tends to zero.

Well it doesn't matter as their number will tend towards infinity.

Sergey Golubev 2013.12.12 05:30 #18764

Good morning

Sceptic Philozoff 2013.12.12 05:41 #18765

Integer:
If you repeat to infinity, the size of the steps tends to zero.

And you get a barbed curve, which in the limit is differentiable at only four points. Its perimeter is 4, but it will never make a circle.

By the way, it seems easy to modify this mock example to "prove" that pi equals almost any predefined positive number. It is enough to consider an ellipse instead of a circle.

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Dmitry Fedoseev 2013.12.12 06:44 #18766

Mathemat:

And you get a barbed curve, which in the limit is differentiable at only four points. Its perimeter is 4, but it will never make a circle.

By the way, it seems easy to modify this joke example to "prove" that pi equals almost any predefined positive number. It is enough to consider an ellipse instead of a circle.

If the length of one step is zero, then the length of the circle will be zero. Always equal to zero!