Can you figure this out?

[Beattie]

Originally posted by: dullard

Originally posted by: LordSnailz
Unless they're not straight lines?

Bingo. They are not all straight lines.

Look closely at the "hypotenuse" (spelling?). On the top figure, the red and dark green triangles clearly align directly on the grid lines (both horizontal and vertical). See how it is exactly 3 gridlines from its base? Follow that vertical gridline down to the bottom figure. The red triangle extends ABOVE the 3rd gridline from the base.

We can do the same thing by starting looking at the bottom figure. Look where the dark green and red triangles meet on the "hypotenuse". They clearly are two gridlines from the base. Now move up that vertical gridline to the top figure. It is clearly well BELOW the 2nd gridline.

The endpoints of the figures are the same, but the "hypotenuse" is not a straight line. In the bottom figure, it bends out (creating half a block of room). In the top figure it bends in (cutting out half a block of room). While the red and dark green shapes are triangles, the combinations of shapes are not triangles at all.

The reason for that is because the triangles have (albeit slightly) different slopes. The same color triangle has the same slope in both pictures. You are incorrect.

 

[dullard]

Originally posted by: Beattie
The reason for that is because the triangles have (albeit slightly) different slopes. The same color triangle has the same slope in both pictures. You are incorrect.

The combination of shapes is not a triangle. Thus there is no one single hypotenuse "slope". Both are four sided figures. Yes the same color triangle has the same slope in both pictures (I said that myself in my post). Nothing I said was incorrect.

 

[Nanotech]

Originally posted by: LordSnailz

Originally posted by: Nanotech

Originally posted by: Beattie
the top triangles are switched and the other blocks are 3x5 =15 one way and 2x8 = 16 the other. 16-15 = 1

And there is the math that no one else wanted to do.

Thanks, Beattie!

you're going to hate me for this, but come again? Where are you getting the 3x5 and 2x8? Also, I did not understand your explanation.

I can understand the different areas if the hypothenuses(sp?) are differrent as dullard pointed about ...

It is all about the middle two pieces! Forget about the triangles and forget about Dullard (no offense) b/c even if they aren't perfectly straight lines they are still triangles and this is still simple math.

In the top figure you have two middle pieces which fit together perfectly forming a 5 X 3 rectangle with an area of 15. Follow?

In the bottom figure those two middle pieces cannot be fit together perfectly so they form a 8 X 2 rectangle with an area of 16. Follow?

16 - 15 = 1

1 = your extra square

If that doesn't help I can't make it any clearer and you certainly don't need a Ph.D. to understand this.

 

[dullard]

Originally posted by: Nanotech
It is all about the middle two pieces! Forget about the triangles and forget about Dullard (no offense) b/c even if they aren't perfectly straight lines they are still triangles and this is still simple math.

In the top figure you have two middle pieces which fit together perfectly forming a 5 X 3 rectangle with an area of 15. Follow?

In the bottom figure those two middle pieces cannot be fit together perfectly so they form a 8 X 2 rectangle with an area of 16. Follow?

16 - 15 = 1

1 = your extra square

If that doesn't help I can't make it any clearer and you certainly don't need a Ph.D. to understand this.

Again that is where the extra hole is now. But where was the hole in the top picture? Can you explain that? No? Oh well, nice try though.

Link 1 "In fact, neither large triangle is an actual triangle."
Link 2 "both upper and lower 5x13 figures are quadrilaterals, not a triangles"
Link 3 "The reason it works is because in neither arrangement is the resulting shape a triangle. The shape is nearly a triangle, but the 'hypotenuse' is not a straight line, so it is actually a quadrilateral."
Link 4 "Anybody who first sees the two shapes assumes that they are triangles, when they are in fact not. To convince yourself of that, look at the slope of the would-be 'hypotenuse'."

Do you own google for "triangle puzzle extra square" and get many more of the same.

 

[biostud]

Originally posted by: Nanotech

Originally posted by: LordSnailz

Originally posted by: Nanotech

Originally posted by: Beattie
the top triangles are switched and the other blocks are 3x5 =15 one way and 2x8 = 16 the other. 16-15 = 1

And there is the math that no one else wanted to do.

Thanks, Beattie!

you're going to hate me for this, but come again? Where are you getting the 3x5 and 2x8? Also, I did not understand your explanation.

I can understand the different areas if the hypothenuses(sp?) are differrent as dullard pointed about ...

It is all about the middle two pieces! Forget about the triangles and forget about Dullard (no offense) b/c even if they aren't perfectly straight lines they are still triangles and this is still simple math.

In the top figure you have two middle pieces which fit together perfectly forming a 5 X 3 rectangle with an area of 15. Follow?

In the bottom figure those two middle pieces cannot be fit together perfectly so they form a 8 X 2 rectangle with an area of 16. Follow?

16 - 15 = 1

1 = your extra square

If that doesn't help I can't make it any clearer and you certainly don't need a Ph.D. to understand this.

No but the thing about this is that you're "supposed" to see it as a large triangle (which it is not). It would be impossible to create a triangle in which you could do this, swapping around.

 

[dullard]

Originally posted by: biostud666
No but the thing about this is that you're "supposed" to see it as a large triangle (which it is not). It would be impossible to create a triangle in which you could do this, swapping around.

Exactly what I explained above. They are not triangles. I showed they are not triangles. Why then was I incorrect?

 

[biostud]

Originally posted by: dullard

Originally posted by: biostud666
No but the thing about this is that you're "supposed" to see it as a large triangle (which it is not). It would be impossible to create a triangle in which you could do this, swapping around.

Exactly what I explained above. They are not triangles. I showed they are not triangles. Why then was I incorrect?

You weren't, I was just to slow to see your post

 

[DrPizza]

I've seen it a hundred times... and I was able to figure it out every time since and including the first time.

 

[Nanotech]

Originally posted by: dullard

Originally posted by: Nanotech
It is all about the middle two pieces! Forget about the triangles and forget about Dullard (no offense) b/c even if they aren't perfectly straight lines they are still triangles and this is still simple math.

In the top figure you have two middle pieces which fit together perfectly forming a 5 X 3 rectangle with an area of 15. Follow?

In the bottom figure those two middle pieces cannot be fit together perfectly so they form a 8 X 2 rectangle with an area of 16. Follow?

16 - 15 = 1

1 = your extra square

If that doesn't help I can't make it any clearer and you certainly don't need a Ph.D. to understand this.

Again that is where the extra hole is now. But where was the hole in the top picture? Can you explain that? No? Oh well, nice try though.

Link 1 "In fact, neither large triangle is an actual triangle."
Link 2 "both upper and lower 5x13 figures are quadrilaterals, not a triangles"
Link 3 "The reason it works is because in neither arrangement is the resulting shape a triangle. The shape is nearly a triangle, but the 'hypotenuse' is not a straight line, so it is actually a quadrilateral."
Link 4 "Anybody who first sees the two shapes assumes that they are triangles, when they are in fact not. To convince yourself of that, look at the slope of the would-be 'hypotenuse'."

Do you own google for "triangle puzzle extra square" and get many more of the same.

I am well aware there was no hole in the top picture and my first post explained that so yes I can. If you want to get technical and say they are not triangles at all that is fine but that does not make the question any less answerable. The question "How can this be true?" is what I have been answering, that is all.

Thank You!

Edit: And I never said you were incorrect I simply told a troubled soul to not listen to you b/c your explanation is far more confusing then mine.

 

[element]

ok ok I get this one but why is 0.999...=1?












haha j/k

 

[LordSnailz]

Originally posted by: Nanotech

Originally posted by: LordSnailz

Originally posted by: Nanotech

Originally posted by: Beattie
the top triangles are switched and the other blocks are 3x5 =15 one way and 2x8 = 16 the other. 16-15 = 1

And there is the math that no one else wanted to do.

Thanks, Beattie!

you're going to hate me for this, but come again? Where are you getting the 3x5 and 2x8? Also, I did not understand your explanation.

I can understand the different areas if the hypothenuses(sp?) are differrent as dullard pointed about ...

It is all about the middle two pieces! Forget about the triangles and forget about Dullard (no offense) b/c even if they aren't perfectly straight lines they are still triangles and this is still simple math.

In the top figure you have two middle pieces which fit together perfectly forming a 5 X 3 rectangle with an area of 15. Follow?

In the bottom figure those two middle pieces cannot be fit together perfectly so they form a 8 X 2 rectangle with an area of 16. Follow?

16 - 15 = 1

1 = your extra square

If that doesn't help I can't make it any clearer and you certainly don't need a Ph.D. to understand this.

Actually this is the wrong explanation. Your explanation says that the extra square is comes from the fact that in one figure, the two middle pieces fit together perfectly while in the second figure they don't, and hence the extra square.

But that is incorrect, the extra square comes from the fact that the "bigger" triangle is not really a triangle.

"The first mosaic has an area of (3*8)/2 + (2*5)/2 + 3*5 = 32 while a triangle with base 13 and height 5 would have an area of (13*5)/2 = 32.5. The missing half unit is the space between a straight line and the caved in "hypotenuse" that you see. In the second mosaic, there is an extra half unit above the hypotenuse. Together they amount to an extra unit (the white square)."


Thanks for the links dullard!

 

[HonkeyDonk]

Originally posted by: LordSnailz

Originally posted by: Nanotech

Originally posted by: LordSnailz

Originally posted by: Nanotech

Originally posted by: Beattie
the top triangles are switched and the other blocks are 3x5 =15 one way and 2x8 = 16 the other. 16-15 = 1

And there is the math that no one else wanted to do.

Thanks, Beattie!

you're going to hate me for this, but come again? Where are you getting the 3x5 and 2x8? Also, I did not understand your explanation.

I can understand the different areas if the hypothenuses(sp?) are differrent as dullard pointed about ...

It is all about the middle two pieces! Forget about the triangles and forget about Dullard (no offense) b/c even if they aren't perfectly straight lines they are still triangles and this is still simple math.

In the top figure you have two middle pieces which fit together perfectly forming a 5 X 3 rectangle with an area of 15. Follow?

In the bottom figure those two middle pieces cannot be fit together perfectly so they form a 8 X 2 rectangle with an area of 16. Follow?

16 - 15 = 1

1 = your extra square

If that doesn't help I can't make it any clearer and you certainly don't need a Ph.D. to understand this.

Actually this is the wrong explanation. Your explanation says that the extra square is comes from the fact that in one figure, the two middle pieces fit together perfectly while in the second figure they don't, and hence the extra square.

But that is incorrect, the extra square comes from the fact that the "bigger" triangle is not really a triangle.

"The first mosaic has an area of (3*8)/2 + (2*5)/2 + 3*5 = 32 while a triangle with base 13 and height 5 would have an area of (13*5)/2 = 32.5. The missing half unit is the space between a straight line and the caved in "hypotenuse" that you see. In the second mosaic, there is an extra half unit above the hypotenuse. Together they amount to an extra unit (the white square)."


Thanks for the links dullard!

Lordsnailz = teh winnar...well so were some other ppl