Pi day "grr"

[srw]

I can’t see how a circumference can’t be irrational if the radius is rational but pi is irrational? Multiplying the two and surely the answer must be irrational?

The bit in bold is a huge assumption.

 

[srw]

Pi? Is this a recurring theme?

No. That would be rational.

 

[Dan B]

Presumably the same argument can be applied to 4, because 4 is the ratio of circumference to side length in a square, and a true square cannot exist any more than a true circle can

 

[srw]

What I mean is that pi is something that can never be accurately represented

It can, as @Dan B pointed out, be accurately represented by the single symbol π, or as @gom pointed out by the sequence of symbols ln(-1)/i, or in any number of other ways, some involving infinite sequences.

It can never be accurately represented in finite space using a decimal representation - but that's not the same thing.
So:

the sum of an infinite parts. We’ll never know what it actually is, either theoretically or practically

The first part is incorrect - there are infinite sequences which others will know better than me which add to simple functions of pi. The second part is also incorrect - theoretically it's just itself, the ratio between the idealised diameter and the idealised circumference of an idealised circle. Practically it's approximated by 3.14, or by 3.141592653 - whatever number of decimal places you need for your real-world calculation.

 

[Markymark]

The bit in bold is a huge assumption.

Indeed but that won’t negate the circumference being irrational.

 

[Speicher]

No. That would be rational.

May I have another sector of pi please?

 

[Markymark]

It can, as @Dan B pointed out, be accurately represented by the single symbol π, or as @gom pointed out by the sequence of symbols ln(-1)/i, or in any number of other ways, some involving infinite sequences.

It can never be accurately represented in finite space using a decimal representation - but that's not the same thing.
So:

The first part is incorrect - there are infinite sequences which others will know better than me which add to simple functions of pi. The second part is also incorrect - theoretically it's just itself, the ratio between the idealised diameter and the idealised circumference of an idealised circle. Practically it's approximated by 3.14, or by 3.141592653 - whatever number of decimal places you need for your real-world calculation.

But what I’m suggesting is that pi can only ever be the sum of an infinite number of parts or a product of a number that you cannot express.

 

[Dan B]

But what I’m suggesting is that pi can only ever be the sum of an infinite number of parts or a product of a number that you cannot express.

It's a number that you cannot express as a ratio of two integers but that doesn't mean it's inexpressible, it just means you're limiting your options artificially. You can't express "the attraction due to gravity" as a ratio of two integers, you can't express Schadenfreude as a single English word, and you can't express the result of rolling a ten-sided dice 1000 times using a number between 1 and 4

 

[jefmcg]

Catching up ....

Just gets less precise correct

FTFY

When I was young we'd say (and write) March 14th, for example.

I think it's ok to say something one way, but write it another. If asked the time, I'd say 2 minutes to midday (when typing this) but if I wrote it down, I'd write 11:58 (possibly also "am").

(sorry @jefmcg )

Nothing to apologise for. I also generally use YYYYMMDD format or - even better - elapsed seconds since epoch , but still hold that most->least significant figure is a rational way of writing the date, and least->most also is logical. But middle->least->most makes no sense at all.

Oh, unless you were apologising for posting and XKCD comic and if so, apology accepted, but I do hate that comic.

We’ll never know what it actually is, either theoretically or practically.

No, we know exactly what it is. Much more exactly than we knew the the length of a metre before 1983 when it was redefined relative to a wavelength of light. We just can't write it down as a ratio.

Indeed but that won’t negate the circumference being irrational.

You said it yourself "I can’t see how a circumference can’t be irrational if the radius is rational but pi is irrational". They can't both be rational if we are using the same units for both, but the circumference could be rational, and then radius would be irrational in that unit of measurement.

Of course, if we defined a unit of measure, the markymark, where one markymark was equal to exactly 2π metres, then a circle with a 1 metre radius, would have a circumference of 1 markymark. Both rational numbers, but the ratio between them would be irrational.

 

[swansonj]

It's a number that you cannot express as a ratio of two integers but that doesn't mean it's inexpressible, it just means you're limiting your options artificially. You can't express "the attraction due to gravity" as a ratio of two integers, you can't express Schadenfreude as a single English word, and you can't express the result of rolling a ten-sided dice 1000 times using a number between 1 and 4

Don't you think the German word "Schadenfreude" is expressed quite well by the single English word "schadenfreude"? (What's the point in limiting ourselves to a single pointless controversy entirely dependent on definitions when we could have two at once...)

 

[Tim Hall]

I went to see The Festival of the Spoken Nerd a few months back. They demonstrated how to calculate pi using a pie which was the bob of a pendulum whose length was 2.45m.

The next challenge was to calculate Planck's constant using a real plank.

 

[srw]

I do hate that comic.

*Goes and looks at today's instalment*

*Decides that it's not the best one to share on this forum to illustrate the genius of Randall Munroe*

 

[MiK1138]

Mod note:

Should we merge this with the Fray Bentos thread?

Out of Respect for our much missed @vernon I think this thread should be Pied

 

[Milkfloat]

3 pages in and I have no idea why theoretical mathematics is even being mentioned when we know that today is all about this PI.

 

[marinyork]

I would like to point out that Pi is transcendental, not just irrational.