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Missing Square

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Science Math Geometry Triangle Shapes Square Missing Magic Illusions
ZackScott
  • By: ZackScott
  • Subscribers: 404
  • Updated: 27-Mar-09
  • Videos: 95
  • International International
  • Comments: 112
  • Views: 171,187
  • Added: 05-Nov-06

Rearrange pieces of a triangle and a square goes missing. Is it magic or math?

  1. Categories: Comedy, People & Stories
  2. Favorite On: teamfresh fractals ahmd999
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Missing Square

112 Comments | Add Comment
  • I will try to explain this so it is easi...

    The video says that the shapes are arranged in the shape of a triangle. It does look like a triangle, but it really isn't a triangle. The angle of the blue piece is NOT the same as the angle of the red piece. To understand this better, carefully draw it out on a piece of graph paper, (and this part is important) NOT by drawing a large triangle and filling it in, but by drawing each piece individually and making sure each individual piece is accurate. Now, make your eyes flat with the paper and look down the long side of the "triangle" you will see that in the first diagram it is "bowed" in a little bit, and the other diagram is "bowed" out a little bit. This difference in area is equal to, and therefore is compensated by, the one "missing" square. If you can't understand it from this, finish Jr. High

    By Davey B 1162791975 Reply Spam [+5] Moderate Up Moderate Down
  • There is no spoon...

    ...

    By Neophyte 1162588152 Reply Spam [+3] Moderate Up Moderate Down
  • not a big triangle with a hole in it.......

    the top shape is not a triangle. its a quadrehedrin. ( 4 sides ) the second shape below is not a triangle either, but an octihedrin. (8 sides ) the angle is fucked, but not enough to notice. we finally figured this thing out, after years of mind trama, and the solution, sadly has demystified the entire puzzle. it really is just an illusion. mathmatics is solid, and when its not, we enter the multidimentional world of superstring theories, but only the super nerdy even care enough to read this and smile.

    By bitz in peices 1162794739 Reply Spam [+2] Moderate Up Moderate Down
  • ridiculous

    I love these new math and shape videos. I don't go to school anymore but I love any brain teaser brought my way! Intrigue should be never ending.

    By fart blossom 1162780450 Reply Spam [+1] Moderate Up Moderate Down
  • old easy quize

    we have 2 triangle(blue & red) which is ture and 2 other shapes (yellow and green) but the problem that they are all together doesn't present the big triagnle as we think at the first. becosue the blue and red triangle diffreant angles.
    we can got that from calculating the shadow of each.
    let study the left angle of each triangle
    the red 3/8
    the blue 2/5
    so becouse 3/8 not equal 2/5 so these 2 triangle does not present a straight line when we put like this...so as a result they the 4 shapes does not present a big triangle.... they present another shape .....

    By digital_alpha 1162714623 Reply Spam [+1] Moderate Up Moderate Down
  • wrong

    3:8 = 13:5

    By vitorcapo 1162524669 Reply Spam [+1] Moderate Up Moderate Down
    • wrong again

      Sometimes you need to put the pencil down and take a step back. Ignore the numbers, look at the pattern. Analyse. Maths is far more elegant than simple division.

      By Inimbrium 1162884764 Reply Spam Moderate Up Moderate Down
  • Explanation

    The angles on the red and blue triangles have to be the same in order for this to be true and there is in fact a missing square. So we have that:
    tan-1(2/5) must be equal to tan-1(3/8)

    tan-1(2/5)=21.801 degrees
    tan-1(3/8)=20.556 degrees

    So the two triangles are different varying by only 1.3 degrees and thus explaining the missing square

    By Vilo 1233812030 Reply Spam Moderate Up Moderate Down
  • Answer is easy!

    The red and blue right angle triangles are different sizes! pretty cool illusion though!

    By Ragnarok3000 1206338600 Reply Spam Moderate Up Moderate Down
  • maybe it is because

    coastlines have an infinite boundry length

    By teamfresh fractals 1197593173 Reply Spam Moderate Up Moderate Down
  • didn't really pay attention

    there are a few puzzles like this, at the end of the day, count squares

    By ibetam 1181610796 Reply Spam Moderate Up Moderate Down
  • FAKE

    FAKE

    By smurf king 1175981471 Reply Spam Moderate Up Moderate Down
  • cool math trick

    http://www.metacafe.com/watch/441990/cool_math_trick/

    By shortdude1619 1172197612 Reply Spam Moderate Up Moderate Down
  • ??????

    i found this out in grade 2

    By youtube_sucks 1170194165 Reply Spam Moderate Up Moderate Down
  • my story

    oke... think of this...
    red covers 12 squares
    green covers 8 squares
    yellow covers 7 squares
    blue covers 5 squares
    meaning... it will fit perfectly in 32 squares

    in the second triangle.. you miss 1 square...
    meaning it willbe 31 ive you count it as no color so you do 32-1 = 31
    or ive you count it as a color.. it will be 32 plus 1 = 33
    so that means you CAN fill it up with a random color, but he didnt... meaning he has 31.
    but you can go to 2 differents way... according to math calculatings when you can go 2 different ways... you need to do situation 1 plus situation 2
    meaning: 31 33 = 64
    but since you can go 2 ways you need to divide 64 by 2 = 32

    By woodswolf 1163787915 Reply Spam Moderate Up Moderate Down
  • that was wierd and scary..

    wheres my blankie...

    By dickflop 1163685063 Reply Spam Moderate Up Moderate Down
  • wtf

    Iwould rather nail my head to a PLANK OF WOOD rather than try to figure out this S**t

    By BanjoBoy 1163624103 Reply Spam Moderate Up Moderate Down
  • why

    Only one question about it .....why did u post this

    By el patcho 1163380886 Reply Spam Moderate Up Moderate Down
  • DISREGARD ALL PREVIOUS POSTS!!!

    The pieces that make up the triangle are not polygons (consisting of straight sides). The pieces that make up the hypoteneuse (did i spell that right?), or the longest side, are ever-so-slightly curved. In one configuration, the curve is concave (curves inward), and the "triangle" is whole. In another configuration, however, the curves of the pieces bend outwards and away, leaving an empty space. CORRECTION: Sorry, but I just remembered that ALL the pieces are curved.

    By Tinglystix 1163379803 Reply Spam Moderate Up Moderate Down
  • Mathemathic

    Thales therorem, not
    aligned points.

    By Djienne 1163290975 Reply Spam Moderate Up Moderate Down
  • WHO GIVES A F**k ?

    It is a triangle cuz it has three sides!
    He inverted the first pice ,therefore all pieces should have been inverted ! But he did not!
    SIMPLE!

    By heczy 1163185324 Reply Spam Moderate Up Moderate Down
  • suqare r same

    hey budyd if u count number of full square...they r 25.... n they r still 25 if u change the pattern... hope u got tat

    By vishalba 1163119588 Reply Spam Moderate Up Moderate Down
  • hermmm!!!!

    who gives a sh*t.......

    By baumann 1163073191 Reply Spam Moderate Up Moderate Down
  • simple...

    The blue triangle has a different slope from the whole "triangle", so it's not a triangle at all...

    By shanshansan 1163002968 Reply Spam Moderate Up Moderate Down
  • tipu ni!!!

    nenek aku pOn leh buat!!!... trick jek lebih!! uppercase!!!

    By MeT4MorPH 1162986908 Reply Spam Moderate Up Moderate Down
  • a simple explanation !!!!!

    Add some sugar in a glass some fruit and water and drink ! What's that ? Just water and sugar ... thats the same with the square that disappear! we just need to add some sugar because the fruit (red triangle) dont mix with the water if you don't "blend" it (blue triangle).

    By thiagosnow 1162936310 Reply Spam Moderate Up Moderate Down
  • -1 clever

    but boring

    By share or p2p dies 1162917860 Reply Spam Moderate Up Moderate Down
  • Exactly what he said

    Exactly what he said.... also there is no spoon

    By h0micidal apple 1162872618 Reply Spam Moderate Up Moderate Down
  • ha

    Its got nothing to do with triangles its to do with how u arrange the shapes

    By matty365 1162845733 Reply Spam Moderate Up Moderate Down
  • wots the point

    ther aint no missing square tho. wots the point to the experiment

    By matty365 1162845362 Reply Spam Moderate Up Moderate Down
  • Has anyone asked

    Has anyone asked "the others"

    I think Jack knows more than he's letting on too

    By hawk299 1162818453 Reply Spam Moderate Up Moderate Down
  • how about this...

    back in high school, what i've learned about triangles is that, eventhough how many times you cut it, when you join the pieces back together, you could still form a straight line (like a straight edge as shown on the second triangle). SO WHO GIVES A DAMN F**k ABOUT THE MISSING SQUARE!!! TO HELL WITH IT!!!

    By loordXP+ 1162806230 Reply Spam Moderate Up Moderate Down
  • Took similar puzzle to my math teacher 3...

    and he told me never to bring him any more puzzles like this again! Personally, I think the missing square inch is lost in the gaps between the elements in the set.

    By 2Winger 1162772430 Reply Spam Moderate Up Moderate Down
  • triangles are diffrent

    red triangle base is 8, height is 3, blue triangle base 5, height 2.there is no ratio between triangles

    By since1453 1162751264 Reply Spam Moderate Up Moderate Down
  • simple

    on every figure that the triangle contains some milimeters missing. the missed milimteres when we add gives you that one blank square.

    By Fane89 1162740652 Reply Spam Moderate Up Moderate Down
  • The two shapes are not true triangles..

    If this were a true triangle its area would be 32.5 squares (13*5/2).
    In the first case the 'shape' only covers 32 squares (black 5sq, red 12sq, green

    By Cabroncito 1162735436 Reply Spam Moderate Up Moderate Down
  • you took it :|

    it was you all along..

    By nikon_slayer 1162713554 Reply Spam Moderate Up Moderate Down
  • ewwww

    the square probably went up your intriging ass ya nerd

    By jermjerms 1162712804 Reply Spam Moderate Up Moderate Down
  • idiots.

    If You look at the top triangle, the gradient of the small red triangle is 3/8, and the blue triangle above it is 2/5.... therefore, these shapes arent actually triangles, but 4 sided shapes. This is how the missing square may be formed. WORD...

    By asdda 1162692479 Reply Spam Moderate Up Moderate Down
  • you foools

    if you work out the angles in the triangles using san/cos/tan (sohcatoah) or something, youll find that the big triangle isnt actually a triangle, but a four sided shape.

    By maxjacobs1234 1162687326 Reply Spam Moderate Up Moderate Down
  • =D

    Only math -discapacitated people would say this trick is stupid or boring, cause it's a very creative trick.

    By metacafe613 1162663605 Reply Spam Moderate Up Moderate Down
    • btw

      The answer is that none of the 2 are real triangles, as the slope of the hypotenuse minor triangles are not equal, which would make the "hyppotenuse" of the big triangle not a line. The slpoes are very close though (.375 and .4), and thus we have a hard time seeing this.

      By metacafe613 1162663754 Reply Spam Moderate Up Moderate Down
  • If you rearrange the pieces

    You have to add another square to match the top one, It never went missing

    By Inuk girl 1162658029 Reply Spam Moderate Up Moderate Down
  • nice

    but i hope next time they tell us what the catch

    By brahim_tnwolf 1162633286 Reply Spam Moderate Up Moderate Down
  • omg

    ,=more math lessons on mc

    By EnCos 1162589558 Reply Spam Moderate Up Moderate Down
  • First Explanetion is the right one, ther...

    a

    By victor_isac_sb 1162569952 Reply Spam Moderate Up Moderate Down
    • Exactly

      If you look closely, there are 4 sides.

      By ZackScott 1162574476 Reply Spam Moderate Up Moderate Down
    • not so exactly

      the area of the 2 shapes (I said 2 shapes because with the missing square the second one isnt a triangle) is the same... BUT... they are not really 13x5 you just have too look to the 13 side... the first one doesn't fills the 13 squares... but the one with the missing square does... =\

      By SerialF 1162635538 Reply Spam Moderate Up Moderate Down
  • up there

    the missing square is at the red triangle as u can see after rearrangement the 2nd triangle is one square higher than the first one...

    By OrgPUtihBODO 1162564791 Reply Spam Moderate Up Moderate Down
  • Error de ubicación

    El amarillo esta en el lugar del verde y vice versa

    By Buscador 1162562304 Reply Spam Moderate Up Moderate Down
  • its not a mathematical trick, its a stu...

    the sum of partial areas is not equal to the total triangle area, so the overall shape is NOT a triangle.. THE trick is the intersection point of the blue and red triangles which will not be exactly at the edge of the right angle of the square grid. the use of paper presentation rather than computer drawing is a must to wrap the paper at position ( -5, -3) so that the exact joining points of blue and red triangles as they are. besides the blue and red trgs. are not similar..


    By J - maze 1162560916 Reply Spam Moderate Up Moderate Down
  • damn u and ur math

    why the F**k would u post math problems? there should be a filter for this kind of bogus edutainment.

    By dmnxx 1162560559 Reply Spam Moderate Up Moderate Down
  • I HATE NEEEEEEEEEEEEEERDS

    WTF

    By jay man 1162547456 Reply Spam Moderate Up Moderate Down
  • the triangles have four sides

    The polygons made by arranging the two triangles (blue and red) and the other L shape areas (green and yellow) are NOT TRIANGLES. The agles of the red and blue triangles are different (except for the straight angle, of course), so their hypotenuses are not collinear. Therefore we're comparing two 4 sided polygons, not two triangles. This becomes more obvius if we calculate the area of the starting shape first by admitting it's a triangle (5x13/2=32.5) and then doing the same calculation by adding the area of each surface (5+12+7+8 =32). Obviously the starting shape is not a triangle, nor the second shape is and while the "hypotenuse" in the first case is concave, in the second case is convex.

    Anyway, nice trick!

    By gesx 1162546748 Reply Spam Moderate Up Moderate Down
    • u r really sad

      .

      By eire 1162577391 Reply Spam [+1] Moderate Up Moderate Down
    • yes

      REALLY REALLY SAD

      By stena 1162745493 Reply Spam Moderate Up Moderate Down
    • no i think it's false

      because it's not because the triangles are not the same look it very gooooood

      By hamza_345 1162604349 Reply Spam [-1] Moderate Up Moderate Down
    • THE RED AND BLUE ARE RIGHT TRIANGLES

      Therefore the angles are the same. The answer to this is simple. Measure the distance between the right angles. The distance is different depending on what color is at the top. I know this may be confusing, but trust me, the red and blue have the same angles AND they are three sided.

      By AliGrill 1162765590 Reply Spam Moderate Up Moderate Down
    • Precisely!

      It's nice to sometimes have comments on here that are purely empirical and not emotional...Of course this an old trick, but still I appreciate your calm explanation to those who may not have been exposed to these kind of tricks...

      By Just mois 1162763701 Reply Spam Moderate Up Moderate Down
    • That was the Perfect way to explain

      Just allow me to add one more note to make it more clear; look carefuly at the Red & Blue triangles, put their Top Acute angles on each other, you will find that the base of the Blue one is NOT the same lenght of the Red one at that same depth (that means 2 squares less the Red one's top), the Blue one is 5 units in length while the Red one is about 5.2 units, & that proves "gesx" point that the two Red & Blue triangles are not the same.

      But anyway, although it's an old trick, but I have to confess that it's is a really good one & it took me months to solve it out :)

      By Johnnie_Habibos 1162606614 Reply Spam Moderate Up Moderate Down
    • you mean

      very old trick!

      By A A A 1162601067 Reply Spam Moderate Up Moderate Down
    • Thanks...

      This is the explanation that I actually understood.

      By Pow! 1162553268 Reply Spam Moderate Up Moderate Down
  • goodness..

    I'm amazed... I didn't believe in majerk before now,,,,derp.

    By ru4angus 1162546591 Reply Spam Moderate Up Moderate Down
  • CALLING ALL MUSLIMS!

    DID YOU FIND ALLAHS NAME IN THERE? I SWEAR IT WAS, THAT MISSING SQUARE IS PROOF THAT ALLAH IS REAL!! WOOOOOW!!

    By aussie72 1162546143 Reply Spam Moderate Up Moderate Down
  • E=MC2

    Why didn`t Einstein think of it.

    By Mantis450c 1162540984 Reply Spam Moderate Up Moderate Down
  • SOLUTION MY ASS

    13+5=18
    18-13=3
    3-3=0 therefor, this equation is totally fucked up.LOL

    By -Ba3BoS- 1162540134 Reply Spam Moderate Up Moderate Down
  • a^2+b^2=c^2

    aha...

    By kenny o_O 1162537645 Reply Spam Moderate Up Moderate Down
  • Wrong from the beginning

    In the first condition, We cannot make such triangle.
    If we look at the yellow & green area (the rectangle) in the first condition and use them as a base, the angled line should stop at (5 , 12.5) instead of (5 , 13).
    Because these are how the angle works:
    (1 , 2.5 ) ; (2 , 5); (3 , 7.5); (4 , 10) ; (5, 12.5) END!
    Other than this, the yellow-green (rectangle shaped) area will get distorted, and we will have either more area or less area than we’re supposed to.
    Sorry about my English..=)
    Nice trick btw..;)

    By Bayoe 1162533067 Reply Spam Moderate Up Moderate Down
  • very simple

    the angles of the red square and the blue square is not equal.This leads to the hypotenuse is not a straight line in the second picture.But it's straigth in the first one. However with your eyes you'll see both hypotenuses are straight.

    The hypotenuse of second picture is a convex line <--- the area of second picture increase along the hypotenus.But the area of the picture is constant.The result is the missing block.

    By luxiphe 1162531348 Reply Spam Moderate Up Moderate Down
  • Your all idiots

    there was never another square in the first place its not that hard to do
    it's simply re making it but it just doesn't fill out the original way

    By Kapital 1162529067 Reply Spam Moderate Up Moderate Down
  • cosa inútil

    Obvio que no falta un cuadro (unidad) si se supone que son las mismas figuras, el área total es la misma nadamás que las unidades estan acomodadas de otra manera y la figura parece que le falta algo pero los pedazos del cuadrito faltante se acomoda en la parte de la hipotenusa fijense!.... aburridooooo!!

    By Alex Vortex 1162526352 Reply Spam Moderate Up Moderate Down
  • its not magic..

    coz the hypotenuse is not a straight line..
    the area that is missing, was put at the area excess of the hypotenuse..
    (imagine a straight line hypotenuse side)

    By asshol3 1162524909 Reply Spam Moderate Up Moderate Down
  • math is cool

    I like getting something from nothing for free

    By luckydogg_420 1162524254 Reply Spam Moderate Up Moderate Down
  • Do u...

    Hey Dude (submiter)...do u think That this is a very Cooooool .....12 y old boy with no Brain can do this..and Notice What you have just did

    By Samgard 1162524092 Reply Spam Moderate Up Moderate Down
  • hmmmmmm

    thats gonna make me up all night .

    By broken_arrow3200 1162523418 Reply Spam Moderate Up Moderate Down
  • where the hell is the magic about it?

    when you reshape the triangles the way he did it, it is possible that you are losing one spot because you are compensating the loss made by the two Red and Blue triangles... as there is now more space below the Red Triangle than it was before making up for reshaping it in length rather than in height....

    By Londoner 1162523414 Reply Spam Moderate Up Moderate Down
    • Magic...

      Magic is just about doing completely real and physical things in a deceiving manner. It is deceiving because what you're looking at is not a triangle, but rather a four-sided shape. It was just an illusion really that can be easily explained once you know the geometry behind it.

      By ZackScott 1162574714 Reply Spam Moderate Up Moderate Down
  • If You Are Intelligent Click Here

    http://www.metacafe.com/watch/526271/if_you_are_intelligent_click_here/

    By zuraschi 1176640588 Reply Spam [-1] Moderate Up Moderate Down
  • very simple to understand

    think of it as area... now you have a certain area given in triangle 1 above, now you can know for a fact that when you split it and rearrange it, that the area did not change.... it is solid paper, the shape changed. not the area. You don't make things disappear by rearranging it. it change how it looks only.

    By MistPerson 1166724715 Reply Spam [-1] Moderate Up Moderate Down
  • of course its math

    the only reason this happens is because the hypotenuse of triangular shape are on different angles.... sry for the big words children =]

    By poke-moan 1162873479 Reply Spam [-1] Moderate Up Moderate Down
  • Very old trick.

    The two "triangles" are not both true triangles. The "hypotenuse" has a kink in the middle that accounts for the extra area covered by the potton one compared to thje top.

    By Toak Reon 1162843338 Reply Spam [-1] Moderate Up Moderate Down
  • wow lot of strange comments here

    .. a triangle is not a triangle???? lol. What happened is that the two triangles in the top figure leave a volume of 3X5 squares which equals 15 squares ( 3x5=15). By swapping the triangles, in the bottom illustration, you then have a missing volume of 2x8 ( 2x8=16)or 16 squares.(16-15=1) This is just one of those things that makes math fun. (Have you ever poured one liquid from one container into another and found out you had less than you started with? its called displacement of volume.... Come on , somebody comment on that statment....lmao, and confuses all you others.) lol... never heard anyone say the triangles are not triangles before
    made my day. ( whats really neat is the person who first discovered this ages ago, and used it to confuse the masses.)

    By elbowjoe 1162726297 Reply Spam [-1] Moderate Up Moderate Down
    • stupid STFU

      you dumb crap! how does 3*5 square represent volume. for your dumb ass, volume is represented in cubic. above video is refering to area. My little 7 year old cousin can tell the difference between area and volume. LMFAO displacement in volume...??? You must be on crack if you see three dimensional triangle in above video.

      By Busted143 1162806333 Reply Spam Moderate Up Moderate Down
  • the Solution

    If you notice you will find that the height and the length of the second square have become longer… the height become more than five and the length become more than 13

    By SaLLoM 1162525630 Reply Spam [-1] Moderate Up Moderate Down
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