Can you show some finite and clear exact representations of π?

Sure! In 1841 Karl Weierstrass [ https://en.wikipedia.org/wiki/Karl_Weierstrass ] defined [math]\pi[/math] directly as an integral: [math]\quad\displaystyle\pi=\int_{-\infty}^{+\infty}\frac{\te…

Top stories for Long   Can you show some finite and clear exact representations of π? Alan Bustany, Trinity Wrangler, 1977 IMO • Answered March 20, 2018 Sure! In 1841 Karl Weierstrass defined [math]\pi[/math] directly as an integral: [math]\quad\displaystyle\pi=\int_{-\infty}^{+\infty}\frac{\text dx}{1+x^2}[/math] If you want finite bounds on the integral you can use: [math]\quad\displaystyle\pi=\int_{-1}^{+1}\frac{\text dx}{\sqrt{1-x^2}}=2\int_{-1}^{+1}\sqrt{1-x^2}\text dx[/math] Or you can use trigonometric functions: [math]\quad\displaystyle\pi=4\arctan1[/math] Or other functi... Read more » 213 16   Have you ever seen an employer fire someone without realizing what a crucial role the employee played? Bug-Z • Answered March 2, 2025 I once saw an employer play "lay off a whole department and replace with cheaper employees" with every department. They kept the occasional employee who was willing to deba... Read more » 576 21   Is a creatinine level of 1.21 dangerous? Theodore Kirsten, Mastermind (2009-present) • Answered January 20 I am a 54-year-old male. My creatinine level was 1.4, and I managed to decrease it to 1.0 with lifestyle changes within one month. Alcohol intake reduced from the baseline o... Read more » 221 12   Why did Perl lose to Python? Dale Gulledge, Real time software developer for mumble years • Answered November 3 As someone who used to user Perl a lot and now uses Python, I can tell why I switched. Perl 6 took an incredibly long time to arrive. It was almost the mirror image of what ... Read more » 95 17   Why should CPU and RAM be separated? Why can't we combine them into one "entity" knowing that the CPU is much faster? Brett Bergan, Building PC's for 30 years • Updated February 22, 2021 I finished building my first PC in December of 1996. It had 16MB of RAM. I remember one Saturday morning staring at my plywood bookshelf thinking how awesome it would be wh... Read more » 1.2K 79   Have you ever confronted a seat kicker on a flight, and what ended up happening when you did? Bob Wilson, Flew 20 times a year for 20 years. • Answered January 18 Yes I did, it was a boy about 4. I leaned over the seat and very calmly told him that it bothered me when he did that. He completely ignored me, and kept kicking the seat w... Read more » 4.8K 203   My landlord hasn't picked up rent for almost 1 year. He doesn't answer the phone or text. What could happen? Shane Conneely • Answered June 24, 2025 Something similar had happened some college friends of mine. Their landlord had gotten divorced and had moved to Saudi and then he just vanished. The bank account that they... Read more » 593 71   Does marijuana lower or increase blood pressure? Brian Butler, former Combat Medic at Retired US Army Combat Vet • Answered March 11, 2024 I am a retired medic. I have high blood pressure and I have been doing my own little research and study on cannabis and blood pressure. So far I have not taken any blood pr... Read more » 1.6K 220   Would a 20mm machine gun be effective against infantry? Roland Bartetzko, Logistics in Ukraine (2022-present) • Answered February 7 I was a 20mm gunner in the German Army on three different platforms: the "Luchs" armored reconnaissance vehicle, as well as the "Kraka" and the "Wiesel" airborne weapons ca... Read more » 1.2K 52   How true is it that saying "arigato" at a store would be acceptable for a foreigner but rude for a native Japanese? Paul Richter, lives in Tokyo • Answered February 4 I assume this about the customer saying "arigato", after the purchase has been completed and the salesperson has thanked the customer. It wouldn't be rude if said by anybody... Read more » 296 14   Why is factoring numbers into primes a difficult problem? Alon Amit, CS degree and many years of coding. • Updated July 28, 2015 I must, sadly, disagree with the posted answers that point to the chaotic distribution of primes as the reason. This has nothing to do with the problem of factorization. Fi... Read more » 743 35   Which actresses aged like a fine wine? Peeyush Bhatnagar, I have read about the life of many celebrities. • Answered January 21 I personally feel Salma Hayek has cracked the code to aging gracefully. Over the years, it feels like she is somehow aging in reverse. She credits her youthful appearance, e... Read more » 2.2K 132 Read more in your feed

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Why do people use Linux on their PCs?

My answer is simply anger. I use(d) a Microsoft surface pro for 5 years for office work it was my favourite lightweight laptop/ tablet device. No problems, but there is no upgrade path for this …

Top stories for Long   Why do people use Linux on their PCs? Rob Edyvane, BA from University of Oxford • Answered December 22 My answer is simply anger. I use(d) a Microsoft surface pro for 5 years for office work it was my favourite lightweight laptop/ tablet device. No problems, but there is no ... Read more » 156 20   Is yellowish urine a sign of diabetes type 2? Arnold Milan, Party Time Nurse (2002-present) • Answered January 18 No. If you have diabetes, your urine will taste sweet. The yellowness in the urine appears due to bilirubin. It gives the brown color to feces as well. You could be not drinki... Read more » 589 65   Have you ever seen an employer fire someone without realizing what a crucial role the employee played? Bug-Z • Answered March 2, 2025 I once saw an employer play "lay off a whole department and replace with cheaper employees" with every department. They kept the occasional employee who was willing to deba... Read more » 576 21   Why is factoring numbers into primes a difficult problem? Alon Amit, CS degree and many years of coding. • Updated July 28, 2015 I must, sadly, disagree with the posted answers that point to the chaotic distribution of primes as the reason. This has nothing to do with the problem of factorization. Fi... Read more » 743 35   How true is it that saying "arigato" at a store would be acceptable for a foreigner but rude for a native Japanese? Paul Richter, lives in Tokyo • Answered February 4 I assume this about the customer saying "arigato", after the purchase has been completed and the salesperson has thanked the customer. It wouldn't be rude if said by anybody... Read more » 296 14   Would a 20mm machine gun be effective against infantry? Roland Bartetzko, Logistics in Ukraine (2022-present) • Answered February 7 I was a 20mm gunner in the German Army on three different platforms: the "Luchs" armored reconnaissance vehicle, as well as the "Kraka" and the "Wiesel" airborne weapons ca... Read more » 1.2K 50   Why are capacitors used in fans? Unnikrishnan Menon, Electronics buff • Updated February 15, 2018 I'm sure you all must have seen these curious little capacitors popping out from your ceiling fans… An ordinary ceiling fan (a split-phase induction motor) essentially consi... Read more » 656 35   Why do marathon runners often get sick immediately after finishing a race? Amy Martin • Answered January 28 Crossing the finish line of a marathon is a moment of athletic triumph, but biologically, it is a moment of extreme vulnerability. For the first 3 to 72 hours after the rac... Read more » 188 13   Why is C faster than C++? Sid Wanderleaf, knows English • Answered February 9 To the extent it is, it's because of classes. More specifically, dynamic polymorphism (any time "virtual" enters the picture). They were great for the 1980s and '90s; but by ... Read more » 63 3   If a trader makes 100–200% annual returns, then how is Warren Buffett the best investor in the world? John Roberson, Stock Trader • Updated June 17, 2017 I'm a professional trader. I know a lot of people who have put up massive returns for 10+ years. But not one is in Warren Buffett's league. Why? Buffett can take advantage of... Read more » 11.9K 335   Why can't Linux read NTFS drives? John Thorpe • Answered December 24 Errr, my laptop can read the vestigial windows drive just fine. I keep Windows for the very rare occasions I need to test something on it. The problem is that NTFS is propri... Read more » 217 38   Kudzu is easy to grow, it hides the ground well, and it can be used as feed for cows, so why is it considered undesirable in the US? Asked in Ask Daddy • Answered by Dormas • October 28 Many people thought the same way you did. America in the 1800s imported arrowroot for exactly that reason. I thought it was a very good idea at the time. Unfortunately, they... Read more » 2.2K 127 Read more in your feed

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