We are probably wandering off from one of the World's finest explorations of the Universe, an' all that. 
But God Bless my Soul, how I love Football!
TBH, teh mine own Minnesota Vikings will probably have to wait 50 years before success, My money is on teh Baltimore Ravens next year.
I have no idea why teh Chiefs paid $450M over 10 years for a Quarterback. Me, I'd buy a couple of Sound Offensive Guards for far less.
Anyhow. The Sporting Money is mostly on the Nags (Horses) here in the UK. And I am well ahead on those. But I still love Passyunk Avenue in London. See ya soon.
But God Bless my Soul, how I love Football!
TBH, teh mine own Minnesota Vikings will probably have to wait 50 years before success, My money is on teh Baltimore Ravens next year.
I have no idea why teh Chiefs paid $450M over 10 years for a Quarterback. Me, I'd buy a couple of Sound Offensive Guards for far less.
Anyhow. The Sporting Money is mostly on the Nags (Horses) here in the UK. And I am well ahead on those. But I still love Passyunk Avenue in London. See ya soon.
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36 is an interesting number. It is a perfect integral square and also has a rich list of factors, which are 1, 2, 3, 4, 6, 9, 12, 18 and 36. 1 is included in the list, because it is the multiplicative identity element of the set of integers. The inclusion of 18 is a direct consequence of 1 being the multiplicative identity.
Sorry if it hurts, but 36 is one of the less interesting numbers in the Universe.
My own opinion, based on some serious Number Theory is that 12^3 is far more interesting.
Taxicab number - Wikipedia
Ramanujan was casually brilliant IMO. Way ahead of his time. Did Elliptic Curves before anybody else.
My own opinion, based on some serious Number Theory is that 12^3 is far more interesting.
Taxicab number - Wikipedia
Ramanujan was casually brilliant IMO. Way ahead of his time. Did Elliptic Curves before anybody else.
Further mathematical thoughts about 36.
Everybody knows that the square of a prime number beyond 7 is 24n+1. You know, 49, 121, 169. Need I go on?
Everybody knows that 3^2 + 4^2 = 5^2. Pythagoras, right?
Not so many people know that: 3^3 + 4^3 + 5^3 = 6^3. (= 216)
So 36 is good, IMO. But 216 better. QED.
Everybody knows that the square of a prime number beyond 7 is 24n+1. You know, 49, 121, 169. Need I go on?
Everybody knows that 3^2 + 4^2 = 5^2. Pythagoras, right?
Not so many people know that: 3^3 + 4^3 + 5^3 = 6^3. (= 216)
So 36 is good, IMO. But 216 better. QED.
Some old Greek Mathematician said if you seek money in Mathematics, take a penny and walk out the door!
Or maybe if you walk in the door, leave your ego behind!
Anyhow, I have discovered the 36 is the eighth Triangular Number.
But I couldn't find out much about it beyond that.
I was hoping it might be a Perfect Number, or even related to a Mersenne Prime.
But no. My money is still in 1728. Short of the Monster Group, that is.
Or maybe if you walk in the door, leave your ego behind!
Anyhow, I have discovered the 36 is the eighth Triangular Number.
But I couldn't find out much about it beyond that.
I was hoping it might be a Perfect Number, or even related to a Mersenne Prime.
But no. My money is still in 1728. Short of the Monster Group, that is.
While you are at it, why don't you post your degree certificates? You must possess several doctorates, I dare say, by Harvard or MIT, or Cambridge, or Oxford, or some other world renowned university. And, why don't you post links to your doctorate thesis? Oh, I will be impressed to death.... and assuming your delusions are correct, JEALOUS.Some old Greek Mathematician said if you seek money in Mathematics, take a penny and walk out the door!
Or maybe if you walk in the door, leave your ego behind!
Anyhow, I have discovered the 36 is the eighth Triangular Number.
But I couldn't find out much about it beyond that.
I was hoping it might be a Perfect Number, or even related to a Mersenne Prime.
But no. My money is still in 1728. Short of the Monster Group, that is.
Why should I be jealous of intelligent people? Oh my God! I used to love intelligent students when I used to teach mathematics, let alone be jealous of them. Mind you, I did not teach adults, but young adolescents, and I am NOT embarrassed about not teaching adults.
Jealousy?! What for? To flog myself for what I cannot control?! That is utterly stupid.
I refuse to be manipulated, Doctor String Puller.
Next one, please!
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There is no smallest number in the Real Domain, that is, in ordinary numbers we use everyday. Real Numbers extend unboundedly to both the negative side and the positive side. The smallest number has to be negative with an infinite modulus (magnetude). And this particular number is peculiar because it can be proven not to exist. If you assume a lower bound to the negative number side, you will hit a contradiction.
I am not embarrassed to the least of not being the smartest on the planet, or even here, in this thread. I am only thankful for whatever God Almighty/Nature blessed me with.
Aw, Galu, don't get all morose about 1 being the loneliest number.
Actually I am quite the expert on curious and interesting numbers:
https://www.amazon.co.uk/Penguin-Dictionary-Curious-Interesting-Numbers/dp/0140261494
Even read Volume 2.
The dullest number in teh Universe actually is quite interesting, just for being the dullest. If you follow?
But I am sticking with 1728 here. Don't push me into detail too much at this time of night, but 1728 is part of the Monster Group:
Quanta Magazine
Actually I am quite the expert on curious and interesting numbers:
https://www.amazon.co.uk/Penguin-Dictionary-Curious-Interesting-Numbers/dp/0140261494
Even read Volume 2.
The dullest number in teh Universe actually is quite interesting, just for being the dullest. If you follow?
But I am sticking with 1728 here. Don't push me into detail too much at this time of night, but 1728 is part of the Monster Group:
Quanta Magazine
I just checked my copy of "Elementary Number Theory" by David M. Burton. Turns out 291 is divisable by 3! So even less interesting than the 291 Bus Route in London from Plumstead to near Woolwich Arsenal.
Not many people know that the Gunners (aka Arsenal F.C.) commenced their lives building guns on the Thames at Woolwich Arsenal.
Also on the Thames were West Ham United F.C, who were originally "Thames Ironworks" with the famous crossed Hammers used to beat iron into shape to give us some goodish gun-platforms or Ships. HMS Warrior (1860) in Portsmouth harbour is therefore really HMS "Come on you Irons!". TBH, I have always liked West Ham.
Naturally we British are peaceful people these days. It was a thing of its time.
1728 seems to be a dull year, but an interesting number, IMO.
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There is a wealth of ardent voices rhapsodically praising the ineffable beauty and divine power of mathematics. However, some numbers are considered so ugly that they do not fit into the idealistic worldview. Trying to give a more rigorous definition of the real numbers, the number system has been extended by adding the strongly paradoxical and rather theological infinity element, which is not a number. While already infinitely big, the universe can still be expanding to be even more infinite.
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