Geometry Question

[kevyk]

100 is the correct answer. You can see that it is true by applying the Pythagorean Theorem.

The length of the hypoteneuse is sqrt(2)*length of side. But each pixel is a square. Therefore, while each pixel is 1 pixel long and wide, its length across the diagonal is sqrt(2) pixels.

number of pixels needed = length of hypoteneuse/diagonal length of pixel.

np= sqrt(2)*100/sqrt(2)*1 = 100

Drawing it also works.

[mostsmooth]

[ QUOTE ]
100 is the correct answer. You can see that it is true by applying the Pythagorean Theorem.

The length of the hypoteneuse is sqrt(2)*length of side. But each pixel is a square. Therefore, while each pixel is 1 pixel long and wide, its length across the diagonal is sqrt(2) pixels.

number of pixels needed = length of hypoteneuse/diagonal length of pixel.

np= sqrt(2)*100/sqrt(2)*1 = 100

Drawing it also works.

[/ QUOTE ]
its ~141.
the question doesnt ask how many pixel diagonals would it take to cover the length, it asks for the distance.
although we dont know exactly how long a pixel is, we do know that the length would be ~141 of them.
you can argue the length is 100 pixel diagonals, but that makes as much sense as measuring things with the diagonal of a ruler. plus, 1 pixel diagonal equals 1.41 pixel heights (which when normal people think of the length of something that would be what they look at, that or the width,which is the same for these pixels. they dont look at diagonals), and multiplying your precious 100 diagonals gives you ~141 pixels

[kevyk]

If the question is "how many pixel lengths (as measured along a flat side of the pixel)" is the hypoteneuse, then you are right.

I take the OP's question to be "how many pixels do you need to span the length of the hypoteneuse?" This is the only way the question is even remotely interesting and the only reason he'd have phrased it the way he did.

[gasgod]

You would be correct if a pixel were a measure of length, but it isn't. A pixel is a member of an array. We don't even require that the vertical distance between pixels be the same as the horizontal distance between them, so treating them as length units is meaningless.

There are 100 array members along the diagonal, so it is 100 pixels "long". (This is actually meaningless too. Rather, we should say that the diagonal contains 100 pixels.)

Edit: Now I see that another poster has made essentially the same argument.

GG

[mostsmooth]

[ QUOTE ]
If the question is "how many pixel lengths (as measured along a flat side of the pixel)" is the hypoteneuse, then you are right.

I take the OP's question to be "how many pixels do you need to span the length of the hypoteneuse?" This is the only way the question is even remotely interesting and the only reason he'd have phrased it the way he did.

[/ QUOTE ]
the question is clear "How many pixels long is the diagonal (hypotenuse) side", no need to interpret.

[mostsmooth]

[ QUOTE ]
You would be correct if a pixel were a measure of length, but it isn't.

[/ QUOTE ] i know its not a measure of length, but it does have a length, we just dont know what it is. we do know that the length of the hyp is ~141 of whatever that length is.[ QUOTE ]
A pixel is a member of an array. We don't even require that the vertical distance between pixels be the same as the horizontal distance between them, so treating them as length units is meaningless.

[/ QUOTE ]on a computer screen they are the same length apart, no?[ QUOTE ]


There are 100 array members along the diagonal, so it is 100 pixels "long". (This is actually meaningless too. Rather, we should say that the diagonal contains 100 pixels.)

[/ QUOTE ]exactly, but he did say long, thus we need a measurement. nobody ive ever heard of uses the diagonal of an object to describe its length.

[gasgod]

To imagine that the diagonal can be measured in pixel lengths is to imagine rotating a pixel 45 degrees. This is simply nonsense.

GG

[mostsmooth]

[ QUOTE ]
To imagine that the diagonal can be measured in pixel lengths is to imagine rotating a pixel 45 degrees. This is simply nonsense.

GG

[/ QUOTE ]
well then the question is nonsense because thats what it asks you to do.

[gasgod]

[ QUOTE ]
[ QUOTE ]
To imagine that the diagonal can be measured in pixel lengths is to imagine rotating a pixel 45 degrees. This is simply nonsense.

GG

[/ QUOTE ]
well then the question is nonsense because thats what it asks you to do.

[/ QUOTE ]

I'll drink to that.

GG

[purnell]

"Imagine a right triangle drawn on a typical computer screen with a horizontal side of 100 pixels and vertical side also of 100 pixels. How many pixels long is the diagonal (hypotenuse) side?"

Your language indicates that a pixel is a unit of length. You need to specifically define the word to be otherwise for this trick to work.