Earlier quoted context omitted.
That seems irrational…
I believe the whole story is imaginary.
There must a right angle to look at it...
Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
141–150 of 248 posts
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#142Earlier quoted context omitted.
How useful are universal truths compared to getting shit done? I only see theorems as useful for complex societies. The son of a gem dealer would have the time to work out universal truths. The reputation of everyone doing it without numbers would reveal the pattern of the universal truth. Finally this looks like it was all done using cuneiform. Which brings up questions of notation and the language to describe a squ…
Getting shit done is the antithesis of progress because it goes hand in hand with "if it was good enough for my father, it will be good enough for me, who are you to disrespect (the methods of) my father!"
I agree but dying for ideals isn’t much progress.
Progress is a luxurious goal.
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#143I recall seeing that there was a 14 000 year old dear scapula found in China that had the "simple proof" diagram engraved on it. The article seems to say that Pythagoras' Theorem was discovered by the Mesopotamians, but neglects mentioning it may be _much_ older.
Someone above commented that just by building ancient peoples would have discovered this relationship.
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#144The mainstream is and was _enamored_ with Ancient Greece. Our Western culture made Ancient Greek into the vocabulary root of our sciences. We have a lineage of philosophy from Ancient Greece to the 19th century. Only in the 19th century with archeology (again a neo-word made from Ancient Greek roots – it suggests to the mainstream that the Ancient Greek had a concept of archaeology, which they obviously didn’t have)…
The Greek still did something remarkable that to my knowledge we don’t have record of from before: they started a culture of free thinking that grew into philosophy, logic, and scientific inquiry. They also sentenced some of their free thinkers to death for not worshipping the gods but that’s a separate issue.
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#145I was surprised to learn that U.S. President Garfield devised a proof of Pythagoras' theorem. It got me wondering what other U.S. Presidents had an aptitude for math.
Jefferson (3rd President) was quite fluent in geometry and surveying, designing his home in Monticello.
Herbert Hoover (31st) was a mining engineer.
Jimmy Carter (39th) was a nuclear engineer by training, having worked in the U.S. Navy's nuclear sub program.
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#146Earlier quoted context omitted.
Why would you need numbers for right angles? You need a straight line and a string. But I agree with the second paragraph: there's a huge difference between a procedure that is handed down as part of "this is how we estimate a building project" and a theorem that is declared universal truth and base for all kinds of other theorems. Even if they are exactly the same thing.
I've personally worked on a project where we used a 3-4-5 right triangle to lay it out on the ground. Straight lines alone do not get you right angles.
You can certainly get close enough with straight lines. If you create a parallelogram, you can get it square by making the diagonals the same length.
And if you can determine that the diagonals are the same length, you have what you need to get close enough to a parallelogram in the first place.
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#147Earlier quoted context omitted.
I'm pretty confused. How do you think an average 8 year old would feel?
Well, they continue to introduce Pythagorean theorem through many stages of elementary math, so 8 is pretty early. But.. here could be a section of a textbook: Pythagoras & The Pythagoreans: Mathematics, Music, and Mystery Pythagoras was an ancient Greek mathematician and philosopher who lived around 500 BC. He traveled widely and gathered knowledge from diverse cultures, like Egypt. He also founded his own school of…
I have thoroughly enjoyed all of your comments! You’re great at showing how learning can be fun. Do you have a blog where you compile these stories and anecdotes?
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#148Earlier quoted context omitted.
Is there an easy explanation of why these are true? I already struggle grasping e^i, and I completely don't understand what e to an irrational power even means, let alone why it would be -1. Why the circle circumference ratio has anything to do with this is completely beyond me.
1. e^x, sin(x) and cos(x) can each be expanded out into an infinite sequence of fractions (Maclaurin series), each fraction of the form x^n / factorial(n). This relies on differential calculus, Taylor series, theory of limits, convergence etc. 2. The e series fractions contain all the integers in the numerator (x^0, x^1, x^2, etc), while the sin series has only odd integers and the cosine series has only even integer…
So that's the part I explain in my note. So if you combine the two explanations together I think we have the whole picture. Yours fills in the gap in my explanation.
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#149[deleted]
Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)
#150The article claims that the Babylonians "discovered" the Pythagorean theorem, but all it shows is that they (probably) believed it to be true.
Until we have better evidence, it still seems to be the case that (at least in the "West", I'm unfamiliar with e.g. Chinese mathematics) the Greeks were the first to come up with the concept of a mathematical proof that is valid deductively, and not inductively.