Pythagoras's theorem is flawed anyways, What is the Square Root of 2?.
If the hypotenuse of your right triangle is 2 and you know one of the other sides, then the answer to the other side is irrational.;-)
Cheers,
The Babylonian empire was the head of gold in the book of the prophet Daniel, which gave way to the Medes and Persians, and then The Greek and Roman empires, from which the European Union has now emerged to the feet of mingled iron and clay.
Pythagoras was a 1000 years too late
> If the hypotenuse of your right triangle is 2 and you know one of the other sides, then the answer to the other side is irrational.
I think that's mis-stated. Counterexample:
hypotenuse = 2
one side = 6/5
other side = 8/5
- Doug
Gordon
It what now?
> Pythagoras's theorem is flawed anyways, What is the Square Root of 2?.
I don't get it... How is the theorem flawed?
> I don't get it... How is the theorem flawed?
Have you ever calculated the square root of 2?
And I don't mean; just press a button on your calculator.
The square root of 2 is an infinite number. Therefore, the question is; what number squared plus what number squared equals infinity?
You can press the buttons on your calculator and it will give you an answer, but how do you know it is right?
irrational != infinite
Irrational numbers are simply numbers that can't be expressed in the form X/Y, where X and Y are two integers. How do irrational numbers imply that the Pythagorean Theorem is flawed?
Forgive me if I am wrong, but I thought that the square root of 2 was the only number that went on, infinitly, to the right of the decimal place.
Like I said, you can calculate an answer and for the most part, it will be correct. But, it won't be abolute....
> Pythagoras's theorem is flawed..
From what I remember of "Philosophy 310: History of Philosophy - Ancient to Medieval"...
One of the tenets of Pythagoreanism was that the entirety of the universe could be expressed in ratios of integers. Legend has it that the first of Pythagoras's followers to postulate the existence of incommensurable (irrational) numbers, Hippasus of Metapontum, was put to death (tossed out of a boat at sea) because of his discovery
There are a lot of irrational numbers. One of them is pi.
"Irrational" does not imply "imaginary". If it did, we couldn't have any round items, because the ratio of the diameter to the circumference of a circle is irrational.
Interesting... Of course, "Pythagoreanism" shouldn't be confused with "the Pythagorean Theorem"...
I also remember that one of the tenets of Pythagorean philosophy was that life was a strange parade and one should just step back and be an observer.
> Forgive me if I am wrong, but I thought that the square root of 2 was the only number that went on, infinitly, to the right of the decimal place.
>
> Like I said, you can calculate an answer and for the most part, it will be correct. But, it won't be abolute....
Lots of others do, too.
?3 = 1.7320508075... on to infinity
?5 = 2.2360679774...
Actually there are quite a few numbers which go on infinitely, to the right of the decimal place. An infinite number of them, actually.
From the fairly mundane (1/3 = 0.3333333333...)
To the more famous (? = 3.1415926535... the golden ratio ? = 1.6180339887... or e = 2.7182818284...)
The difference is that unlike 1/3, numbers like ?, ?3, ?5 and e are irrational numbers like ?2 because the decimal not only goes on infinitely, it is also nonrepeating.
Imaginary numbers are a different animal - they are ones which need to rely on ?-1
I understand irrational numbers.
But a component of the Pythagorean Theorem is the square root.
Instead of square root, I like to think of it as; what number times it self equals 2? You can't give that an absolute answer, therefore, it's flawed.
Now, thanks to Dave, I have 3 and 5;-)
There was a mid-western town with two colleges, a men's college and a women's college.
Every year at the beginning of the school term the men's college would invite the women's college over for a dance. The secret motivation for the men's college administration was to find out which of their young men were engineers and which were scientists.
The women were lined up along one wall of the gym and the men along the other wall.
The Dean of the Men's college got up on the podium and announced that the men could cross the gymnasium floor and dance with the women just as long as the length of their single stride was the square root of two feet. The scientists immediately left because they knew it is impossible to calculate the exact length of a stride that is the square root of 2 feet. The engineers knew that while it is theoretically impossible to stride at the square root of 2 feet, you could get close enough for practical purposes.
Therefore the engineers promptly strode across the gym floor being careful to keep the length of their single strides to 1.41 feet plus or minus.
