Fun facts!
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- Registrado
- 28 de Dic, 2014
Seems to check out.
1+2+3+4+5=15 15^2 = 225
1^3 (1) + 2^3 (8) + 3^3 (27) + 4^3 (64) + 5^3 (125) = 225
Is this actually proven or is it just one of those conjectures where we just haven't found an exception?
(Apparently it's proven and called the Nichomachus theorem.)
Now prove the Collatz conjecture, smartass.
- Registrado
- 24 de Ago, 2014
The first n numbers sum up to n(n+1)/2; the first n cubes sum up to the square of that, i.e. n²(n+1)²/4. Both formulas are easily proved by induction.
Bonus fact about the number 13
ELEVEN + TWO = TWELVE + ONE
Both sides of the equal sign are anagrams.
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- Registrado
- 28 de Dic, 2014
I always thought the Beatles song "Michelle" (a McCartney number) was an imitation of Serge Gainsbourg, but I was wrong. He actually wrote it pre-Beatles, and would sing it at parties to pick up chicks. It didn't even originally have French lyrics. He just sang vaguely French-sounding gibberish. The actual lyrics were added later. So the chronology is wrong for influence.
In fact, the reason a lot of Beatles songs sound like Serge Gainsbourg is not that they imitated him, but exactly the opposite. Even the name of the musical movement (one of many) he's considered a leader of, yé-yé, is actually directly taken from English lyrics of songs of bands like the Beatles: "She loves you yeah yeah yeah."
Paul even later wrote a song for Serge's daughter Charlotte. So there was influence there but it was in completely the other direction. So they don't sound like Serge so much because they imitated him. They sound like him because he imitated them.
In fact, the reason a lot of Beatles songs sound like Serge Gainsbourg is not that they imitated him, but exactly the opposite. Even the name of the musical movement (one of many) he's considered a leader of, yé-yé, is actually directly taken from English lyrics of songs of bands like the Beatles: "She loves you yeah yeah yeah."
Paul even later wrote a song for Serge's daughter Charlotte. So there was influence there but it was in completely the other direction. So they don't sound like Serge so much because they imitated him. They sound like him because he imitated them.
- Registrado
- 24 de Ene, 2020
This still works, by the way. I specifically learned this song under the same motivation:
- Registrado
- 28 de Dic, 2014
Fun fact if (A^x + B^y = C^z), where (A, B, C, x, y and (z) are all positive integers and the exponents (x, y,) and (z) are strictly greater than (2) (i.e., (x, y, z > 2)), then the bases (A, B,) and (C) must share a common prime factor.
Oh wait it isn't a fun fact though. It SEEMS like it HAS to be true, but nobody has been able to prove it.
In fact, the fun fact is that it remains unproven, although its proponent Andrew Beal, professional banker and amateur high stakes poker player and mathematician, has offered a million bucks to anyone who can prove it.
Oh wait it isn't a fun fact though. It SEEMS like it HAS to be true, but nobody has been able to prove it.
In fact, the fun fact is that it remains unproven, although its proponent Andrew Beal, professional banker and amateur high stakes poker player and mathematician, has offered a million bucks to anyone who can prove it.