742 may be "just a number", but I know why the "Simpsons'" writers picked it. Creator Matt Groening grew up in 742 Evergreen Terrace, Portland, Oregon.
+Kimberly Rae Actually no non-zero rational number solutions but, of course, this follows directly from the fact that there are no positive integer solutions. For all non-zero integers _i_, _j_ and _k_ and all positive integers _x_, _y_, _z_ and _n_, (_i_/_x_)^_n_ + (_j_/_y_)^_n_ = (_k_/_z_)^_n_ iff (_iyz_)^_n_ + (_jxz_)^_n_ = (_kxy_)^_n_ Let _a_ = | _iyz_ | _b_ = | _jxz_ | _c_ = | _kxy_ | These are all positive integers. So, supposing that there is a solution to the above equation, here's what we get. If _n_ is even, then _a_^_n_ + _b_^_n_ = _c_^_n_ If _n_ is odd and _i_, _j_ and _k_ are positive, then _a_^_n_ + _b_^_n_ = _c_^_n_ If _n_ is odd and _i_, _j_ and _k_ are negative, then (multiplying both sides by -1) _a_^_n_ + _b_^_n_ = _c_^_n_ If _n_ is odd, _i_ is negative and _j_ and _k_ are positive, then (rearranging) _a_^_n_ + _c_^_n_ = _b_^_n_ If _n_ is odd, _i_ is positive and _j_ and _k_ are negative, then (rearranging) _a_^_n_ + _c_^_n_ = _b_^_n_ If _n_ is odd, _j_ is negative and _i_ and _k_ are positive, then (rearranging) _b_^_n_ + _c_^_n_ = _a_^_n_ If _n_ is odd, _j_ is positive and _i_ and _k_ are negative, then (rearranging) _b_^_n_ + _c_^_n_ = _a_^_n_ If _n_ is odd, _k_ is positive and _i_ and _j_ are negative, there'll be a positive on one side and a negative on the other. The same will happen if _n_ is odd, _k_ is negative and _i_ and _j_ are positive. There'd be no solution possible to this. So, if there exists a non-zero rational solution, there must exist a positive integer solution.
+jimpozcaner this is complicated. (a/b)^n+(c/d)^n=(e/f)^n Multiply by (bdf)^n (adf)^n+(cbf)^n=(ebd)^n No numbers can fit this equation, so no numbers can fit the first one, so there are no rational solutions
+Patrick Wienhöft oh and for negatives: a^n+b^n=c^n When n is even, x^n = (-x)^n, so that doesn't change anything. When n is uneven: a, b and c negative: multiply by -1 and you have Fermat. c negative: left side positive, right side negative => impossible a or b negative: add the negative one ^n to both sides and you get fermat any two negative: multiply by -1 and use one of the two options above. For rational n that works very similar. However I can't prove it for irrational n and rational a,b,c that quickly
The association of the main numbers in the field of mathematics with each other, reflects numerical sequences that correspond to the dimensions of the Earth, the Moon, and the Sun in the unit of measurement in meters, which is: 1' (second) / 299792458 m/s (speed of light in a vacuum). Perfect Number: 8,128 is the fourth of the numbers considered perfect. Earth's equatorial diameter 12,756 km. 8,128 / 12,756 x (10^4) = 6,371.90 Earth's average radius: 6,371 km. Golden Angle: 137.5 Perfect Number: 8.128 Pi: 3.14 (137.5 ^ 3.14) / 8.128 x 10 - 1 = 6,371.16 Earth's average radius: 6,371 km. Ramanujan number: 1,729 Earth's equatorial radius: 6,378 km. Golden number: 1.61803... • (1,729 x 6,378 x (10^-3)) ^1.61803 x (10^-3) = 3,474.18 Moon's diameter: 3,474 km. Ramanujan number: 1,729 Speed of light: 299,792,458 m/s Earth's Equatorial Diameter: 12,756 km. Earth's Equatorial Radius: 6,378 km. • (1,729 x 299,792,458) / 12,756 / 6,378) = 6,371 Earth's average radius: 6,371 km. The Cubit The cubit = Pi - phi^2 = 0.5236 Lunar distance: 384,400 km. (0.5236 x (10^6) - 384,400) x 10 = 1,392,000 Sun´s diameter: 1,392,000 km. Higgs Boson: 125.35 (GeV) Phi: 1.61803... (125.35 x (10^-1) - 1.61803) x (10^3) = 10,916.97 Circumference of the Moon: 10,916 km. Golden number: 1.618 Golden Angle: 137.5 Earth's equatorial radius: 6,378 Universal Gravitation G = 6.67 x 10^-11 N.m^2/kg^2. (((1.618 ^137.5) / 6,378) / 6.67) x (10^-20) = 12,756.62 Earth’s equatorial diameter: 12,756 km. The Euler Number is approximately: 2.71828... Newton’s law of gravitation: G = 6.67 x 10^-11 N.m^2/kg^2. Golden number: 1.618ɸ (2.71828 ^ 6.67) x 1.618 x 10 = 12,756.23 Earth’s equatorial diameter: 12,756 km. Planck’s constant: 6.63 × 10-34 m2 kg. Circumference of the Moon: 10,916. Gold equation: 1,618 ɸ (((6.63 ^ (10,916 x 10^-4 )) x 1.618 x (10^3)= 12,756.82 Earth’s equatorial diameter: 12,756 km. Planck's temperature: 1.41679 x 10^32 Kelvin. Newton’s law of gravitation: G = 6.67 x 10^-11 N.m^2/kg^2. Speed of Sound: 340.29 m/s (1.41679 ^ 6.67) x 340.29 - 1 = 3,474.81 Moon's diameter:: 3,474 km. Cosmic microwave background radiation 2.725 kelvins ,160.4 GHz, Pi: 3.14 Earth's polar radius: 6,357 km. ((2,725 x 160.4) / 3.14 x (10^4) - (6,357 x 10^-3) = 1,392,000 The diameter of the Sun: 1,392,000 km. Numbers 3, 6 & 9 - Nikola Tesla One Parsec = 206265 AU = 3.26 light-years = 3.086 × 10^13 km. The Numbers: 3, 6 and 9 ((3^6) x 9) - (3.086 x (10^3)) -1 = 3,474 The Moon's diameter: 3,474 km. Now we will use the diameter of the Moon. Moon's diameter: 3,474 km. (3.474 + 369 + 1) x (10^2) = 384,400 The term L.D (Lunar Distance) refers to the average distance between the Earth and the Moon, which is 384,400 km. Moon's diameter: 3,474 km. ((3+6+9) x 3 x 6 x 9) - 9 - 3 + 3,474 = 6,378 Earth's equatorial radius: 6,378 km. Book: Orion. The Connection between Heaven and Earth eBook / By: Gustavo Muniz
You started it! It would mean there is no such thing as an uninteresting number; each boring number being converted in turn infinitely. The *"King's Paradox"* Sounds impressive to me.
***** 1.This still has absolutely nothing to do with Fermat's last theorem. 2.Why would someone even post a comment retelling what that guy said in the video?
+Sebastian Portalatin The theorem says that x, y and z are all integers - so there are no solutions for it at all because it doesn't fit with the hypothesis; of course if you don't care what type of numbers x,y and z are there are an infinite number of solutions for any value of n - but that's boring.
I think a lot a time was passed , I don't have interest in solution, but, the real solution is laying in Murgu Millennium Equations and I was hoping Mr. Andrew will adapt it to those equations even if a part are named God Equations Of Balance. But when?#MurguMillenniumEquations explain P versus NP impossible for a pure computer.
8 ปีที่แล้ว +2
Matt Groening created both The Simpsons and Futurama.
+CyberSERT Of course there are, but there are also an infinite number of numbers that aren't... "Not many" refers to the sparseness of the set - if you pick a natural number at random how likely is it to be the sum of two primes. Measuring fractions of infinite sets (of equal cardinality) is a difficult problem.
F ∝ RAI^2 where F=failure of attempt to look cool, Rh=ridiculousness of haircut and A=age of wearer. I=intelligence (Squared because of his squareness)
Fermat's Great Theorem 1637 - 2016 ! I have proved on 09/14/2016 the ONLY POSSIBLE proof of the Great Fermat's Last Theorem . I can pronounce the formula for the proof of Fermat's Great Theorem: 1 - Fermath's great theorem NEVER! and nobody! NOT! HAS BEEN PROVEN !!! 2 - proven! THE ONLY ONE!!! - POSSIBLE! proof of Fermat's last theorem !!! 3 - Fermat's Great Theorem is proved universally-proven for all numbers 4 - Fermat's Great Theorem is proven in the requirements of himself! Fermat 1637 y. 5 - Fermat's Great Theorem proved in 2 pages of a notebook 6 - Fermat's Great Theorem is proved in the apparatus of Diophantus arithmetic 7 - the proof of the great Fermat's last theorem, as well as the formulation, is easy for a student of the 5th grade of the school to understand !!! 8 - Me! opened the GREAT! A GREAT Mystery! Fermat's last theorem! (not "simple" - "mechanical" proof) Me! opened : - the GREAT! A GREAT Mystery! of the Fermat's Last theorem! (- !!! not "simple" - "mechanical" proof) Me! opened : - Pierre de Fermat - was proved! the Fermat's Last theorem! Me! opened : - my formula of my Proof is completely and absolutely identical with the words of Pierre de Fermat ! !!!!- NO ONE! and NEVER! and FOR NOTHING! NOT! will find a valid proof!
Had him as a lecturer at a physics event this week in London. Truly a fascinating speaker
Simon Singh's haircut was great. He looked like a college gangster.
One of my favorite Simpson references was to Sideshow Bob's prisoner number being 24601
Its also Marge's prisoner number in "Marge in Chains."
The last line below Fermat's last theorem is a topology shenanigan. A torus cannot be deformed to a sphere. :P
You aren't taking in to account the "donut hole". Donut shops sell donuts and donut holes. The donut is a torus while the donut holes are spheres. ;)
Poincare Conjecture. Nice
742 may be "just a number", but I know why the "Simpsons'" writers picked it. Creator Matt Groening grew up in 742 Evergreen Terrace, Portland, Oregon.
+Darrel Jones I think the most impotent bit of this number: It's where the Simpsons live.
7 + 4 + 2 = 13
Another way to look at 742 is that it is the digits 7 and 7^2 - 7.
He should not just say "There's no solution". He should say "There are no POSITIVE INTEGERS that satisfy the equation for n>2".
+ishma01 It's actually "no rational number"
+Kimberly Rae Actually no non-zero rational number solutions but, of course, this follows directly from the fact that there are no positive integer solutions.
For all non-zero integers _i_, _j_ and _k_ and all positive integers _x_, _y_, _z_ and _n_,
(_i_/_x_)^_n_ + (_j_/_y_)^_n_ = (_k_/_z_)^_n_
iff
(_iyz_)^_n_ + (_jxz_)^_n_ = (_kxy_)^_n_
Let
_a_ = | _iyz_ |
_b_ = | _jxz_ |
_c_ = | _kxy_ |
These are all positive integers. So, supposing that there is a solution to the above equation, here's what we get.
If _n_ is even, then
_a_^_n_ + _b_^_n_ = _c_^_n_
If _n_ is odd and _i_, _j_ and _k_ are positive, then
_a_^_n_ + _b_^_n_ = _c_^_n_
If _n_ is odd and _i_, _j_ and _k_ are negative, then (multiplying both sides by -1)
_a_^_n_ + _b_^_n_ = _c_^_n_
If _n_ is odd, _i_ is negative and _j_ and _k_ are positive, then (rearranging)
_a_^_n_ + _c_^_n_ = _b_^_n_
If _n_ is odd, _i_ is positive and _j_ and _k_ are negative, then (rearranging)
_a_^_n_ + _c_^_n_ = _b_^_n_
If _n_ is odd, _j_ is negative and _i_ and _k_ are positive, then (rearranging)
_b_^_n_ + _c_^_n_ = _a_^_n_
If _n_ is odd, _j_ is positive and _i_ and _k_ are negative, then (rearranging)
_b_^_n_ + _c_^_n_ = _a_^_n_
If _n_ is odd, _k_ is positive and _i_ and _j_ are negative, there'll be a positive on one side and a negative on the other. The same will happen if _n_ is odd, _k_ is negative and _i_ and _j_ are positive. There'd be no solution possible to this.
So, if there exists a non-zero rational solution, there must exist a positive integer solution.
+jimpozcaner this is complicated.
(a/b)^n+(c/d)^n=(e/f)^n
Multiply by (bdf)^n
(adf)^n+(cbf)^n=(ebd)^n
No numbers can fit this equation, so no numbers can fit the first one, so there are no rational solutions
+Patrick Wienhöft oh and for negatives:
a^n+b^n=c^n
When n is even, x^n = (-x)^n, so that doesn't change anything.
When n is uneven:
a, b and c negative: multiply by -1 and you have Fermat.
c negative: left side positive, right side negative => impossible
a or b negative: add the negative one ^n to both sides and you get fermat
any two negative: multiply by -1 and use one of the two options above.
For rational n that works very similar. However I can't prove it for irrational n and rational a,b,c that quickly
4^5√=4^4√+4^3√
The association of the main numbers in the field of mathematics with each other, reflects numerical sequences that correspond to the dimensions of the Earth, the Moon, and the Sun in the unit of measurement in meters, which is: 1' (second) / 299792458 m/s (speed of light in a vacuum).
Perfect Number: 8,128 is the fourth of the numbers considered perfect.
Earth's equatorial diameter 12,756 km.
8,128 / 12,756 x (10^4) = 6,371.90
Earth's average radius: 6,371 km.
Golden Angle: 137.5
Perfect Number: 8.128
Pi: 3.14
(137.5 ^ 3.14) / 8.128 x 10 - 1 = 6,371.16
Earth's average radius: 6,371 km.
Ramanujan number: 1,729
Earth's equatorial radius: 6,378 km.
Golden number: 1.61803...
• (1,729 x 6,378 x (10^-3)) ^1.61803 x (10^-3) = 3,474.18
Moon's diameter: 3,474 km.
Ramanujan number: 1,729
Speed of light: 299,792,458 m/s
Earth's Equatorial Diameter: 12,756 km. Earth's Equatorial Radius: 6,378 km.
• (1,729 x 299,792,458) / 12,756 / 6,378) = 6,371
Earth's average radius: 6,371 km.
The Cubit
The cubit = Pi - phi^2 = 0.5236
Lunar distance: 384,400 km.
(0.5236 x (10^6) - 384,400) x 10 = 1,392,000
Sun´s diameter: 1,392,000 km.
Higgs Boson: 125.35 (GeV)
Phi: 1.61803...
(125.35 x (10^-1) - 1.61803) x (10^3) = 10,916.97
Circumference of the Moon: 10,916 km.
Golden number: 1.618
Golden Angle: 137.5
Earth's equatorial radius: 6,378
Universal Gravitation G = 6.67 x 10^-11 N.m^2/kg^2.
(((1.618 ^137.5) / 6,378) / 6.67) x (10^-20) = 12,756.62
Earth’s equatorial diameter: 12,756 km.
The Euler Number is approximately: 2.71828...
Newton’s law of gravitation: G = 6.67 x 10^-11 N.m^2/kg^2. Golden number: 1.618ɸ
(2.71828 ^ 6.67) x 1.618 x 10 = 12,756.23
Earth’s equatorial diameter: 12,756 km.
Planck’s constant: 6.63 × 10-34 m2 kg.
Circumference of the Moon: 10,916.
Gold equation: 1,618 ɸ
(((6.63 ^ (10,916 x 10^-4 )) x 1.618 x (10^3)= 12,756.82
Earth’s equatorial diameter: 12,756 km.
Planck's temperature: 1.41679 x 10^32 Kelvin.
Newton’s law of gravitation: G = 6.67 x 10^-11 N.m^2/kg^2.
Speed of Sound: 340.29 m/s
(1.41679 ^ 6.67) x 340.29 - 1 = 3,474.81
Moon's diameter:: 3,474 km.
Cosmic microwave background radiation
2.725 kelvins ,160.4 GHz,
Pi: 3.14
Earth's polar radius: 6,357 km.
((2,725 x 160.4) / 3.14 x (10^4) - (6,357 x 10^-3) = 1,392,000
The diameter of the Sun: 1,392,000 km.
Numbers 3, 6 & 9 - Nikola Tesla
One Parsec = 206265 AU = 3.26 light-years = 3.086 × 10^13 km.
The Numbers: 3, 6 and 9
((3^6) x 9) - (3.086 x (10^3)) -1 = 3,474
The Moon's diameter: 3,474 km.
Now we will use the diameter of the Moon.
Moon's diameter: 3,474 km.
(3.474 + 369 + 1) x (10^2) = 384,400
The term L.D (Lunar Distance) refers to the average distance between the Earth and the Moon, which is 384,400 km.
Moon's diameter: 3,474 km.
((3+6+9) x 3 x 6 x 9) - 9 - 3 + 3,474 = 6,378
Earth's equatorial radius: 6,378 km.
Book: Orion. The Connection between Heaven and Earth eBook / By: Gustavo Muniz
Homer's Parker Square solution
anyone else accidentally read his name as Simpson Singh?
Fun fact: 742 is the smallest number that isn't interesting
+Christopher King
But that makes it interesting.
Yuck Fooh Shhh, you are about to cause a paradox.
You started it!
It would mean there is no such thing as an uninteresting number; each boring number being converted in turn infinitely.
The *"King's Paradox"*
Sounds impressive to me.
Christopher King
But then again if all numbers were interesting that would be boring...
+Christopher King That's interesting! Oops. I just ruined it.
1729 smallest a^2+b^2=c^3+d^3 , a=10 b=9 c=1 and d=12...its story I read in a mathematics magazine in my school days
+jdisira sorry all cubes
This has nothing to do with Fermat's last theorem.
***** I watched it, those numbers have nothing to do with Fermat's theorem. They must have the same power greater than 2, and only 3 numbers.
***** 1.This still has absolutely nothing to do with Fermat's last theorem.
2.Why would someone even post a comment retelling what that guy said in the video?
***** I've seen, and I consider them pointless.
Has anybody read the book? I've seen lots of Simon Singh's videos on youtube. Does the book have more new stuff?
Yes it’s a brilliant book. A friend lent it to me when I was about 8, and I first read it a few years ago at the age of 15. Really interesting stuff.
@@gddanielk8491 oh neat thanks!
There are plenty of solutions to that equation, just none where all numbers are integers.
+Kamizushi Akinari That's what the theorems stated. "There are no INTEGER solution."
jonyb0b13 I know that's what the theorem says, but he never actually says that in the video. It's a pretty big detail to forget don't you think?
You know... There are infinite solutions to the equations where all numbers are integers. You are literally failing at being a smartass, how pathetic.
@Fresh Rock Papa-E
Not sure if trolling or just stupid.
Wonderful!
742 is interesting, because it’s the only non-noteworthy number in the history of the Simpsons.
* INTEGER solutions, no INTEGER solutions
1729 is also the third Carmichael number (aka Fermat pseudoprime)
Yeah 742 is just a number, but I literally just got to the end at that part and my phone was 7:07... and I had 42% charge. spoooooooky
Fermat's Last Theorem and P versus NP by Ion Murgu From OHIO,USA
Ahhhhh... It irks me because the Theorem is that it has no WHOLE NUMBER solutions, not not solutions in general.
+Sebastian Portalatin The theorem says that x, y and z are all integers - so there are no solutions for it at all because it doesn't fit with the hypothesis; of course if you don't care what type of numbers x,y and z are there are an infinite number of solutions for any value of n - but that's boring.
3:26 when is the theorem mentioned in doctor who?
In the first episode with Amy the Doctor proves who he is by sending a proof of Fermat's last theorem that he calls 'the real one.'
The episode title is "The Eleventh Hour" and it was first shown in 2010.
I think a lot a time was passed , I don't have interest in solution, but, the real solution is laying in Murgu Millennium Equations and I was hoping Mr. Andrew will adapt it to those equations even if a part are named God Equations Of Balance. But when?#MurguMillenniumEquations explain P versus NP impossible for a pure computer.
Matt Groening created both The Simpsons and Futurama.
Ok
He said "Not many numbers are the sum of 2 cubes." (11:57) In fact, there is an infinite number of numbers that are the sum of 2 cubes.
+CyberSERT Of course there are, but there are also an infinite number of numbers that aren't... "Not many" refers to the sparseness of the set - if you pick a natural number at random how likely is it to be the sum of two primes. Measuring fractions of infinite sets (of equal cardinality) is a difficult problem.
#mathroasted
There are as many numbers that are sum of 2 cubes as numbers that aren't. Learn about infinite sets before talking marc.
can you gys tell me what's about the 911 number appearing in the same serie it canfused me a lot i need an answer plz . thnks
murican police phone number
badie rida да it's American 999
F ∝ RAI^2
where F=failure of attempt to look cool, Rh=ridiculousness of haircut and A=age of wearer. I=intelligence (Squared because of his squareness)
742
7*6=42
4+2=6
There's an easy to understand proof of it on my channel for those curious.
Does this mean that Fermat's last theorem is false because. He never states that any of the variable have to be whole numbers
the point of it is, he wrote a book about it, buy it
7th person before me made the 1729th view of this video...
Fermat's Great Theorem 1637 - 2016 !
I have proved on 09/14/2016 the ONLY POSSIBLE proof of the Great Fermat's Last Theorem .
I can pronounce the formula for the proof of Fermat's Great Theorem:
1 - Fermath's great theorem NEVER! and nobody! NOT! HAS BEEN PROVEN !!!
2 - proven! THE ONLY ONE!!! - POSSIBLE! proof of Fermat's last theorem !!!
3 - Fermat's Great Theorem is proved universally-proven for all numbers
4 - Fermat's Great Theorem is proven in the requirements of himself! Fermat 1637 y.
5 - Fermat's Great Theorem proved in 2 pages of a notebook
6 - Fermat's Great Theorem is proved in the apparatus of Diophantus arithmetic
7 - the proof of the great Fermat's last theorem, as well as the formulation, is easy for a student of the 5th grade of the school to understand !!!
8 - Me! opened the GREAT! A GREAT Mystery! Fermat's last theorem! (not "simple" - "mechanical" proof)
Me! opened : - the GREAT! A GREAT Mystery! of the Fermat's Last theorem! (- !!! not "simple" - "mechanical" proof)
Me! opened : - Pierre de Fermat - was proved! the Fermat's Last theorem!
Me! opened : - my formula of my Proof is completely and absolutely identical with the words of Pierre de Fermat !
!!!!- NO ONE! and NEVER! and FOR NOTHING! NOT! will find a valid proof!
Haha my class met Simon without even knowing he was a dr
That is the reason mathematics don't get a Nobel prize!
is it possible that Fermat was just joking about the proof????
Nikhil Abhishek Possible? Certainly. Probable? Unsure. Fermat was brilliant.
Maybe, but it got proven .
He even looks like Mathologer. Are they the same person?
Wtf there's nothing in common lol
1729 is a taxi cab number
jeetaram rabary ayyy good one
Who came here cuz Kobe's death?
So, are we assuming 0 is not in the range of possible solutions?
of course ...
+yriafehtivan any n greater than 1 that is a whole number