Can some one please explane this trick...

[Richie]

This Area defying one....
http://img74.imageshack.us/img74/6248/howonearthld3.jpg
as it's totally stumped me...[-o<


same size shapes in the same area but when rearanged the space appears...

I've even printed the shapes out then cut them out to compair sizes and then arranged them myself as an experiment with the kids.... No Still can not explane to a 7 and 10 year old how it works....

Can anyone help and explane....
PLEASE...

[Rai86]

oooooooo i like that one

[dizzyblonde]

On shape B the sticky out bit has 2 squares. When you put the yellow sticky out bit to it, it won't fit together because the yellow sticky out bit has 3 squares, so you get the gap

then again I'm probably wrong in my blonde logic

[Dangerous Dave]

On shape B the sticky out bit has 2 squares. When you put the yellow sticky out bit to it, it won't fit together because the yellow sticky out bit has 3 squares, so you get the gap
All that physics jargon confused me... ;)

[dizzyblonde]

well i'm currently trying to explain it to a 7 yr old...lol

[Rai86]

i think the gradient is slightly different

edit: doh

[wyrdness]

I can see it.

[Richie]

I've cut these shapes out and placed them ontop of each other... each differant colour shape is the same area...

I can not see it...:smt019

Please Explane

[Richie]

right photoshopped A on B...


http://img135.imageshack.us/img135/5215/howonearth1uj5.jpg (http://imageshack.us)
so I'm still confussed

[Rai86]

hmmmmmm...let me think on it

[dizzyblonde]

when you move the yellow shape, you also change the area to 16 squares instead of 15 because of the gap?

[MCN_LiamM]

I failed Physics at AS level... I got a U.
So I'm not even going to bother attempting to explain this

[thedonal]

Yeah - I agree re the gradients of the red and green triangles.

Compare where the slope crosses the grid on A and B. Not the same places.

[Rai86]

well its lucky its maths then ;-)

[MCN_LiamM]

See... I told you I was pants.

[Rai86]

Yeah - I agree re the gradients of the red and green triangles.

Compare where the slope crosses the grid on A and B. Not the same places.

yeah thats what i thought but then in the photo shopped one, its not a significant difference....might be enough to make up a square tho

[dizzyblonde]

its the moving of the shapes that changes the surface area. you can't put a square peg in a round hole as they say.
When you move the yellow and green shape, you change the height and width of the rectangles surface area, that they create

[Biker Biggles]

If the squares are slightly smaller on the other graph you get an extra one over the 75 square total area.Not enough to see with the naked eye,but accounts for the very slight differences where the hypotenuse crosses some squares.

[Richie]

I've cut out the shapes and laid one ontop of the other, each shape in A and B are totally the same area and size..... and then I draw the 3 points of the triangle on another piece of paper... Sill works... and I'm still baffeled.
Kids are having an early night as I don't want to see them again tonight...

[Raf]

Use the grid Luke.

They are letting your eyes play a trick on you. It looks like that the red triangle is just an extension of the green triangle, but in fact it's not.

In 7 squares the red triangle went up 3 squares, and in 5 squares the green triangle went up 2 squares. Which means that the read triangle has a gradient of 3:7 & the green one 2:5. One is steeper than the other.

[Richie]

I see it.... I See it...

ohh, ohh, Kids come down stairs......;)

http://img46.imageshack.us/img46/4056/howonearth2sh0.jpg

thank you, Angles were differant... just like that drive way with snow on it...

[dizzyblonde]

wooohhhoooo :-)

[Rai86]

yayyy

[Richie]

thank god, I can now goto bed... thank you and goodnight

[flymo]

just worked out the angles at the left hand point of each triangle. The smaller triangle has an angle of 21.8deg, the larger triangle has an angle of 20.56deg (approx). So, definately a different gradiant or slope to the triangles accounting for the difference in area of one square on the diagram.

:-)

[dizzyblonde]

The mathematician of the house says its nowt to do with the angle. You change the surface area by moving the shapes, and creating the gap. The angle stays the same, as the tangent is still a straight line

confused...I am!

[Richie]

so it I move my shed to the side of the house I gain more Area of my house land...

no... I dont think thats it DB...

[dizzyblonde]

hey I'm only quoting the guy with tha engineering degree :-(

[Mr Speirs]

If both triangle were exactly the same they should be 32.5 squares but they aren't.

Triangle A's surface area is 32 squares
Triangle B's surface area is still 32 squares but including the gap is 33.

Both together make up the full 65 squares.

Due to the way two triangles are slightly different arranging them in A means it takes up less room .5 of a square to be exact.

Arranging them like they are in B takes up .5 of a square of more room and allows there to be 1 square gap.

HTH

[flymo]

The mathematician of the house says its nowt to do with the angle. You change the surface area by moving the shapes, and creating the gap. The angle stays the same, as the tangent is still a straight line

confused...I am!

The gradiant is different on each triangle, explaining the difference in area when re-arranged. The point of the diagram is that its an optical illusion making it appear that the slope of the shaded area is uniform and remains the same for each layout. It doesnt of course.

The slope is different though and the second layout takes up less area allowing for a 'spare' square.

[dizzyblonde]

he said it were an optical illusion when he walked in the door..lol >>>>>>>>

eeeee am still scratching me head :-)

[Baph]

I see it.... I See it...

Teach the kids SOHCAHTOA. ;) That's just the more complex way to work out the gradient of the different coloured triangles. Once you prove the angles are different, it's pretty easy to see.

[Bibio]

well my son hit it on the head. think of the sliding tile game... and as far as i can see it has to do with the base line on the triangles. although it takes up the same area, the 2 L shaped pieces that make up the rectangle in A have to be rearranged to fit under the large triangle base line for it to work. its the rearangement of the shapes. they still take up the same area as they did in A but leaving a gap.

[Warthog]

Raf got it first, and this explains it the best:
The gradiant is different on each triangle, explaining the difference in area when re-arranged. The point of the diagram is that its an optical illusion making it appear that the slope of the shaded area is uniform and remains the same for each layout. It doesnt of course.

The slope is different though and the second layout takes up less area allowing for a 'spare' square.

I have drawn two exagerated drawings to demonstrate!
In either case, the true diagonal of the overal rectangular space is shown with the red line. because the two triangles are slightly different gradients, they create two different shapes when rearranged with different areas under the curve.

[Richie]

Teach the kids SOHCAHTOA. ;) That's just the more complex way to work out the gradient of the different coloured triangles. Once you prove the angles are different, it's pretty easy to see.


Yea... I remember that one

Some Old Hippie Cought Another Hippie Tripping On Acid
i totally forgot what formula to use for tan, but then i remembered the acid poem (sohcahtoa)

[missyburd]

hmmm lemme just see if I remember....Sine Opposite Hypotenuse, Cos Adjacent Hypotenuse, Tan Opposite Adjacent? hmmm not sure...

[Baph]

Yea... I remember that one

Some Old Hippie Cought Another Hippie Tripping On Acid
i totally forgot what formula to use for tan, but then i remembered the acid poem (sohcahtoa)

hmmm lemme just see if I remember....Sine Opposite Hypotenuse, Cos Adjacent Hypotenuse, Tan Opposite Adjacent? hmmm not sure...

SOH is Sine = Opposite / Hypotenuse
CAH is Cosine = Adjacent / Hypotenuse
TOA is Tan = Opposite / Adjacent.

Exactly right MYC, only minus 2 marks for forgetting that you divide the length of the respective sides in order to get a ratio, then inverse the trigonometry function to get the angle. ;)

Scary thing is, I remember all the common ones. For example, both tan 45 & cot 45 are 1, and csc 30 = sec 60 etc. That's from my A-Level 7 years ago!

[missyburd]

hehe, cheers for clearing that up Baph :-D, sadly this was only 3/4 years ago for me, my memory's very poor :oops:

[Mr Speirs]

Last time I studied any of that stuff...almost 8 years ago now. It is positively not in there anymore.
But I have never ever had to use it in real life.

[dizzyblonde]

hmmm I think I'm going senile then:rolleyes:

[454697819]

its tessalation, the space appears because they are arranged differently... its a simple as...

But I do have a simplistic approach

[carty]

Scary thing is, I remember all the common ones. For example, both tan 45 & cot 45 are 1, and csc 30 = sec 60 etc. That's from my A-Level 7 years ago!

So you should! 7 years ago isn't that long to keep in memory! :smt115

[missyburd]

So you should! 7 years ago isn't that long to keep in memory! :smt115
3 or 4's even worse, did you miss my post? :D

[dizzyblonde]

its tessalation, the space appears because they are arranged differently... its a simple as...

But I do have a simplistic approach

but tessellations leave no gaps do they:confused:
meh, I'll leave the maths to everyone else:(

[Mr Speirs]

Its magic richie. Pure and simple magic.

[carty]

but tessellations leave no gaps do they:confused:


Correct - the individual bits tessellate properly in the first picture, but not in the second, which leaves the gap, ie, the parts no longer tesellate correctly. The trick is that it appears there should be no gap.

[Richie]

Its magic richie. Pure and simple magic.


And I Still believe in Father Christmas...

Cheers for all your input, I've took the trick to his school and showed Tracey his teacher and asked her to explane it...
She hates me now, teehee...

[flymo]

its tessalation, the space appears because they are arranged differently... its a simple as...

But I do have a simplistic approach

nah, the slopes on the triangles are different. we've proved that. The combined slope of both triangles is therefor not a straight line, it cant be.

So, by swapping the triangles in position you either add or remove area to the right hand area of the diagram. Thats were the space comes from.

[Tim in Belgium]

All I know is that the triangles are ugly, one could almost say "pointy". I much prefer curvy shapes ;)

PS wrt the changing gradient if you have a lap top you can hold the screen up and look down the edge, noticing the difference in the two apparent triangles.

[Warthog]

I thought my diagram showed it nicely :( I'll shut up in the future :(

*slopes off slowly, hands in pockets, kicking a rock*

[dizzyblonde]

this one??
http://forums.sv650.org/attachment.php?attachmentid=2844&d=1228429339 (http://forums.sv650.org/attachment.php?attachmentid=2844&d=1228429339)

yes it was a very pretty picture. I liked it very much:p

[Frank]

I thought my diagram showed it nicely :( I'll shut up in the future :(

*slopes off slowly, hands in pockets, kicking a rock*
mardy baby

[Warthog]

mardy baby

ooooooh :p

[Warthog]

this one??
http://forums.sv650.org/attachment.php?attachmentid=2844&d=1228429339 (http://forums.sv650.org/attachment.php?attachmentid=2844&d=1228429339)

yes it was a very pretty picture. I liked it very much:p

Thank you :takeabow: