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 Posted: Sun Apr 29, 2007 3:41 pm
What is the easiest way to explain the pythagorean theorem? can anyone provide an example?
oh yeah, and what`s an irrational number?
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Posted: Sun Apr 29, 2007 5:51 pm
The Pythagorean theoram is
a^2 + b^2 = c^2
so an example would be:
3^2 + 4^2 = c^2
(9) + (16) = 25
The square root of 25 is 5 so c = 5.
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Posted: Sun Apr 29, 2007 11:19 pm
Pyrgusfinn The Pythagorean theoram is a^2 + b^2 = c^2 so an example would be: 3^2 + 4^2 = c^2 (9) + (16) = 25 The square root of 25 is 5 so c = 5. wait, so a^2 + b^2 = square root of c^2?
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Posted: Mon Apr 30, 2007 3:14 pm
Pyr probably should've added that this theorem is for right triangles, or triangles with a 90º angle in them. a and b are the two short sides of the triangle, and c is the hypotenuse (long side across from the 90º angle).
Usually, you'll know two of the sides. Let's say you're given that a=3 and b=4. As Pyr said, you would write:
a^2 + b^2 = c^2.
So you get 3^2 + 4^2 = c^2.
So 9 + 16 = c^2
So c^2 = 25.
But we want c, not c^2. You take the square root of both sides to get c. That's why c is 5.
Suppose you're given b = 12, and c = 13.
a^2 + 12^2 = 13^2
So a^2 + 144 = 169.
Subtract 144 from both sides...
a^2 = 25.
But we want a, not a^2.
So a=5.
An irrational number is one that can not be written as a fraction, a/b, with a and b being nonzero integers.
So, if you can't make it a fraction, chances are it's irrational.
They take the form of nonterminating (infinitely long), nonrepeating (so not like 0.141414... for example) decimals. So if you see an infinite decimal with no pattern, it's irrational.
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Posted: Tue May 01, 2007 4:54 pm
Mooby the Golden Sock Pyr probably should've added that this theorem is for right triangles, or triangles with a 90º angle in them. a and b are the two short sides of the triangle, and c is the hypotenuse (long side across from the 90º angle). Usually, you'll know two of the sides. Let's say you're given that a=3 and b=4. As Pyr said, you would write: a^2 + b^2 = c^2. So you get 3^2 + 4^2 = c^2. So 9 + 16 = c^2 So c^2 = 25. But we want c, not c^2. You take the square root of both sides to get c. That's why c is 5. Suppose you're given b = 12, and c = 13. a^2 + 12^2 = 13^2 So a^2 + 144 = 169. Subtract 144 from both sides... a^2 = 25. But we want a, not a^2. So a=5. An irrational number is one that can not be written as a fraction, a/b, with a and b being nonzero integers. So, if you can't make it a fraction, chances are it's irrational. They take the form of nonterminating (infinitely long), nonrepeating (so not like 0.141414... for example) decimals. So if you see an infinite decimal with no pattern, it's irrational. thank you. this has helped me much. this is now a resolved thread.
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Posted: Sun Jan 06, 2008 12:04 pm
Mooby the Golden Sock So, if you can't make it a fraction, chances are it's irrational.. If you can't make it a fraction (aka ratio), it IS ir rational. (Sorry for resurrecting the thread, but I had to comment.)
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