Approximating Irrational Numbers (Duffin-Schaeffer Conjecture) - Numberphile
video description
-You don''t use an accountant to tell you how much profit you will make. you use them afterwards to tell you why you made so little-. or another way --accountants are there to knife the wounded-.
In the above you could have used Mathematician instead of accountant with engineering projects that went wrong.
Engineers will tend to use high precision numerical mathematics when calculating stresses, strains etc and Pi would be to a similar accuracy.
Date: 2022-04-09
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Comments and reviews: 9
John
When I worked for a lumber company, the in-house woodworker was using 22/7 (3. 142857) for pi, and forced to make all sorts of compromises on his measurements to approximate values. He knew I was into math and asked me to find a 'shop value' for pi. I came up with 3-9/64 (3. 140625--no dots, and found it was accurate (just slightly over) to about 8 feet circumferences. This was ideal for him, as he worked mostly on smaller wood-shop projects. He loved it. I present here knowing that there is no new thing under the sun--someone must have thought of this decades ago!
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When I worked for a lumber company, the in-house woodworker was using 22/7 (3. 142857) for pi, and forced to make all sorts of compromises on his measurements to approximate values. He knew I was into math and asked me to find a 'shop value' for pi. I came up with 3-9/64 (3. 140625--no dots, and found it was accurate (just slightly over) to about 8 feet circumferences. This was ideal for him, as he worked mostly on smaller wood-shop projects. He loved it. I present here knowing that there is no new thing under the sun--someone must have thought of this decades ago!
reply
adir
I'm sorry to tell you, but that 'machine' is useless.
ALL fractions, with no exception, are a perfect approximation to an infinite number of irrational numbers.
Just add 0. 0000. 0003141592.
Where the 3 dots in the center is Graham's number of zeros.
And the 3 dots at the end is any irrational number.
You'll get an infinite amount of numbers, that are practically perfectly approximated with a fraction.
reply
I'm sorry to tell you, but that 'machine' is useless.
ALL fractions, with no exception, are a perfect approximation to an infinite number of irrational numbers.
Just add 0. 0000. 0003141592.
Where the 3 dots in the center is Graham's number of zeros.
And the 3 dots at the end is any irrational number.
You'll get an infinite amount of numbers, that are practically perfectly approximated with a fraction.
reply
Brendan
James has previously noted that 2 is the most problematic prime number, in that it is an exception to many generalizations about prime numbers. Similarly 3 is incredibly problematic although less than 2. I would love to hear a numberphile video about the smallest prime that is a less frequent exception in proofs about primes than a prime smaller than it.
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James has previously noted that 2 is the most problematic prime number, in that it is an exception to many generalizations about prime numbers. Similarly 3 is incredibly problematic although less than 2. I would love to hear a numberphile video about the smallest prime that is a less frequent exception in proofs about primes than a prime smaller than it.
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thierry
His humility and relativism! He said -really complicated problems and subtle problems that we really don't understand very well at all as mathematicians-. Wow! He lets the door open to some magician, priest or spiritual guru to claim understanding it better than him?
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His humility and relativism! He said -really complicated problems and subtle problems that we really don't understand very well at all as mathematicians-. Wow! He lets the door open to some magician, priest or spiritual guru to claim understanding it better than him?
reply
Jithin
I'm 26 years old and i just realized 22/7 is an approximation of pi. I was confused when he said pi is irrational and I was thinking ' wait. Isn't pi 22/7? That seems rational. ' because i was taught in school that pi was 22/7. I've been lied to!
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I'm 26 years old and i just realized 22/7 is an approximation of pi. I was confused when he said pi is irrational and I was thinking ' wait. Isn't pi 22/7? That seems rational. ' because i was taught in school that pi was 22/7. I've been lied to!
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Doug
I memorised pi to IEEE-754 double precision (precise to about 1 part in 2-53): 3. 14159265358979323. I find it quite easy to remember actually, for some reason. I think I remember the 1415 and 9265 35 8979 323 as single things.
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I memorised pi to IEEE-754 double precision (precise to about 1 part in 2-53): 3. 14159265358979323. I find it quite easy to remember actually, for some reason. I think I remember the 1415 and 9265 35 8979 323 as single things.
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douro20
It's nice to see that we are still discovering new things about the types of mathematics the ancient Greeks and Chinese were working with. I'd personally like to know how Zu Chongzhi came up with 355/113.
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It's nice to see that we are still discovering new things about the types of mathematics the ancient Greeks and Chinese were working with. I'd personally like to know how Zu Chongzhi came up with 355/113.
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SchrodingerBraCat
The zoo (of irrational numbers) and the regions outside the zoo are both infinite.
But the zoo is _bigger_ than the regions outside the zoo (the rational numbers.
Go figure!
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The zoo (of irrational numbers) and the regions outside the zoo are both infinite.
But the zoo is _bigger_ than the regions outside the zoo (the rational numbers.
Go figure!
reply
David
so what is the really simple test, and what are the special, cases. eg can q be primes, squares, n-2-n. and when he says almost all numbers does he mean almost all alpha or all, ost all q
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so what is the really simple test, and what are the special, cases. eg can q be primes, squares, n-2-n. and when he says almost all numbers does he mean almost all alpha or all, ost all q
reply
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