I know this trick. You divide the tiiiiiiny space inside of the square among the outer edges. It`s such an insignificant amount of extra size that you don`t even notice it, but it`s the exact same quantity of cardboard. It`s just hard to notice that it`s a bit bigger.

this is simple.. how do people not understand? when things are in a certain position they won`t fit because of the angles (thus creating a hole in the middle) but when sides align and create 180 degrees then no hole will be prevalent..

In a perfect environment, you can`t have a yellow area inside the white square that has a small gap in the middle, and then magically by re-arranging the yellow shapes within that white square the area has increased in size enough to fill the gap. That increase in area would have to come from somewhere.

It comes from the fact that this is a visual trick of the eye done in a non-perfect environment caused by our limits of human sight. Like others have previously said, all that white area in the first arrangement is actually being distributed along the black lines around the outside. When you re-arrange the squares just a touch more of the outside line is visible.

@Angelmassb: same idea. This one`s easy to see, skip back and forth from the beginning to the end and you see the extra space that`s gained/lost in the black line plain as day.

The white square is evidence that the entire square is imperfect, so that when the pieces are cut at angles and rearranged, the imbalance in the sides of the square are evident as "negative space" in the final result...

The right side of the square is slightly shorter than the left side, and the top is slightly shorter than the bottom. This difference could add up to a mere 1 sq cm, which is hard to really notice when looking at the larger picture, but when the pieces are cut and rearranged, the 1 sq cm is what is left in the center...

I dont understand why this is "!?!?" or special. It`s like saying "OMG IF YOU PUT A DIAMOND IN A SQUARE SPACE IT DOESNT FIT... oh wait, turn that around. shi-IT FITS! MAGIC!?!!!?!?!?!"

If you noticed, there`s some stop motion used in some frames I wouldn`t be surprised if the size of one or two of those yellow boxed was changed ever so lightly to fill it. OTHERWISE, this is a trick that doesn`t use straight line. The edges are in fact, slightly curved, and when not aligned properly, create gaps between the pieces. Its the same trick as the triangle made from different shapes and there`s a block missing in one configuration but there aren`t any missing pieces.

"Where`s the confusing part? Seems pretty simple to me."

Go back to math class. The area of a shape doesn`t change by simply rotating it.

At the beginning, the 4 yellow shapes had a combined area less than that of the square. By rotating them, the combined area of the 4 shapes grew to the same area of the square. That is mathematically illogical.

this isnt hard at all.......i mean all he did was when he cut the pieces he didnt make them straight cuts across, vertical and horizontal, he cut them with a bit of a slant... easy..

The sides of the new large square is slightly smaller than the original one. The geometrical explaining is: If x is the side of the large square and y is the angle between two opposing sides in each quadrilateral, then the quotient between the two areas is given by sec2y minus 1. For y equals 5 degrees, this is approximately 1.00765, which is a difference of about 0.8 percent or the size of the gap in the first position.

The pieces don`t quite fit together at the start, one gap is plainly visible. Plus, the pieces slop into the black border in the original configuration. That adds up to the gap seen in the beginning.

The `trick` here is along the outside border or edge of this puzzle. Notice how thin the line is when the hole is on the center and how thick the border is when the pieces are turned around.

For a shape roughly the shape of a square, area is the width (or height) squared. So a small increase in width / height of a large square increases it area much more than a comparable small increase in width / height of a small square. The empty space you see in the small area of the center has a very small area compared to the large square. Rearranging the blocks to form the more compact square actually reduces the overall dimension of the large square slightly, but the amount is not very noticeable because the larger square has such a large area compared to the small square.

"The `trick` here is along the outside border or edge of this puzzle. Notice how thin the line is when the hole is on the center and how thick the border is when the pieces are turned around." Precisely. The area in the center is displaced into the edges since the lines are angled.

RobSwindol: Yes, I think it`s easy because I know nothing about area and not because it`s possible that the paper was cut all slanted at first and rearranged...

Turning paper clockwise with your hands always makes it larger. If he`d turned them counter-clockwise instead, the square in the center would have grown. It`s the law of Orthogonal Digital Displacementarianism.

I can`t believe that people are saying the answer is in the outside lines, or "stop motion"... I also can`t believe people don`t remember this stuff from high school geometry class. (over 10 years for me, and I remember it... and I was the biggest pothead in my school)

Allow me to REPOST my earlier explanation.

The white square is evidence that the entire square is imperfect, so that when the pieces are cut at angles and rearranged, the imbalance in the sides of the square are evident as "negative space" in the final result...

The right side of the square is slightly shorter than the left side, and the top is slightly shorter than the bottom. This difference could add up to a mere 1 sq cm, which is hard to really notice when looking at the larger picture, but when the pieces are cut and rearranged, the 1 sq cm is what is left in the center...

Didn`t anyone ever watch Mr Wizard? I seem to remember him doing an example of this in a

i fail to see anything surprising here. look at the black border... at no point does either configuration make an actual sqaure. the peices aren`t the size they appear to be due to the optical illusion created by the uneven angles of the cut (and slight curvature of the sides) of each piece in relation to the piece next to it. rotating them alters that illusion thus changing the apparent shape of the piece.

- Any math smarties know how this trick works? Seems like the pieces shouldn`t fit.
Triangle Puzzle

In a perfect environment, you can`t have a yellow area inside the white square that has a small gap in the middle, and then magically by re-arranging the yellow shapes within that white square the area has increased in size enough to fill the gap. That increase in area would have to come from somewhere.

It comes from the fact that this is a visual trick of the eye done in a non-perfect environment caused by our limits of human sight. Like others have previously said, all that white area in the first arrangement is actually being distributed along the black lines around the outside. When you re-arrange the squares just a touch more of the outside line is visible.

The white square is evidence that the entire square is imperfect, so that when the pieces are cut at angles and rearranged, the imbalance in the sides of the square are evident as "negative space" in the final result...

The right side of the square is slightly shorter than the left side, and the top is slightly shorter than the bottom. This difference could add up to a mere 1 sq cm, which is hard to really notice when looking at the larger picture, but when the pieces are cut and rearranged, the 1 sq cm is what is left in the center...

Go back to math class. The area of a shape doesn`t change by simply rotating it.

At the beginning, the 4 yellow shapes had a combined area less than that of the square. By rotating them, the combined area of the 4 shapes grew to the same area of the square. That is mathematically illogical.

Precisely. The area in the center is displaced into the edges since the lines are angled.

Allow me to REPOST my earlier explanation.

The white square is evidence that the entire square is imperfect, so that when the pieces are cut at angles and rearranged, the imbalance in the sides of the square are evident as "negative space" in the final result...

The right side of the square is slightly shorter than the left side, and the top is slightly shorter than the bottom. This difference could add up to a mere 1 sq cm, which is hard to really notice when looking at the larger picture, but when the pieces are cut and rearranged, the 1 sq cm is what is left in the center...

Didn`t anyone ever watch Mr Wizard? I seem to remember him doing an example of this in a

the peices aren`t the size they appear to be due to the optical illusion created by the uneven angles of the cut (and slight curvature of the sides) of each piece in relation to the piece next to it. rotating them alters that illusion thus changing the apparent shape of the piece.

Mr Wizard taught me so much about life, I consider him a father figure.