Pythagorean Theorem Found On Ancient Babylonian Clay Tablets Predating Pythagoras By 1,000 Years

[rangerrebew]

Pythagorean Theorem Found On Ancient Babylonian Clay Tablets Predating Pythagoras By 1,000 Years

https://www.msn.com/en-us/video/animals/pythagorean-theorem-found-on-ancient-babylonian-clay-tablets-predating-pythagoras-by-1-000-years/vi-BB1kPwHx?ocid=msedgntp&pc=HCTS&cvid=45930da9b6914990898b7b69110012e3&ei=36

[BobfromWB]

Pythagorean Theorem Found On Ancient Babylonian Clay Tablets Predating Pythagoras By 1,000 Years

https://www.msn.com/en-us/video/animals/pythagorean-theorem-found-on-ancient-babylonian-clay-tablets-predating-pythagoras-by-1-000-years/vi-BB1kPwHx?ocid=msedgntp&pc=HCTS&cvid=45930da9b6914990898b7b69110012e3&ei=36

Pythagoras spent many years in Egypt where he learned the "Pythagorean Theorem" from the Egyptians.

[The_Reader_David]

Is it really the Pythagorean theorem (with proof, since otherwise it wasn't a theorem yet, just a conjecture) or a statement of the general fact without proof, or one or more instances of the theorem (e.g. a list of Pythagorean triple 3,4,5; 5,12,13; etc.)?

There are lots of instance of special cases being known by a variety of cultures before Pythagoras, but if it isn't the general statement with proof, it's not the Pythagorean theorem.

I can't tell since the video that is linked is broken.

[roamer_1]

Most of geometry is self evident when laying out sites with a string... Just saying.

Squaring a corner by the 3,4,5 method is so stupid easy that I cannot abide the idea that our forefathers couldn't figure it out. Same thing with spirit levels to use for level and plumb bobs for plumb.

I DO believe there are lost technologies... but a whole lot of ancient construction can be readily accomplished with general knowledge.

Pythagoras just wrote it down. So he gets the props. and that's alright.

[Hoodat]

The Pythagorean Theorum is the Law of Cosines applied to a right angle.  Cos (90°) = 0

[The_Reader_David]

The Pythagorean Theorum is the Law of Cosines applied to a right angle.

But the law of cosines was only discovered centuries after Pythagoras proved his eponymous theorem.  It is more accurate to say the law of cosines is the Pythagorean theorem generalized to apply to non-right triangles.

[roamer_1]

But the law of cosines was only discovered centuries after Pythagoras proved his eponymous theorem.  It is more accurate to say the law of cosines is the Pythagorean theorem generalized to apply to non-right triangles.

Yet the building was writing in had square corners and plumb walls. Go figger.

[The_Reader_David]

Pythagoras just wrote it down. So he gets the props. and that's alright.

Pythagoras wrote it down and gave a proof.  And a difficult proof since he used only the notions from Euclid's elements.  The really pretty proof of starting with an a+b by a+b square and putting four right triangles with legs of length a and b and hypotenuse c into it in two ways, one so that the left-over bit is a square of with sides of length c, and the other so the left over bit is two squares one with sides of length a and one with sides of length b, depends on notions about area and rigid motions of plane figures that weren't fully formulated until the 19th century.  (It's also so beautiful that when my eight-year old grandson who had previously learned the Pythagorean theorem as a bald fact learned it he got so excited he hyperventilated.)

[roamer_1]

Pythagoras wrote it down and gave a proof.  And a difficult proof since he used only the notions from Euclid's elements.  The really pretty proof of starting with an a+b by a+b square and putting four right triangles with legs of length a and b and hypotenuse c into it in two ways, one so that the left-over bit is a square of with sides of length c, and the other so the left over bit is two squares one with sides of length a and one with sides of length b, depends on notions about area and rigid motions of plane figures that weren't fully formulated until the 19th century.  (It's also so beautiful that when my eight-year old grandson who had previously learned the Pythagorean theorem as a bald fact learned it he got so excited he hyperventilated.)

Right, right... and all that.... But he was writing down that proof in a building with plumb walls and square corners. That said with emphasis, because I defy you to find square corners without pythagoras (3,4,5) ... That said because the proof was scratched in the ground in order to make the building. Laying out two parallel lines and squaring them to each other is an old, old thing...  Sometimes science is too big for its britches, jussayin. 

[The_Reader_David]

...But he was writing down that proof in a building with plumb walls and square corners. That said with emphasis, because I defy you to find square corners without pythagoras (3,4,5) ...

Yes, specific instances of the theorem were known by the Egyptians, the Babylonians (according to the article that stared the thread), the Chinese, before Pythagoras proved the theorem.  Do you really think I'm claiming he thought of the idea and gave a proof without having known examples?  Almost all theorems in mathematics are conjectured on the basis of previously known examples, then proven.  That a triangle with sides of lengths 3, 4 and 5 have a right angle is not the Pythagorean theorem, it's an example of the validity of the theorem, the theorem is about all right triangles, not just the ones with integer lengths.

[roamer_1]

Yes, specific instances of the theorem were known by the Egyptians, the Babylonians (according to the article that stared the thread), the Chinese, before Pythagoras proved the theorem.  Do you really think I'm claiming he thought of the idea and gave a proof without having known examples?  Almost all theorems in mathematics are conjectured on the basis of previously known examples, then proven.  That a triangle with sides of lengths 3, 4 and 5 have a right angle is not the Pythagorean theorem, it's an example of the validity of the theorem, the theorem is about all right triangles, not just the ones with integer lengths.

Yes - But then there is determining whether the two parallel lines with two 90 degree angles are truly made or merely a parallelogram.. 3,4,5 is fair dinkum, but in the end a cross measurement between the 4 corners is the final proof - so long as the cross measurements are equal, then the building is square. At the same time  that cross (which are each side an hypotenuse) can be calculated to find an expected length which also proves the layout. That is proper Pythagoras again... and again, and again... it is used throughout construction. It is general knowledge that must necessarily be there in any item that is square or plumb.

Jussayin.