You make the flawed conclusion that because you don't know much mathematics no one else does. Mathematicians (and scientists in general) do not blindly parrot the work of previous generations, they understand them and can examine previous work and check methods and proofs. Furthermore, the methods of modern mathematics are radically different from those of the ancient Greeks. The fields of analysis and set theory didn't exist 2000 years ago or even in Newton's day. They were formulated in the last few hundred years and then used to reprove known results in a rigorous manner, before going on to be applied to new results. For instance, Newton and Leibnitz invented calculus. However, the methods they used are considered, by modern standards, to be quite imprecise. Never-the-less calculus is valid mathematics because all the results have been proven using things like functional analysis. The people of the 1800s and 1900s didn't take Newton's word for it, they went about proving he was correct from much much more rigorous and clear starting axioms. In fact Russell and Whitehead spent more than a decade writing Principia Mathematica (not to be confused with Newton's book of the same name) where they set about starting with the most fundamental axioms of logic and constructing all mathematical algebra. It was so rigorous and started from such a basic level that it took them more than 350 pages before they'd got far enough to prove 1+1=2. Clearly those two mathematicians didn't take anything for granted and thus you can't claim that current mathematics is somehow poisoned by the work of the Greeks. No, you don't have to calculate the decimal value for pi to prove its irrational. I don't need to know the decimal value of \(\sqrt{2}\) to prove it is irrational. It is quite clear you don't even understand how mathematics is done. This demonstrates the fact you haven't even understood how mathematics is done again. In the proofs of the irrationality of pi it is not necessary to construct the decimal expansion of pi. The very fact its irrational means decimal expansions are not appropriate. You can barely string together a coherent sentence and obviously have no understanding or knowledge of even basic mathematics. Why should any one listen to you? Why are you an expert on something you have no knowledge or experience of? (Sound familiar Walter? Please Register or Log in to view the hidden image!)
I have a really old, really obscure, really hard to find book containing roughly 300 different proofs of the Pythagorean theorem. One of the proofs is even credited to former US President James Garfield (once upon a time you had to be a genius to get elected as President). Anyhow, my vague recollection is that the ancient Babylonians were the first to discover a proof and that several were already known to Euclid when he began his work. I would presume the same goes for the Pythagoreans, a couple hundred years earlier; the Pythagorean theorem is so named because the Pythagoreans made it famous, not because they were the first to discover it.
Quite interesting. The Wiki article references the Babylonians as possibly having a proof. I had thought that Pythagoras discovered the proof which Euclid then placed in his Elements. Perhaps there was an earlier proof he improved upon? In any event, when I've taught Geometry classes I've always credited "Pythagoras" with that particular proof. I usually give 'extra credit' to students who can do the proof from memory, as it is far more involved than the simpler proofs usually taught in most Geometry texts. Any way you can get your book material uploaded to the internet? There is still a lot of information in books/magazines not yet available on the internet.
Alphanumeric don't allow programing to dictate your life. Don't be an automaton, to use yourself that way is for efficientcy not progress and not meaningful expansion. The choice is yours to own too bad your too ignorant to know your whole argument is based on a flaw based on an error that will always be an error the irrationality of pi. Wait patiently for your lesson.
on top of what everyone is saying, isn't a rational fraction impossible in general because rationals are only whole numbers?
well then what the heck is the difference between rational and irrational? I could never really get that.
Simple explanation: a rational fraction is one that can be expressed using whole numbers. E.g. 0.5 is 1/2, 0.3333 is 1/3. Whereas pi can't be written that way (except as an approximation). I.e. 22/7 (or any other way of writing it as a fraction gives a near enough value but doesn't give a totally accurate one. Wiki says: Pi doesn't end and doesn't settle down to a repeating sequence, that's why it's irrational.
oh wow so irrational things continuous and non-repeating sequences/series? Then what else is irrational besides pi and the square root of 2?
All roots (square roots, cube roots, etc) of whole numbers are either irrational unless they are whole numbers. You can't get a fractional cube root of a whole number, for example. Also e (the natural growth constant), phi (the golden ratio), and most values for trigonometry, eg sin(75°)
It's not 'programming' or me being an 'automaton', its called knowledge and understanding. I don't blindly accept the things I'm taught because I actually understand them. When you understand something you are able to evaluate its validity, to grasp the methodology and to apply it to other things. The proof of the irrationality of pi I linked to is basic high school level mathematics so anyone who did decently at maths in school can follow it. There's no holes in the logic, its a proof. Your attitude smacks of someone who is desperately trying to justify their ignorance. You didn't understand mathematics in school and now you're trying to convince yourself that you didn't need to because it was wrong. Learning from other people isn't being 'programmed', the exchange of knowledge and information is essential. If you really believed what you say and you were able to do mathematics you'd not be just saying "Its wrong, you're all robots!" you'd be providing clear rigorous proof that its wrong. The best way to destroy a paradigm is to know it inside out because then you know the methods it involves, the things is assumes or implies, the claims/results it makes. Cranks always refuse to learn something before denouncing it. I know a great many more problems with mainstream physics than a crank does because I actually know some mainstream physics. Arguing from ignorance does nothing more than demonstrate you're a deceptive liar.
Patience is a virtue when the time is right I will reveal all the proof you need at the moment I give others the chance to reach the simple conclusion of the truth if they can find it within themselves. There is no argument to be had for this fact that pi is a rational fraction already determined is but a small peace of pi. e in the greater meaning of our conscious existence. I am just here to do what must be done nothing else.
You are being trained by idiots. e and pi are transcendental which are irrational but not describable in any language in this universe. This is different from being irrational. How can you have an object in the universe that is a member of the universe and yet the universe cannot describe it through any axioms or language? This is an important issue.
Pete and AN know what they are talking about. I put my 14 years in University math behind that opinion. It is no more complicated than what Pete said - Occam's Razor. (citation) The linked Wiki formal proofs float. Run through those a few more times if you need to. Please Register or Log in to view the hidden image!
You may want to abandon a host of your opinions. You and Pete can therefore give me the language and recipe to completely describe PI. I want an algebraic expression to describe it. I do not want some version of the pinching theorem and trust that somehow out to infinity two sequence converge to a number that has no description that can be tersted against the result. That number cannot be validated to be correct since you do not have any language or algebra that I can validate out to infinity the number found is correct. You all let me know.
The book is so old (I think it was printed in the 1920's) that there's probably no legal repercussions for scanning it onto the web as you suggest. Maybe I'll do that over the summer or something. It would be a little bit tedious for me though as I consider the book something of a prized possession, so I wouldn't be willing to rip off the binding and feed the pages in the way quick, professional scans are done. You'd think there'd be enough interest to collect all the known proofs on a single website, but I haven't been able to find any archives containing said ~300 proofs.
