can anyone explain what's happening here ?

[Cheech]

I'm confused...

[Cheech]

I loaded it into photoshop, cut each piece on the top drawing and placed them over their new locations on the bottom one, they all fit, but there's still that empty square.


very very confused...

[dirtydawg10]

:duh:I'm not smart enough to figure that one out.

[Sploke]

I'm confused - if you calculate the area of the entire triangle, you get an area of 32.5 square units. But, if you calculate the area of each piece - large triangle, small triangle, and rectangular section, you get 12 + 5 + 15 square units which only adds up to 32.

[Cheech]

:duh:I'm not smart enough to figure that one out.


grrr. Neither am I...

Where are you, smart people?

[Cheech]

I'm confused - if you calculate the area of the entire triangle, you get an area of 32.5 square units. But, if you calculate the area of each piece - large triangle, small triangle, and rectangular section, you get 12 + 5 + 15 square units which only adds up to 32.


I don't understand. I can completely overlap the top triangle over the bottom one. Also, if you rotate the top triangle and place it on the bottom, it makes a perfect rectangle.

[dirtydawg10]

I'm confused - if you calculate the area of the entire triangle, you get an area of 32.5 square units. But, if you calculate the area of each piece - large triangle, small triangle, and rectangular section, you get 12 + 5 + 15 square units which only adds up to 32.

I know I tried the same thing and it is baffling.

[dixienut]

.

[vampie]

It works because the two smaller triangles have different shapes, which means the hypotenuse of the big triangle isn't a straight line.

In the first one, the hypotenuse is pointed inwards, and the second one, it's pointed outwards, which is where the space from the empty box goes.

[dirtydawg10]

The hypotenuse is not a straight line in the second one.

[dirtydawg10]

It works because the two smaller triangles have different shapes, which means the hypotenuse of the big triangle isn't a straight line.

In the first one, the hypotenuse is pointed inwards, and the second one, it's pointed outwards, which is where the space from the empty box goes.

Nice! You beat me by that much...lol.

[Sploke]

Ah I got it. Its an optical illusion, or at least just close enough that no one notices it is off.

We are assuming that the hypotenuse of the overall large triangle is a straight line - it is not.

For this to work, the smaller triangles would have to be similar, i.e. all three angles would need to be equal, regardless of leg length. If you call the smaller acute angle of the grey triangle alpha, and the smaller acute angle of the red triangle beta, then tan(alpha)=tan(beta). If you calculate this out (tan = opposite leg length over adjacent leg length), tan(alpha) = 2/5 and tan(beta) = 3/8. 2/5 != 3/8. Basically, the gray triangle has a slightly steeper slope than the red triangle, but between the thickness of the black outline and the closeness of the angle, it looks like a straight line. The additional area taken up by that angle break in the hypotenuse is what gives the extra .5 units of area over what should be taken up by the larger outer triangle.

[vampie]

Nice! You beat me by that much...lol.

Oh, it's only because I typed faster since I've been dying to use the word hypotenuse ever since I heard it on Family Guy.

Now to figure out how I'm going to fit interrobang into a conversation.

[Cheech]

Wow.... so basically that extra little curveture of both triangles together with the thickness of the highlighted black line around the triangle actually makes up the extra square missing in that area.

That's messed up.


Thank goodness for smart people.!

[Inka4040]

Ah yes, the hippopotamus hypnotist strikes again.

[dirtydawg10]

Oh, it's only because I typed faster since I've been dying to use the word hypotenuse ever since I heard it on Family Guy.

Now to figure out how I'm going to fit interrobang into a conversation.

lmao!

[Vicious_Fish]

Math makes my head hurt.

[coach_z]

The hypotenuse is not a straight line in the second one.

if the hypotenuse is not a straight line then the object is not a triangle and that 'line' cannot be referred to as a hypotenuse.

Albeit, that is not the reason it doesnt work. it is a triangle but it is misrepresented in its size in your drawing.

to get more technical i made one of those to scale, one of your blocks = one inch in my drawing. note the line i drew across the top right point and the bottom left point. The triangles are not proportionate in size.

enjoy.

[Cheech]

if the hypotenuse is not a straight line then the object is not a triangle and that 'line' cannot be referred to as a hypotenuse.

Albeit, that is not the reason it doesnt work. it is a triangle but it is misrepresented in its size in your drawing.

to get more technical i made one of those to scale, one of your blocks = one inch in my drawing. note the line i drew across the top right point and the bottom left point. The triangles are not proportionate in size.

enjoy.


and the surface area of the "extra" areas (beyond the curves) are equal to that of the empty box?

[coach_z]

I'm confused - if you calculate the area of the entire triangle, you get an area of 32.5 square units. But, if you calculate the area of each piece - large triangle, small triangle, and rectangular section, you get 12 + 5 + 15 square units which only adds up to 32.

after a few minutes of messing around i came up with this^^^^^^^^

response to your last question....sure....why not
but keep in mind that all of those are straight lines so it would be the area of the obtuse triangle.
which should measure: Leg 1 8.5442 Leg 2 5.3851 Hypotnuse 13.9284 in.
figure out the area of that and you should have your answer

[Cheech]

Curves shmurves!!

I wasn't convinced, so I redrew the thing in cad, to scale, using only thin lines... No curves.

And I get the same result.

I really don't get it.

[vampie]

Your picture is a better example than the original one.

Look at the points where the two triangles meet.
http://i4.photobucket.com/albums/y109/prissmonster/43ce37a0.jpg

And this is the two triangles overlapping.
http://i4.photobucket.com/albums/y109/prissmonster/c1393731.jpg

Now do you get it ‽

I did it! Interrobang'd!

[bettaobsession]

you guys are confusing me!!!!

[Cheech]

OK ok ok ... I got it. lol...

there are no curves . .. It's the fact that the triangles themselves are different. The big triangles, not the pieces in them . . . Thanks!


Pretty interesting illusion!

[cam191919]

you guys are confusing me!!!!

i second that notion

[Cheech]

OK so I redrew the first triangle, but in this example, I used a perfect triangle by joining the extremities of the larger triangle. Then I divided it, and copied the pieces to the second drawing, which clearly shows that if the larger triangle is in fact a perfect one, it can't be rearranged in the way the illusion tries to trick us into seeing it.


OK enough geometry for today.

[coach_z]

i think that is what i was trying to say?
i am not sure.

why were you doing this?

[Cheech]

i think that is what i was trying to say?
i am not sure.

why were you doing this?

yep, except I didn't understand until afterwards. lol... Thanks for clearing it up.


why I did it? no reason really. I just like it when things make sense.

[Sploke]

Right, technically the larger figure is not a triangle...it is a quadrilateral with one of the angles being nearly 180 degrees.

[Coler]

Yep.

[Coler]

Like Duh btw. Sheesh. Dumbos.

[247Plants]

Glad you guys figured that out before I came in here and kicked the knowledge.

[coach_z]

if my girlfriend wasnt int he middle of teaching 7th grade math (area, perimeter, geometry etc...) i was ready to call her!

i write for a living....no math junk.