A2+ b2 = c2.

He spent 12 years coming up with these theries.

Heres my question,
Did pothagorean have a socil life?

He spent 12 years thinking about right triangles...

I went through 3 100 page books about his theries and figured out every single thing in the book on my own in about 30 minutes

Sincerly,
Skidochufada,
The curious 14 year old

Did you notice how he was quite good at spelling?

yea, im 14, and la is my only BAD subject :( well im preaty sure most ppl with an iq of 80+ can read my trying to write it right.

I went through 3 100 page books about his theries and figured out every single thing in the book on my own in about 30 minutes

Wow, you must be smarter than Pythagoras (and an incredibly fast reader). I'm sure it had nothing to do with the fact that his work (and the work of his followers) was laid out neatly for you to understand while they had to come up with it on their own and had no outline to follow. While we're at it, Newton and Leibniz were pansies. Look how many people can understand calculus today without problems.

In hindsight, everything is easy. Reading existing theory is nothing at all like building it from scratch.

I am, of course, assuming skidochufada read it in the original Greek. Look lad, I invented the electric motor when I was twelve. As shmoe points out, once the primary work has been done the pieces will fall readily into place. Anyone with an IQ over 130 who doesn't have that kind of experience would be well advised to stay clear of any creative endeavour.

skidochufada:

Can you please post a brief proof of the Pythogorean theorem here for us?

Thankyou.

proof of the pythogoran theorem? a2 + b2 = c2?

do you mean the the legs of the right triangles added together will always equal the hypotanuse?

leg1 = two u 2 leg2 = four u 2 hypotanuse = six u 2?

Did Pythagoras have a social life?


Before I attempt to answer this question, I have to confess that I'm not privy to any sort of extensive or detailed knowledge of the life of Pythagoras. About 3 minutes ago, I googled his name and pulled up this:
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Pythagoras.html

At any rate, from the looks of it, Pythagoras was not like Isaac Newton (who is a prime example).
Newton was an extremely isolated recluse, and spent a lot of time locked away in a room obsessing over mathematical concepts---which of course meant that he had no social life.

I get basicaly all my examples from school text books.

And i looked at the topic (aka right traingles) in about 1 minute of looking at investigation one, i figured it all.

So after studying the explanation of Pythagoras's theorem you understood it! Hmm, impressive I am sure. Now would you care to comply with JamesR's request and post a proof of the Theorem.

What proof of it? the proof of the therom?

no, i just reproved his, but took me way less time (aka 11 months 29 days, 23 hours, 55 minutes earlier)

Skido, a word of advice: the only person you are impressing is yourself. Graciously concede that maybe you aren't quite as smart as you think you are and we can all go about our business. There is nothing wrong with being cocky, but it helps to pull it off, if you have something of substance to back you up.

skidochufada:

Approximately 1 week passed between my post to you and your reply. You claimed to have reproduced all Pythagoras's proofs in 30 minutes. Yet you couldn't post a simple proof of the Pythagorean theorem here given 1 week?

no, i just reproved his, but took me way less time (aka 11 months 29 days, 23 hours, 55 minutes earlier)

Hey,

It's really good that you're looking through everything and this interested in math being only 14. We need more people interested in math. However, you must understand that there is a large difference in understanding how the equation works and being able to prove the equation. For example, you may know that the equation for the volume of a sphere is 4/3*pi*r^3. However, can you prove that? I don't mean filling up a sphere of a certain volume and measuring it to see if it has the correct volume, I mean a true mathematical proof.

Remember that Pythagoras lived in a time where Greeks believed that everything could be expressed in terms of whole number ratios. When it was discovered that two sides of some triangles could not be expressed that way, it was absolutely groundbreaking. So much so that some Greeks have been reported to have killed themselves because the whole foundation of their math (which they believe was God's language) was falling apart.

Imagine discovering something like a^2 + b^2 = c^2 when the existence of sqrt(2) did not exist.

Read a bit more and you'll discover that many of the equations that you may know how to use you don't necessarily know why they work. You'll begin to appriciate math even more when you discover this. :)

I think it was matt grime who said, "Every theorem is trivial once it has been proven."

There are many proofs of the Pythagorean theorem. If I remember correctly Newton gives a proof of a more general form (The 90 degree angle not required) relating the three sides of a triangle which if the angle is 90 degrees, colapses to the Pythagorean theorem. What is really impressive about this is it is a geometric proof as in his day, mathematicians only considered that type of proof to be a valid proof. (much like some to day reject exhaustive proofs by computers.)

Also i think Newton was unfairly painted as non-social. I thinkhe stayed in the country, saw few people mainly during he plage. later in life he was more social, held political office, was active in religious groups etc. I think but all this from memory.

Didnt know you meant to give an example to prove it, baron

Skidochufada: it's great that you're interested in this, and with some further education, you could go quite far.

But the fact is, you don't know what you don't know.

It isn't a *theory* he came up with, it's a *proof*.

Wiki 'mathematical proof' and you will begin to get an inkling of what Pythagorus did.

This thread is very amusing. :D

We're learning that in math class. :)
I don't see how Pythagorus got his answers without using a calculator. Espically the really large numbers. I know I can't function w/o a calculator for an entire class period, but then again math has never been my strong point.

...I don't see how Pythagorus got his answers without using a calculator. ...Even if he had one, he would not have used it (except perhaps at the local wine store etc.) Furthermore, even if he used one and produced 1000 diffent cases / examples of a^2 + B^2 = c^2, no one would be interested or think they proved anything.

Even as late as Newton's day, numbers were not used in proofs.* A prove was made by geometric arguements. Read Newton's great book (or part of it) Principles of Mathematics and see how powerful geometric proof tools can be in the hands of some one like Newton. It is full of proofs, but not one uses numbers. (at least as I recall - It has been many years.)
____________________________________
*I may not have the dates completely correct - certainly after DesCarte invented analytic Geometry, a few began to think numbers could be used to prove things. Please note he was careful to call it a form of geometry, or it would not have been accepted for many more years. For at least 1000 years proof = geometry.

poliwog, contrary to popular belief, mathematics isn't actually about calculations. In fact, when I entered the university on a Math/Computer Science program, my trusty brick of a calculator was flashing low battery. It did so for years! Fact is, mathematics is more about the study of structure than anything else, really.

So when Pythagoras proved his theorem, he wouldn't necessarily have done many calculations involving lots of numbers; instead he realized something deep about the nature of right-angled triangles, and was able to formalize this into a proof. This is a much stronger concept than "merely" having checked that the equation holds for "a lot of numbers and triangles".

Indeed. Pythagoras's theorem tells us something deep about ALL right angled triangles, not merely the millions of right angled triangles which people happen to have "checked" over the years.

It is a pity that so little actual mathematics is taught in schools these days, since that leaves many people with the impression that mathematics and arithmetic are the same thing.

but what is the difference?

but what is the difference?

If you checked that Pythagorus' Theorem was true for 1,000,000 cases by drawing and measuring triangles (assuming for the moment that you had some way of doing this), you only know it's true for these 1,000,000 cases. The problem is, there are more than 1,000,000 right angled triangles, there are infinitely many. If you meet some triangle not on your list of 1,000,000, you have to check it.

This is the difference between some amount of calculations and a proof of a general principle, having proven a^2+b^2=c^2 is true for an arbitrary right angled triangle, you can be sure that it's true for the 1,000,000 that some sap just checked with his calculator and for any possible right angled triangle you might meet with no more work involved.

Contrary to funkstar though, my calculator has functioning batteries. But this is only because it has a clock on it and I haven't owned a watch for years. ;)