Math gurus - tell me why this is wrong.

[her209]

Illustration

Why is the total length of the red line in the case where N = 8 equal to v(a²+b²) and not equal to a + b, illustrated in the case where N = 1, N = 2, ...?

 

[Mathlete]

It is infinite!

 

[mugs]

Buh........

 

[Toastedlightly]

pathagoras would cry?

 

[txrandom]

Is it trying to show the "steps" in the slop. The first one has "one step", the second has "two steps", and the third has infinite.

 

[Toastedlightly]

lets do us a little calc... wait.. screw that. I am bored. Lets talk about WiI!

 

[George P Burdell]

Calc I

 

[Xyclone]

Originally posted by: txrandom
Is it trying to show the "steps" in the slop. The first one has "one step", the second has "two steps", and the third has infinite.

winnar

 

[txrandom]

I never remember doing this in Calc 1 or Calc 2 unless it is trying to explain integration. Nonetheless, a pretty simple answer.

 

[her209]

Originally posted by: txrandom
I never remember doing this in Calc 1 or Calc 2 unless it is trying to explain integration. Nonetheless, a pretty simple answer.

IIRC, integration involves find the area under a "curve". In this case a straight line.

 

[txrandom]

Originally posted by: her209

Originally posted by: txrandom
I never remember doing this in Calc 1 or Calc 2 unless it is trying to explain integration. Nonetheless, a pretty simple answer.

IIRC, integration involves find the area under a "curve". In this case a straight line.

I'm talking about how the pictures were splitting the boxes up by steps kind of like Riemman Sums. I think integration is just an infinite Riemman sum.

 

[her209]

Originally posted by: txrandom

Originally posted by: her209

Originally posted by: txrandom
I never remember doing this in Calc 1 or Calc 2 unless it is trying to explain integration. Nonetheless, a pretty simple answer.

IIRC, integration involves find the area under a "curve". In this case a straight line.

I'm talking about how the pictures were splitting the boxes up by steps kind of like Riemman Sums. I think integration is just an infinite Riemman sum.

Correct, but its adding up the area of the infinite boxes therefore the result is the area under the "curve". I'm asking about finding the length of the red line using the process of induction given case N = 1, N =2.

 

[hypn0tik]

It's trying to illustrate that as N gets larger, the steps will approach a straight line. The length of the line can be found using the pythagorean theorem.

 

[her209]

Anyone else?

 

[madman300]

I remember having this exact same conversation with my roomates in college. We stumbled on a simple but very revolutionary answer... but I forgot what it was.

 

[KLin]

Originally posted by: Toastedlightly
pathagoras would cry?

Pythagoras?

 

[BrownTown]

umm, this has got to be the easiest answer ever. (length + width) anyone? Its pretty darn obvious and reuires no calculus, no algebra, and no geometry.

 

[reverend boltron]

Originally posted by: BrownTown
umm, this has got to be the easiest answer ever. (length + width) anyone? Its pretty darn obvious and reuires no calculus, no algebra, and no geometry.

What two numbers can you add together to get infinity? I don't think you can because infinity isn't a number, it's a concept. Aleph null, that is a quantity, but you can't have 1/2 aleph null or (aleph null)^(1/2) .. because they're still equal to aleph null.

 

[BrownTown]

Don't use your brain, use your eyes .

 

[bleeb]

This is the fundamental theorem of Calculus.

 

[MrChad]

For N = 1:

L = (a/1) + (b/1)

For N = 2:

L = (a/2) + (b/2) + (a/2) + (b/2)

For N = 3:

L = (a/3) + (b/3) + (a/3) + (b/3) + (a/3) + (b/3)

Extrapolate that out to N = 8

L = (a/8) + (b/8) + (a/8) + (b/8) + (a/8) + (b/8) + (a/8) + (b/8) + ...

The formula breaks down as N approaches infinity, because essentially you start adding up an infinite number of 0-length sides.

 

[five40]

Pythagorean Theorem - a²+b² = c²..........c=v(a²+b²)

 

[BrownTown]

nothing breaks down. Its the sum from 0->N of X/N + Y/N, so thats XN/N + YN/N which equals X+Y. If you want to use calculus be my guest.

 

[MrChad]

Originally posted by: BrownTown
nothing breaks down. Its the sum from 0->N of X/N + Y/N, so thats XN/N + YN/N which equals X+Y. If you want to use calculus be my guest.

Yes, it does break down.

The length of the hypotenuse of a right triangle is NOT X + Y.

 

[hypn0tik]

Originally posted by: MrChad
For N = 1:

L = (a/1) + (b/1)

For N = 2:

L = (a/2) + (b/2) + (a/2) + (b/2)
L = 2*(a/2) + 2*(b/2)

For N = 3:

L = (a/3) + (b/3) + (a/3) + (b/3) + (a/3) + (b/3)
L = 3*(a/3) + 3*(b/3)

For N = n
L = n*(a/n) + n*(b/n)

Now, take the limit as n -> 8

You find that the n's cancel out and you are left with a + b.

Now, I know that's not the expected result, but I can't see why.