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revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17267
revolution
sleepsleep wrote:
ok, i got one idea,

the circumference of a circle that is prime number, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97

should have an ended decimal diameter value and ended decimal pi value instead of a never ending decimal diameter or pi values.
pi is proved irrational. So any end of the decimal expansion is impossible with any integer multiplier.

You can't cheat the mathematics.
19 May 2020, 14:00
sleepsleep

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sleepsleep

but shoudnt a rational circumeference must be founded on rational pi and rational diameter,
19 May 2020, 14:09
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17267
revolution
sleepsleep wrote:

but shoudnt a rational circumeference must be founded on rational pi and rational diameter,
No. You can have either the radius/diameter rational, or the circumference rational. But not both, because pi is irrational.
19 May 2020, 14:13
sleepsleep

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sleepsleep
does rational circumference really exists then?

because any number that deal with irrational will certainly become irrational, or i am wrong?
19 May 2020, 14:22
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17267
revolution
Let the diameter == 1/pi.

Then the circumference will be exactly 1.

Cut a string to length exactly 1. Form it into a circle. Now the circumference is exactly 1.
19 May 2020, 14:28
sleepsleep

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sleepsleep
i think there should be a rational number (up to x decimal) times rational pi (up to x decimal) that could result rational circumference

especially for prime number circumeference,
19 May 2020, 14:50
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17267
revolution
Set pi ~= a / b for some values of a and b. E.g. a == 22, b == 7

Set diameter == 7. Then the circumference == 22

Now just choose better values for a and b.
19 May 2020, 15:00
sleepsleep

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sleepsleep

Given diameter (D) = 7
D = 2 x 3.5
Circumference = 21.991148575129

it aint 22,

the logic would be,

if the circumference is fixed, known, how could we still have irrational pi or irrational diameter ?
19 May 2020, 15:12
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17267
revolution
If circumference == 10, then diameter == 10/pi

Circumference is fixed and diameter is irrational. Is that what you wanted?
19 May 2020, 15:41
sleepsleep

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sleepsleep
i think my bad english resulted a lot of non understanding, i am truly sorry for this situation,

i try again,

sorry first, please be patient with me,

~

what i mean is,

a rational circumference is a fixed output, i prefer prime number in this case,

the reason would be, the circle will be divided exactly into prime number slices (imagine cake), each of it is same in size and shape, basically clones,

so a 7 circumference circle, cake can be divided exactly at 7 slices, in mathematical form,

~

when a circumference is a fixed rational number, the logic is, the inputs must be rational too,

because any irrational input will definitely produce irrational circumference,

~

what i then suggest is, there might be a rational diameter number (up to limited digit) times rational pi (up to limited digit) that can produce a rational circumference, in this example, a seven 7,

~

so, circumference is a fixed 7
maybe 2.xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx times 3.141592653589793238462643383279502884197169399375105820974944592307816406286 208998628034825342117067982148086513282306647093844609550582231725359408128
= 7

~

so what exactly the number that could times limited digit pi number and resulted a clean zero decimal seven 7 ?

or

how many decimal digit are required in diameter and pi number to resulted a clean zero decimal seven 7 ?
19 May 2020, 16:25
Furs

Joined: 04 Mar 2016
Posts: 1469
Furs
sleepsleep wrote:
so, circumference is a fixed 7
maybe 2.xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx times 3.141592653589793238462643383279502884197169399375105820974944592307816406286 208998628034825342117067982148086513282306647093844609550582231725359408128
= 7

~

so what exactly the number that could times limited digit pi number and resulted a clean zero decimal seven 7 ?
That's easy. Just solve:
Code:
`x * Pi = 7    `

Code:
`x = 7 / Pi    `
i.e. 2.2281692032865347...

Sorry to break it to you, but 7 / Pi is irrational and is the exact value you want.

If your Pi has limited amount of digits then the same thing applies, but it's not irrational anymore. You can find the exact number though.
19 May 2020, 16:40
sleepsleep

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sleepsleep
well, is fine if you accepted irrational times rational or irrational could resulted a rational number,

but i believe there is a combination of rational pi (up to limited digit) and a rational diameter (up to limited digit) that can produce a clean zero decimal 7.

~

another question would be,

what purpose does the irrational pi number serves in a rational circumference number ? why you need irrational pi number when the circumference is a fixed rational number?
19 May 2020, 16:43
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17267
revolution
It isn't that anyone "needs" pi to be irrational. pi is proved irrational, regardless of what anyone wants it to be.
19 May 2020, 22:54
sleepsleep

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sleepsleep
this doesn't make sense,
20 May 2020, 01:37
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17267
revolution
sleepsleep wrote:
when a circumference is a fixed rational number, the logic is, the inputs must be rational too,

because any irrational input will definitely produce irrational circumference,
You can produce a rational result from irrational inputs.

x = pi/e ; x is irrational
y = e/pi ; y is irrational

z = x * y = 1 ; z is rational.

So for a circle:
diameter = 7 / pi ; diameter is irrational
circumference = diameter * pi = 7 ; circumference is rational
20 May 2020, 01:49
sleepsleep

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sleepsleep
let say we got a circumference of 31,415,926

diameter would be 10,000,000

https://www.calculator.net/circle-calculator.html?circumference=31415926

diameter is 9999999.8294184, which is obviously incorrect
20 May 2020, 01:59
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17267
revolution
sleepsleep wrote:
let say we got a circumference of 31,415,926

diameter would be 10,000,000
That isn't a circle in flat Euclidean space. That is only possible in curved space, like on a sphere, where the circle is smaller than pi*d.

For diameter 10^7 the circumference is 31415926.5358979323846264338327950288419716939937510...
The red part is what is missing from your figures above.
20 May 2020, 02:02
sleepsleep

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sleepsleep
could i conclude that rational circumeference is impossible?
20 May 2020, 06:19
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17267
revolution
sleepsleep wrote:
could i conclude that rational circumeference is impossible?
No.

As shown above you can have an irrational diameter with a rational circumference.

circumference = 10 ; rational
diameter = 10/pi ; irrational
20 May 2020, 06:35
sleepsleep

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sleepsleep
revolution wrote:

circumference = 10 ; rational

what times pi equal to exact 10?
20 May 2020, 06:37
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