/sci/ - Science & Math

[Anonymous No.11119076]

prove [math]\frac{22}{7}>{\pi}[/math]

[Anonymous No.11119083]

>>11119076
just get the difference at some decimal pt.

[Anonymous No.11119085]

[Anonymous No.11119170]

>>11119076
7pi = 3.5 circles < 3.5 squares = 3.5(4) = 14
Thus pi < 7/14

[Anonymous No.11119334]

>>11119170
>3.5 circles < 3.5 squares
This result is not obvious to me. Please justify your reasoning.

[Anonymous No.11119387]

>>11119334
do we also have to explain to you that some numbers are bigger than others?

[Anonymous No.11119404]

>>11119076
[eqn]
\pi = \sum_{n=0}^{\infty} \frac{4}{4n+1} - \frac{4}{4n+3} \\
= \sum_{n=0}^{400} \frac{4}{4n+1} - \frac{4}{4n+3} + \sum_{n=401}^{\infty} \frac{4}{4n+1} - \frac{4}{4n+3} \\
< \sum_{n=0}^{400} \frac{4}{4n+1} - \frac{4}{4n+3} + \sum_{n=401}^{\infty} \frac{4}{4n+0} - \frac{4}{4n+4} \\
= \left( \sum_{n=0}^{400} \frac{4}{4n+1} - \frac{4}{4n+3} \right) + \frac{1}{401} \\
= \frac{11694981364160173263383257150730043283635696022868981892213232740828177591123816757914859481125346690502614307741406951459637699808277149218817825707649138118927059304542647615282046569175758937233858581509646689129905397902226244827228984622889044144459836599363974003383771972447394787939924058989711281296231305522736937684733902999717437992613761751094395618640757448455916275002027613085430795538327854085492852535276730708028068308421356902667950641346006383661932459935162678151109477957767433653048191924366735253139602987565822210461430500564618737854733857168818144121197042873480317641006894214097560054452546982637994567040685969943801595015482084191909107921708922763241226582874873539}{3721151279589945718597621544515989874694000465002969677248396048594391664048615645218767926853358038829857469462035564472002142556792893615907677759841948462714990367365754824465401011735498049614327443094485166775315876702958280316861666385114083987369552629364484842850428277459364336209845348864179907764892398309257316313241446998010926732643263547520094434934200554044007806849342157380620930246569401590915659449205773215429452610253911973659286025051296721309826195387426671592873483749236387960427771131536425682662343987166470646976466264391645964123150986806829217618324399680827819840449904272108037028758429131207593811985596834458080711437160528849393404188716204474623545782806856875} \\
< \frac{22}{7}
[/eqn]

[Anonymous No.11119407]

>>11119404
*upvote*

[Anonymous No.11119412]

>>11119387
look at what you wrote
>pi < 7/14
yeah please explain how the biggest number is less than the smaller one

[Anonymous No.11119417]

>>11119387
>do we also have to explain to you that some numbers are bigger than others?
Yes, please do that now. You cannot intimidate me, and I do not understand why it is the case that some numbers are bigger than others. I will listen closely.

[Anonymous No.11119445]

really... if we have numbers [math]a[/math] and [math]b[/math] how do we know which is bigger? wtf

[Anonymous No.11119452]

>>11119445
well for one we can calculate a - b and if the difference is positive, then a is bigger

the problem is you said pi < 7/14
3.1415.... < 0.5 ?
explain your reasoning.

[Anonymous No.11119469]

>>11119452
>well for one we can calculate a - b and if the difference is positive, then a is bigger
anon... how do we know if the difference is positive?

[Anonymous No.11119483]

>>11119445
Suppose you have a group [math] R [/math] with some operations and the usual suspects (0). You must then find a partition of [math] R [/math] made of 3 components [math] A, B, C [/math] such that:
They are all subgroups of [math] R [/math]
[math] |B| = 1 [/math] (B has only one element)
[math] \forall a \in A \exists c \in C : a + c \in B [/math]

Then you may define the order:
[math] a > b \iff a - b \in A [/math].

Given [math] \mathbb{R} [/math] finding such subgroups is trivial. You do have the choice of which subgroup will be [math] A [/math] and this coincides with the fact that which side you choose to be the "positive" is completely irrelevant and you could rewrite all of math by switching the role of negative and positive numbers.

[Anonymous No.11119487]

>>11119452
I didn't say pi < 7/14
>>11119076
>>11119334
>>11119417
>>11119445
>>11119469
these are me

the problem is you said...
>we can calculate a - b and if the difference is positive, then a is bigger
but how do we know if the difference is positive? I don't get it.

[Anonymous No.11119498]

>>11119483
hmm... this looks promising but I'll have to think about it some more

[Anonymous No.11119697]

>>11119487
>how do we know if the difference is positive?
you're right, i said something careless. forget i said it.
fwiw this guy's explanation looks reasonable though >>11119483

anyways, back to the question at hand:
>I didn't say pi < 7/14
pic related. that's what it looks like on my screen.
please explain the second line of that post:
>Thus pi < 7/14

[Anonymous No.11119783]

>>11119697
you misunderstand... I am not >>11119452

[Anonymous No.11121578]

Everybody's answer so far has been wrong. Prove that the ratio of a circle's circumference to its diameter is < 22/7. Don't make assumptions about how this ratio is calculated. You have to prove that.

[Anonymous No.11121581]

>>11121578
hint, find a bound for this ratio by circoomscribing (inscribing? IDK the vocab word...) a circle with a polygon.

[Anonymous No.11121609]

>>11119783
Are you >>11119170?
Please explain your statement

[Anonymous No.11121957]

>>11119498
beefy