"Guess how many points I have?"
One. Huh. Lame-O. I suck. You see, I suck at archery. But I'm getting better. I mean, I suck physically, and on only the third day, I hit the target. *chants victory song* I learned more aboout the Pythagorean Theorem: When a and b are the legs of a right triangle, and c is the hypertenuse [how do you spell it? o.O],
a2 + b2 = c2
Okie-dokey? Lololololol. Hmmm.... Fermat's last Theorem... Sometimes
a2 + b2 = c2
is true, but
a3 + b3 = c3
IS NEVER TRUE!
Some guy proved/disproved it. I forgot. It puzzled people for years. If memory serves, [hey memory, are you a waiter yet?] the guy spent seven years trying to prove it. Check out the problems below.
Edit (9:01) ~ Look.
Slightly modified. I think.
When a,b,c is a Pythagorean Triple:
(a(n))2+(b(n))2 ?= (c(n))2
a(n)(a(n)) + b(n)(b(n)) ?= c(n)(c(n))
aann + bbnn ?= ccnn
(aa+bb)nn ?= ccnn
(aa+bb)nn • 1/nn ?= ccnn • 1/nn
(aa+bb)nn • (1/nn ?= ccnn • 1/nn)
aa+bb ?= cc
a2 + b2 = c2
______________________________
~Pandu
My random math problems of the day:
Problem 1: Prove, or disprove if it's untrue that doubling every number of a Pythagorean Triple [or whatever it's called] maintains it [meaning it will still be a Pythagorean Triple].
Answer [You might have done it a different way, and I may be wrong, as I just learned this stuff today. And I have never proved any mathematical rule/thingies, so this may be wrong. Anyway, I think it's right, but I did it wrong. o.O]:
Problem 2: You have a square. It measures the square root of 8 units on each side. You have a line from the bottom left to the top right. How long is the line?
Answer:
a2 + b2 = c2
Okie-dokey? Lololololol. Hmmm.... Fermat's last Theorem... Sometimes
a2 + b2 = c2
is true, but
a3 + b3 = c3
IS NEVER TRUE!
Some guy proved/disproved it. I forgot. It puzzled people for years. If memory serves, [hey memory, are you a waiter yet?] the guy spent seven years trying to prove it. Check out the problems below.
Edit (9:01) ~ Look.
Slightly modified. I think.
When a,b,c is a Pythagorean Triple:
(a(n))2+(b(n))2 ?= (c(n))2
a(n)(a(n)) + b(n)(b(n)) ?= c(n)(c(n))
aann + bbnn ?= ccnn
(aa+bb)nn ?= ccnn
(aa+bb)nn • 1/nn ?= ccnn • 1/nn
(aa+bb)nn • (1/nn ?= ccnn • 1/nn)
aa+bb ?= cc
a2 + b2 = c2
______________________________
~Pandu
My random math problems of the day:
Problem 1: Prove, or disprove if it's untrue that doubling every number of a Pythagorean Triple [or whatever it's called] maintains it [meaning it will still be a Pythagorean Triple].
Answer [You might have done it a different way, and I may be wrong, as I just learned this stuff today. And I have never proved any mathematical rule/thingies, so this may be wrong. Anyway, I think it's right, but I did it wrong. o.O]:
When a,b,c is a Pythagorean Triple:
(a(2))2+(b(2))2 ?= (c(2))2
a(2)(a(2)) + b(2)(b(2)) ?= c(2)(c(2))
aa4 + bb4 ?= cc4
(aa+bb)4 ?= cc4
(aa+bb)4 • 1/4 ?= cc4 • 1/4
(aa+bb)(4 • 1/4) ?= cc(4 • 1/4)
aa+bb ?= cc
a2 + b2 = c2
Now isn't that the Pythagorean Theorem? *points to line above*
(a(2))2+(b(2))2 ?= (c(2))2
a(2)(a(2)) + b(2)(b(2)) ?= c(2)(c(2))
aa4 + bb4 ?= cc4
(aa+bb)4 ?= cc4
(aa+bb)4 • 1/4 ?= cc4 • 1/4
(aa+bb)(4 • 1/4) ?= cc(4 • 1/4)
aa+bb ?= cc
a2 + b2 = c2
Now isn't that the Pythagorean Theorem? *points to line above*
Problem 2: You have a square. It measures the square root of 8 units on each side. You have a line from the bottom left to the top right. How long is the line?
Answer:
4 units
