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Heather Mills - Amputee Forum
Jim T.

Puzzled

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Hi Afet

I was hollering for help on sizing this, but I think I lucked out and accidently hit the right button.

I haven't quite figured out the "save" on the Irfanview program that you sent me.

Thanks anyway - for now. I'm sure that I will be hollering for your help again in the future. I'm learning - slowly.

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Hmmmm, good one Jim. I'll be anxiously awaiting the answer for that puzzle! My mind doesn't work well that way, I'm better at word puzzles, like Scrabble! :)

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I haven't quite figured out the "save" on the Irfanview program that you sent me.

Hi Jim,

I'll send you a PM about this. ;)

Good job on posting it though! B)

Oh, and by the way, I can't work it out either, and I'm usually good at things like that.

:huh:

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Brilliant!!! :D

Thanks Dorota!!!

How's the blood pressure now, Awesome?! :unsure:

Roz. :)

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Hi Dorota. As they say on that TV show that I've heard advertised, but have never watched - "Good Answer"

My first thought was that it was an illusion also. However, when I drew it out on my draft paper, making sure that the lines were straight, and the angles exact, it still came out with one space empty. No curves or slight of hand.

I'm sure that there is a mathematical way of solving this, but that is so far back in my history that I can't even think it out right now.

Thanks though, but I don't think that is it. At least you've got one theory.

P.S. I'm impressed with your drawings. I wish I knew how you did that, and got it on the site.

Ha! So much to learn - So little time.

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Hi Jim;

I believe that Dorota's answer is the correct answer - for the following reasons:

The height to length ratio of the dark green triangle is 2:5;

The same ratio for the red triangle is 3:8.

When the green triangle is on the bottom line, starting from the left, if you count 5 spaces to the right, the height is therefore 2 spaces.

When the red triangle is on the botton line, starting from the left, if you count 5 spaces to the right, the height is 5/8 of 3, which is 1.875.

This proves that in your top diagram, the top line of the entire shape is concave, and that in your bottom diagram, the top line of the entire shape is convex.

The area enclosed by the difference between the concave and convex top lines equals the area of the "missing" square, which is only present when the components of the entire shape are assembled so that its top line is in the convex configuration.

QED!

I'd seen this many years ago (and been perlexed by it), but only Dorota's illustration of the illusion has clarified it!

Roz. :)

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A less mathematical approach ....

Just goes to show:

Not everything is what it seems B) :unsure: Yep, it's just an illusion....in all this confusion :blink: ...

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Guest Dorota

I got if from here - http://forums.britxbox.co.uk/viewtopic.php...c3be0a96c94bc23

They also have more theories on this website.

Talking about posting pictures on the forum, below emoticons there is a form – “File Attachments” , you click “Browse” and look for the picture that you want to post and click "ok." or you can click IMG and post a direct link to the image which is available on the internet already.

And here are more optical illusions -

http://www.lukaroski.com/humor/optical_ill...illusion_11.asp

Dorota

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Hi Dorota, really nice site, but after looking at those black dots, I believe 4th illusion in, nothing will ever look the same! :unsure::blink: :D

Sheila lbk

Maine USA

Keep Smiling :)

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BTW Dorota, granny says, it's past your bedtime!!! :P :lol: :lol: ;)

Sheila

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It's past your bedtime too, granny....

kind regards, mum . hehe

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That's where I'm heading <_< and you too my child!! :P :lol: :lol:

Sheila

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Guest Dorota

Haha, yeah all those illusions are funny.

Anyway, OK Granny! I am just about going to go to bed now haha... so I will reply your private message tomorrow.

Baby

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You betcha!!! <_< <_<

Sheila :)

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Dorota and Roz.

I am wanting very much to accept your answer - BUT The problem is that when I draw it out on a graph table with ABSOLUTELY STRAIGHT lines with the same angles, it still comes out the same.

No curves or hidden deminsions. All lines intesecting each square at the same spot. Try to draw it yourself.

Where am I going wrong? I checked out the other web site, and what I got was their take on it; nothing definitve.

I know, I'm dense, but it just isn't getting through. Heeeeeeelp!!!

P.S. Thanks for the optical illusion site. Neat things.

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Hi Jim;

I would try carefully making each separate part of the total arrangement out of graph paper, with the correct lengths and heights in graph paper squares (particularly important for the triangular shapes).

Then place them on the same scale of graph paper in the arrangements shown, and draw around them - first one, then the other arrangement, placed on the same base line, with the same right hand border.

I think you'll find in the drawn outlines that there is a "concave" and a "convex" top line to the different complete arrangements, and the area between the concave and convex top lines will equal one square.

Since I don't have any graph paper I've only done this in my mind's eye, so I'll be interested to hear if it works!

Roz. :)

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Okay - I give in. You make a very persuading case - and the most logical. I still don't see it when I draw it out on the graph paper, so I know that I am missing something. That's not unusual though.

One of these days, it will sink in.

It was a fun exercise though.

BUT......... still???????

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Am I missing something here? :unsure:

I thought that it was similar to the problem I currently have with my sweater drawer - if I don't put the green sweater on the left side of the drawer and the blue sweater on the right, I can't shut the drawer!

Lizzie :)

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Am I missing something here? :unsure:

I thought that it was similar to the problem I currently have with my sweater drawer - if I don't put the green sweater on the left side of the drawer and the blue sweater on the right, I can't shut the drawer!

Lizzie :)

Lizzie ... That's it ... I knew there would be a simple explanation and boy do I need simple :(

Roz the blood pressure is coming down. It's just re entered at the top of the Richter scale :blink:

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BUT......... still???????

Try thinking of it this way, Jim. If you compute the area of each piece in the first figure, you get:

Red - 12 squares (3x8/2)

Dark green - 5 squares (2x5/2)

Orange - 7 squares

Light green - 8 squares

Sum - 32 squares

However, if you compute the area of the composite triangle (5x13/2), it's 32.5 squares.

The sum af the areas of the pieces in the second figure is 33 squares (32+1 extra).

Does this help explain the optical illusion? It's the same thing Roz was saying about the grades of the hypotenuses of the red and green triangles not being equal. Her explanation meant that the sum of the parts would not equal the whole in either figure. The above area calculations prove her explanation to be correct!

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Okay - I think I have put one theory to rest. The one of optical illusion

Being an old carpenter, I got a piece of plywood this morning from my shop, and cut it exactly into two triangles of the same deminsions.

One I cut into the pieces, (Quickly, so don't look for cabinetry work), the second I used for a format. I know that the lines are straight, and the base angle is 90 degrees.

Then, cutting them apart, (allowing for the saw cut width, including one sloppy cut with the dremel tool), I put them together. I used a full duplicate triangle underneath to insure that the same surface was being covered at all times. I don't know if I can get all of the pictures on this one post, so I will do them seperately.

The point being is that without computing it myself, I agree with Snowyh's approach. I do believe that the solution is mathematical and not illusional. I just haven't figured out the formula.

What you see in the pictures, are the same pieces, covering the same area in a different configuration. No curves, bends, or slight of hand.

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