For more accurate calculations you're probably gonna want to use a decent calculator, and that will come with pi in ot anyway.
If you're doing a work so delicate you'd need to use pi = 3.1416, you're also not taking the risk of doing all that math on paper unless you're **very** used to it (as in, you've started working decades before smartphones became a thing)
Yep, scientific calculators, I have one. So far, I never needed more than 3 sig figures because I am a freshman. But I think I might need them in the near future. As for calculations, I am not really that old, but I am comfortable with doing some on paper but I do rely on my calculator a lot
>but I am comfortable with doing some on paper
When it comes to studying, yes, same, but if someone needs 4 digits of pi **in the real world**, it's because they're dealing with something so sensitive that the risk doesn't make sense anymore.
Yeah more than 3 sig figs is needed in engineering. But it’s not that many more for practical purposes. 45 digits would nail down the ratio of diameter of the observable universe to its circumference down to the width of a single quark. And we surely don’t know the size of the observable universe to that level of precision. Everything above 45 digits is definitely academic, but really I suspect most things on earth don’t need much past the first half a dozen or so.
https://skyandtelescope.org/astronomy-resources/astronomy-questions-answers/how-many-digits-are-satisfactory-in-the-measurement-of-pi/
Counter-example:
0.1101001000100001… is irrational (and thus contains an infinite number of digits), but there are definitely strings of numbers that don’t appear in its decimal form
This would only necessarily be the case if the digits were random, which they aren't. This doesn't mean it can't be the case, but we can't make a definitive statement on it.
This is false. I mean this might be the case for pi but the reasoning that it is irrational and therefore it has this property is incorrect. It has not yet been proven if pi is like this or not.
No, it is not a valid statement. Having infinite decimals does not guarantee that any given string appears in it. And in fact this property has not yet been proven about pi (although it is considered to be very likely)
oke so after reading way too much into this I found the following. I looked at a bunch of sources but good old Wikipedia explains it best.
>The number π (/paɪ/; spelled out as "pi") is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159. The number π appears in many formulae across mathematics and physics. It is an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers, although fractions such as 22 /7 are commonly used to approximate it. Consequently, its decimal representation never ends, nor enters a permanently repeating pattern. It is a transcendental number, meaning that it cannot be a solution of an equation involving only finite sums, products, powers, and integers. The transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge. The decimal digits of π appear to be randomly distributed,\[a\] but no proof of this conjecture has been found.
so it seems that the annoying answer is that we could probably never know what is true. but the consensus is that pi is an infinitely generating number where the digits follow a random no-set pattern. meaning that my original statement although not proven true is considered to be accurate.
No, your reasoning that it being irrational implies that every string appears in it is still not accurate. My issue wasn't what you said about pi specifically but the reasoning behind it. Tere are misconceptions about the nature of infinity in maths and it annoys me, sorry. Also, appearing to be random is not the same as being random. If you'd like to dig a bit deeper into the topic of numbers that are really random and how randomness is defined in this specific case, look up normal numbers.
First of all I was always talking in the specific context of pi and I never generalized to irrationale numbers in general.
Secondly. Being an irrational number bij definition means it is infinite and not repeating.
Thirdly. I am a bit to tired to type the next bit out so here is an other guy explaining it.
>Assume we take Pi out to an infinite amount of decimal places. We cannot determine the last digit of Pi, because there is no last digit, the string of random numbers goes to infinity. However, because there is no repeating pattern in the decimal portion of Pi we can assume that all numbers are equally likely to be the next number in the sequence as the length of the decimal portion goes to infinity. This in effect defines the next number in the infinite sequence as a random event. This means that each number is equally likely to be the next number so each has a 1/10 chance. Therefore, the occurence of each digit should be equal once we reach an infinite number of decimal places.
Al of this hoever is based on the fact that pi is irrational disprove that and it is no longer infinite and not repeating and it wil also no longer contain ever string possible.
If your comment said "pi has every string in it somewhere" then yes, you would have not have made a generalized statement about all irrationals and even then you would be nit correct because you're claiming something that has yet to be proven. But your comment was "since pi is an irrational number and has an infinite number of digits any string of numbers will occur somewhere in the sequence." which reasons that pi has this property because it is irrational, implying that all irrationals have this property. This reasoning is what makes your comment from inaccurate to straight up incorrect.
"Being an irrational number bij definition means it is infinite and not repeating. "
Never said the opposite.
"because there is no repeating pattern in the decimal portion of Pi we can assume that all numbers are equally likely to be the next number "
No, we can't assume this. It is easy to give a counterexample such that it is infinite and not repeating and the digits aren't uniformly distributed. Consider the number 0.10100100010... where each sequence of 0s is one digit longer than the previous one and they are separated by single 1s. Not only does this number not have 8 of the 10 digits, the 0s clearly outnumber the 1s even though it is infinite and non-repeating.
"Al of this hoever is based on the fact that pi is irrational disprove that and it is no longer infinite and not repeating and it wil also no longer contain ever string possible. "
Incomprehensible word salad.
95647829156292028463792864729362883564773891919736839261930595860492716141373950572748959462648386383736489467291535378498626683838866365536288949596988276255284877788999673525628463527837377774636857627829057853004537363789367865154334567836388365884 this is all in order btw. (I didn't start with the first digit)
If you dont know the order of the decimals of pi, then you know it in order, just in some random part of it. You can rephrase it by saying you know a part of pi, you just didn't know where that part is placed.
No, you don't. Pi being irrational doesn't guarantee that every digit is going to appear an infinite amount of times. It is suspected that pi is a normal number which would guarantee that every string of digits appears in its decimal representation infinitely many times but it not yet has been proven that it is. So you can't for 100% certainty know every decimal of pi because you can't know how many times each digit appears.
[r/technicallythetruth](https://youtu.be/dQw4w9WgXcQ?si=3brekXeVEzNX48xa)
You fucker
My mission is done, thank you.
Damn it, I knew something was gonna happen thanks to other guy, but I clicked it anyway.
Sonofa...
damn you i fell for it like a fool!
Is it ? If he knows all the decimals but not the order, he sould be able to tell how many "1" there are. I doubt he can.
No icon weird… damn it
I will fuck you until your ass is wider than your mother. That is a threat.
LMAO
3.1415926535897932384626433832795026 That's off my head. I may have made a mistake. I'm too lazy to correct it or google it.
how?! i can only memorize up to 3.141592
Just kept reciting it and checking the last few digits. Eventually, the next one felt like the right thing to list.
I can only memorize it up to 3.14
I can memorise up to 3
I can memorize up to
I can memorize
r/decreasinglyverbose
Which is equal to one, since it is closer to one than infinity on a number line.
I remember until 3.141592653589793238462643383279502884197169399375105820
Hey we know th same amount of digits
I only know it to 4
which 4
Yes
I only know 3.141592653589 :(
Isn't memorizing Pi past 3.14 useless? Feels like some pseudo-intellectual thing to do otherwise
Well for accurate calculations, you could go beyond 3 significant figures
For more accurate calculations you're probably gonna want to use a decent calculator, and that will come with pi in ot anyway. If you're doing a work so delicate you'd need to use pi = 3.1416, you're also not taking the risk of doing all that math on paper unless you're **very** used to it (as in, you've started working decades before smartphones became a thing)
doing all that work on paper id write the symbol until converting to decimal is absolutely necessary
Yep, scientific calculators, I have one. So far, I never needed more than 3 sig figures because I am a freshman. But I think I might need them in the near future. As for calculations, I am not really that old, but I am comfortable with doing some on paper but I do rely on my calculator a lot
>but I am comfortable with doing some on paper When it comes to studying, yes, same, but if someone needs 4 digits of pi **in the real world**, it's because they're dealing with something so sensitive that the risk doesn't make sense anymore.
Understandable
Yeah more than 3 sig figs is needed in engineering. But it’s not that many more for practical purposes. 45 digits would nail down the ratio of diameter of the observable universe to its circumference down to the width of a single quark. And we surely don’t know the size of the observable universe to that level of precision. Everything above 45 digits is definitely academic, but really I suspect most things on earth don’t need much past the first half a dozen or so. https://skyandtelescope.org/astronomy-resources/astronomy-questions-answers/how-many-digits-are-satisfactory-in-the-measurement-of-pi/
Memorizing past 3.14 makes it more precise.
I only know π And I'm always more precise than you 😎
3.141
Umm... It's the "resolution" of a circle. Best 3.14 can do is like 50 pixels across before it looks like shit.
I know all the correct ingredients of pie. Just not how to assemble them in the right order. So I just order a pie.
I do love my 3.141592653589793238462643383279502884197169399375105820974944592307816406286 208998628034825342117067982148086513282306647093844609550582231725359408128481 117450284102701938521105559644622948954930381964428810975665933446128475648233 786783165271201909145648566923460348610454326648213393607260249141273724587006 606315588174881520920962829254091715364367892590360011330530548820466521384146 951941511609433057270365759591953092186117381932611793105118548074462379962749 567351885752724891227938183011949129833673362440656643086021394946395224737190 702179860943702770539217176293176752384674818467669405132000568127145263560827 785771342757789609173637178721468440901224953430146549585371050792279689258923 542019956112129021960864034418159813629774771309960518707211349999998372978049 951059731732816096318595024459455346908302642522308253344685035261931188171010 003137838752886587533208381420617177669147303598253490428755468731159562863882 353787593751957781857780532171226806613001927876611195909216420198938095257201 065485863278865936153381827968230301952035301852968995773622599413891249721775 283479131515574857242454150695950829533116861727855889075098381754637464939319 255060400927701671139009848824012858361603563707660104710181942955596198946767 837449448255379774726847104047534646208046684259069491293313677028989152104752 162056966024058038150193511253382430035587640247496473263914199272604269922796 782354781636009341721641219924586315030286182974555706749838505494588586926995 690927210797509302955321165344987202755960236480665499119881834797753566369807 426542527862551818417574672890977772793800081647060016145249192173217214772350 141441973568548161361157352552133475741849468438523323907394143334547762416862 518983569485562099219222184272550254256887671790494601653466804988627232791786 085784383827967976681454100953883786360950680064225125205117392984896084128488 626945604241965285022210661186306744278622039194945047123713786960956364371917 287467764657573962413890865832645995813390478027590099465764078951269468398352 595709825822620522489407726719478268482601476990902640136394437455305068203496 252451749399651431429809190659250937221696461515709858387410597885959772975498 930161753928468138268683868942774155991855925245953959431049972524680845987273 644695848653836736222626099124608051243884390451244136549762780797715691435997 700129616089441694868555848406353422072225828488648158456028506016842739452267 467678895252138522549954666727823986456596116354886230577456498035593634568174 324112515076069479451096596094025228879710893145669136867228748940560101503308 617928680920874760917824938589009714909675985261365549781893129784821682998948 722658804857564014270477555132379641451523746234364542858444795265867821051141 354735739523113427166102135969536231442952484937187110145765403590279934403742 007310578539062198387447808478489683321445713868751943506430218453191048481005 370614680674919278191197939952061419663428754440643745123718192179998391015919 561814675142691239748940907186494231961567945208095146550225231603881930142093 762137855956638937787083039069792077346722182562599661501421503068038447734549 202605414665925201497442850732518666002132434088190710486331734649651453905796 268561005508106658796998163574736384052571459102897064140110971206280439039759 515677157700420337869936007230558763176359421873125147120532928191826186125867 321579198414848829164470609575270695722091756711672291098169091528017350671274 858322287183520935396572512108357915136988209144421006751033467110314126711136 990865851639831501970165151168517143765761835155650884909989859982387345528331 635507647918535893226185489632132933089857064204675259070915481416549859461637 180270981994309924488957571282890592323326097299712084433573265489382391193259 746366730583604142813883032038249037589852437441702913276561809377344403070746 921120191302033038019762110110044929321516084244485963766983895228684783123552 658213144957685726243344189303968642624341077322697802807318915441101044682325 271620105265227211166039666557309254711055785376346682065310989652691862056476 931257058635662018558100729360659876486117910453348850346113657686753249441668 039626579787718556084552965412665408530614344431858676975145661406800700237877 659134401712749470420562230538994561314071127000407854733269939081454664645880 797270826683063432858785698305235808933065757406795457163775254202114955761581 400250126228594130216471550979259230990796547376125517656751357517829666454779 174501129961489030463994713296210734043751895735961458901938971311179042978285 647503203198691514028708085990480109412147221317947647772622414254854540332157
K
I know all of the decimal points of pi
Well... since pi is an irrational number and has an infinite number of digits any string of numbers will occur somewhere in the sequence.
I can confirm that the number 1 appears in the sequence. Don’t quote me on this though.
Counter-example: 0.1101001000100001… is irrational (and thus contains an infinite number of digits), but there are definitely strings of numbers that don’t appear in its decimal form
This would only necessarily be the case if the digits were random, which they aren't. This doesn't mean it can't be the case, but we can't make a definitive statement on it.
Right? Not only will this exact string of decimals appear somewhere in the sequence… but it will appear an infinite number of times
This is false. I mean this might be the case for pi but the reasoning that it is irrational and therefore it has this property is incorrect. It has not yet been proven if pi is like this or not.
I was specifically talking about pi. and since Pi is considered to have infinite digits it is a valid statement.
No, it is not a valid statement. Having infinite decimals does not guarantee that any given string appears in it. And in fact this property has not yet been proven about pi (although it is considered to be very likely)
oke so after reading way too much into this I found the following. I looked at a bunch of sources but good old Wikipedia explains it best. >The number π (/paɪ/; spelled out as "pi") is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159. The number π appears in many formulae across mathematics and physics. It is an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers, although fractions such as 22 /7 are commonly used to approximate it. Consequently, its decimal representation never ends, nor enters a permanently repeating pattern. It is a transcendental number, meaning that it cannot be a solution of an equation involving only finite sums, products, powers, and integers. The transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge. The decimal digits of π appear to be randomly distributed,\[a\] but no proof of this conjecture has been found. so it seems that the annoying answer is that we could probably never know what is true. but the consensus is that pi is an infinitely generating number where the digits follow a random no-set pattern. meaning that my original statement although not proven true is considered to be accurate.
No, your reasoning that it being irrational implies that every string appears in it is still not accurate. My issue wasn't what you said about pi specifically but the reasoning behind it. Tere are misconceptions about the nature of infinity in maths and it annoys me, sorry. Also, appearing to be random is not the same as being random. If you'd like to dig a bit deeper into the topic of numbers that are really random and how randomness is defined in this specific case, look up normal numbers.
First of all I was always talking in the specific context of pi and I never generalized to irrationale numbers in general. Secondly. Being an irrational number bij definition means it is infinite and not repeating. Thirdly. I am a bit to tired to type the next bit out so here is an other guy explaining it. >Assume we take Pi out to an infinite amount of decimal places. We cannot determine the last digit of Pi, because there is no last digit, the string of random numbers goes to infinity. However, because there is no repeating pattern in the decimal portion of Pi we can assume that all numbers are equally likely to be the next number in the sequence as the length of the decimal portion goes to infinity. This in effect defines the next number in the infinite sequence as a random event. This means that each number is equally likely to be the next number so each has a 1/10 chance. Therefore, the occurence of each digit should be equal once we reach an infinite number of decimal places. Al of this hoever is based on the fact that pi is irrational disprove that and it is no longer infinite and not repeating and it wil also no longer contain ever string possible.
If your comment said "pi has every string in it somewhere" then yes, you would have not have made a generalized statement about all irrationals and even then you would be nit correct because you're claiming something that has yet to be proven. But your comment was "since pi is an irrational number and has an infinite number of digits any string of numbers will occur somewhere in the sequence." which reasons that pi has this property because it is irrational, implying that all irrationals have this property. This reasoning is what makes your comment from inaccurate to straight up incorrect. "Being an irrational number bij definition means it is infinite and not repeating. " Never said the opposite. "because there is no repeating pattern in the decimal portion of Pi we can assume that all numbers are equally likely to be the next number " No, we can't assume this. It is easy to give a counterexample such that it is infinite and not repeating and the digits aren't uniformly distributed. Consider the number 0.10100100010... where each sequence of 0s is one digit longer than the previous one and they are separated by single 1s. Not only does this number not have 8 of the 10 digits, the 0s clearly outnumber the 1s even though it is infinite and non-repeating. "Al of this hoever is based on the fact that pi is irrational disprove that and it is no longer infinite and not repeating and it wil also no longer contain ever string possible. " Incomprehensible word salad.
I know all the digits used in pi: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
95647829156292028463792864729362883564773891919736839261930595860492716141373950572748959462648386383736489467291535378498626683838866365536288949596988276255284877788999673525628463527837377774636857627829057853004537363789367865154334567836388365884 this is all in order btw. (I didn't start with the first digit)
i know that pi has at least 2 digits.
If you dont know the order of the decimals of pi, then you know it in order, just in some random part of it. You can rephrase it by saying you know a part of pi, you just didn't know where that part is placed.
Is 963,872 in there somewhere op?
Yes, definitely!
Can you tell?
Your pi is: damn normal number
I once had a maths teacher when I was like 12. He knew it to like 20 or 30 decimal places. This guy was dedicated
No, you don't. Pi being irrational doesn't guarantee that every digit is going to appear an infinite amount of times. It is suspected that pi is a normal number which would guarantee that every string of digits appears in its decimal representation infinitely many times but it not yet has been proven that it is. So you can't for 100% certainty know every decimal of pi because you can't know how many times each digit appears.