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harbormaster
01-10-2003, 08:42 PM
Can anyone answer this one?

http://www.donzi.net/photos/illusion_2.jpg

MOP
01-12-2003, 07:44 AM
Hey guy post the one with thr rotating circles!

Tidbart
01-17-2003, 05:00 PM
Evidently, the hole came straight from HELL!
This one has pissed me off enough. What gives? I need to know...............I am loosing it.

3 days of looking at these stupid polygons is driving me nuts.

Bob

Ed Donnelly
01-17-2003, 11:01 PM
The top image left to right at 45 deg is concave . Bottom image is straight. Or my screen and glasses are dirty, thereby creating an optical illustion.Now my head hurts....Ed

harbormaster
01-18-2003, 06:58 AM
Don't think thats it Ed.

goatee
01-18-2003, 10:50 AM
i dont understand the mystery in this one. its pretty self explanitory. the green and tan blocks at the top are to give height. if you switch the triangular peices, now they need to be longer, the green stays the same, but the tan comes down a notch and has to slide out to make up the slack.

Ed Donnelly
01-18-2003, 04:13 PM
My solution made perfect sense to my 6yr. old...Ed

Tidbart
01-18-2003, 04:41 PM
goatee,
All you did was explain how the rearrangement ocurred, not where the blank, or as you put it, 'slack' came from.

Both pictures contain the same area, 32.5 squares, but the bottom picture has got the extra square. To verify the area amounts to be the same, I printed out the pictures, cut them out and layed them over each other. I could find no differences between any of the shapes from one object to the next.

I am going to keep thinking about this one. I hate when something that appears to be simple at first glance is not easily explained.

Bob frown

goatee
01-18-2003, 08:39 PM
i'm sure they are equal. but i still cant figure out the mystery. the green and tan blocks are not the same shape. if you switch the red and green, now there is a differnt height and length to accomodate. "8" blocks. the green is only "5" blocks, the tan "2". so it has to be moved over "1" block. the only way i can explain it is "simple but true" dont over think it.

Ed Donnelly
01-19-2003, 12:54 PM
Its been 9 days since you posted this nightmare,and still no explanation..I spoke to God this morning at church and he says you may not know the answer..Your from" Texas" prove God wrong for me....Ed

goatee
01-19-2003, 01:11 PM
can you explain the missing $1 in mine? that one is pretty easy, and has a definate explaination to it.

goatee
01-19-2003, 01:12 PM
although i like all the jokes,,, makes me want to wait longer to give the answer:)

Formula Jr
01-20-2003, 04:01 AM
Ed and his six year old are right. The red and green triangles have slightly different acute angles. There for the larger shape that these pieces make, isn't a true triangle. Its a four sided polygon that looks alike like a triangle. The differences between a true triangle and the two configurations of the pieces is the illusion. You think the large shape is a triangle - it isn't.

Sagbay32
01-20-2003, 03:07 PM
OK this wasn't that bad....
The answer lies in the area (# squares). Lets assume each square is a "unit." Lets check the total area vs. the sum of the areas of the colors.
We have 2 equal triangles, so the total area is simply the height x width, or 13x5=65 units. Adding the areas of the colors of both triangles:
Red = 8x3=24
light green=2x8=16
yellow=2x7=14
dark green=2x5=10
Total colored area=24+16+14+10=64....doesn't add up to the 65 total area; 65-64=1 unit w/ no color.

Formula Jr
01-21-2003, 12:45 PM
If the red and Blue triangles had the same degree angles then the ratios of the lenghts and heights would be egual due to them being right angle triangles.

Blue triangle:
Base Length 5 divided by height 2 = 2.5

Red triangle:
Base Length 8 divided by height 3 = 2.66666

There is a difference of ratios of .1666666.... repeat 6.

Is is impossible for these two triangles to have the same acute angles as the ratio of base to hieght is different. So they are not simular and therefore the larger shape can not be a triangle.

Tidbart
01-21-2003, 04:40 PM
You are absolutely correct Formula. The red acute angle is 43.12 deg and the green is 42.87 degrees. The ever-so-slight change is where the extra area comes from.(pardon my grammar)

If I sat down and drew this out on graph paper, instead of looking at the screen, it would have immediately become evident.

Touche'

Bob :D

Ed Donnelly
01-21-2003, 10:53 PM
Scot,since Formula Jr. Tidbart ,Shannon(my 6 yr.old) and God all agree with me,I feel an explanation is in order. Otherwise I refuse to accept the $10,000 prize money....Ed

Tidbart
01-23-2003, 06:54 PM
Ed,
Let me try to explain in the simplest way I can think to do.
Look at the top triangle.
Now look at the longest side, the hypotenuse.
If you look real closely, I mean real closely, you can see that it is not exactly a straight line.
The best way to see this is to print it out and then take a straight edge and run it along the longest side from one corner to the other.
You will see an ever so slight bend, if you will, in the line. It bends where the red and green triangles meet.
Now, back to the straight edge. There is a very small gap between the str. edge and the hypotenuse. This gap is the difference.
The area of the small gap is equal to area of one block.
So, when you rearrange the 4 pieces, see the lower triangle, you are left with one white square equal in area to that little gap.

This the best I can do in print. It would be easier to show you on paper.
Hope this helps.

This can be explained several different ways as some of the other post will show. As Formula said, neither of the two objects is a trangle. They just look like they are. That is the illusion.

Bob :D

Ed Donnelly
01-23-2003, 09:23 PM
If it is a slight bend, could you not say concave?Scot must be howling over this topic..Ed

Ed Donnelly
02-02-2003, 11:36 AM
Scot. We are now into February and still no answer to this puzzle. What gives????????I can't eat,can't sleep, I've lost 20 lbs, I'm up to 2 packs a day now.. My mental and physical health is now in your hands..HELP before it is too late. Fading fast.......Ed

Formula Jr
02-04-2003, 01:53 AM
Ed, the puzzle has been solved. The illusion is that the larger shape is a triangle, which falsely leads one to assume that there will be conservation of total Area with the rearraged placements of the two right triangles. However the larger shape is not a true right triangle. Since the two componet trangles have different slopes. Therefore, your first analysis was correct. One arrangment is slightly concave and the other arrangement is slightly convex. I'm using those terms in a very loose way here, but they suffice to explain the illusion. The difference equals exactly one square unit of area.

goatee
02-04-2003, 09:45 PM
ummm... yeah! what he said..

Ed Donnelly
02-04-2003, 11:02 PM
Guys, We still need confirmation from the big guy himself. He started it, he must finish it...Ed

Fish boy
02-05-2003, 08:19 AM
Holy crap! I just stumbled across this one and you guys are really scaring me. Apparently your skzools had math or sumptin fancy like that.

Fish