More than likely, you are. 
Random Thoughts XIII - Radioenergopithecocracy
- Thread starter Takhisis
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Possibly **
It'd be good if the Guardian stopped being so dumb:
This is about a proof that is supposedly "solely trigonometrical". But basic knowledge of trigonometry will tell you that its formulae (eg for relations of sin, cos, tan etc) are dependent on the pythagorean theorem being true (=> you are using formulae that are true due to x, to try to prove that x is true).
Good for the highschool kids trying something cool, but it is well established that trigonometric formulae being true implies pyth theorem is true.
This is an abstract from the kids' proof:
But the law of sines is true (though implicitly) due to the inferred right-angle connections between those non-right angles.
Trivia: you can also read the law of cosines, in Euclid's book II (propositions 12-13), again as direct consequence of pyth.
Re the Guardian, seriously, Pythagoras lived in the 6th century BC. Do the elementary math about the theorem's age, it is 2500 years old
^^
All that said, while their proof likely won't be accepted as being "solely trigonometrical" (since law of sines is still tied), it is a very elegant new proof, and worth it for that alone
Their actual construction seems to be this, by the way:
It's not ingenious or wondrous, but it is elegant. My suspicion is that the mere fact that properties of right angles are used in the definition of what sin is (because it has to be in a right-angled triangle to start with, then extrapolate to the related non-right one), already means the ratios between angles imply the pyth theorem. But obviously this proof can be part of books of proofs of the theorem, despite not being "the fully trigonometric one" as marketed.
Sidenote: if they had marketed it as such on purpose, that was really a great idea
This is about a proof that is supposedly "solely trigonometrical". But basic knowledge of trigonometry will tell you that its formulae (eg for relations of sin, cos, tan etc) are dependent on the pythagorean theorem being true (=> you are using formulae that are true due to x, to try to prove that x is true).
Good for the highschool kids trying something cool, but it is well established that trigonometric formulae being true implies pyth theorem is true.
This is an abstract from the kids' proof:
But the law of sines is true (though implicitly) due to the inferred right-angle connections between those non-right angles.
Trivia: you can also read the law of cosines, in Euclid's book II (propositions 12-13), again as direct consequence of pyth.
Re the Guardian, seriously, Pythagoras lived in the 6th century BC. Do the elementary math about the theorem's age, it is 2500 years old
^^All that said, while their proof likely won't be accepted as being "solely trigonometrical" (since law of sines is still tied), it is a very elegant new proof, and worth it for that alone
Their actual construction seems to be this, by the way:
It's not ingenious or wondrous, but it is elegant. My suspicion is that the mere fact that properties of right angles are used in the definition of what sin is (because it has to be in a right-angled triangle to start with, then extrapolate to the related non-right one), already means the ratios between angles imply the pyth theorem. But obviously this proof can be part of books of proofs of the theorem, despite not being "the fully trigonometric one" as marketed.
Sidenote: if they had marketed it as such on purpose, that was really a great idea
Last edited:
Kyriakos said:
*Valka's brain promptly glazes over*
Okay.
*Valka wanders off to the kitchen in search of pizza and milk, then settles down to catch up on some Harry Potter fanfiction in which Hermione and Arthur Weasley are married...*
Gori the Grey
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If I programmed a bot, I would name it Ding-Bot.
I didn't know that the conclusion of the Deluge (Polish saga in the 17th century) was at the time of Newton - only a few years before 1666.
Shows why you shouldn't be so greedy with territory - also that the tatars had no loyalty to anyone.
In the longterm, this secured the formation of that "army with a country".
Shows why you shouldn't be so greedy with territory - also that the tatars had no loyalty to anyone.
In the longterm, this secured the formation of that "army with a country".
EgonSpengler
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Someone on the radio noted that one of the favorites on the women's side of the Boston Marathon ran her previous marathon in 2 hours, 15 minutes.
I can't even watch a movie in 2 hours, 15 minutes.
I can't even watch a movie in 2 hours, 15 minutes.
r16
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uh , elections and stuff so like ı can't be talking too much which invariably and fully justifiably tends to be about New Turkey . Are you questioning war preparations , Putin's support for New Turkey influencing the general status of the war , that Fleet Standart 71 Phantoms files have been found in a safe behind wall cabinets and Greek intel types are like what and what else ?
r16
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bad side cosplaying the Great Patriotic War have been assembling reserves . The good side gets limited supplies to prolong the war until the next election cycle , like in places where they speak English . Like do not enrage people in a way so that they will extend their 1984 elsewhere in the forum .
r16
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victoria Nuland rejects she is following the deeds of good people here , while like lesser Americans sprout stuff on how it won't happen again .
there should be more to this where Lucy promises it won't happen again , Charlie Brown to go back and start running again . Yeah , right there ... Say , the specific thing that kinda sorta starts this particular one is the good side's based-on-Soviet-era model engines on New Turkey's heavy election helicopter . So important . That the little twerps who comment on the blog that dispenses Pentagon's lies have been forced to stop bad talking for the day . Those kinda lesser Americans now kind of insist ı should recognize the thing because a kid of people who live in the same street with me knows some people who work on it in Ankara . You know , at a time when the thing is currently so ugly that the entire global aviation industry will think ı have got nothing to do with it .
there should be more to this where Lucy promises it won't happen again , Charlie Brown to go back and start running again . Yeah , right there ... Say , the specific thing that kinda sorta starts this particular one is the good side's based-on-Soviet-era model engines on New Turkey's heavy election helicopter . So important . That the little twerps who comment on the blog that dispenses Pentagon's lies have been forced to stop bad talking for the day . Those kinda lesser Americans now kind of insist ı should recognize the thing because a kid of people who live in the same street with me knows some people who work on it in Ankara . You know , at a time when the thing is currently so ugly that the entire global aviation industry will think ı have got nothing to do with it .
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