Put simply looking at the square, the orange and blue shapes have the slope of 2 across for 5 up whereas the red and green shapes have slope 8 across for 3 up. 5/2 is not 8/3 henceforth impossible
just as everyone pointed out, in one part of the figure, the diagonal goes 2.5 squares right and for 1 square up, and in another part, it goes 3 right for 1 up, therefore it's not the same line
This is a visual trick the angle of the two inclines is not the same one is 2/5 and one is 3/8 so the diagonals are not a straight line and creat a ramboid whose surface area is equal to one.. Therefore 8x8 is not equal to the 5x13.
0:22 The square's sides don't coincide exactly. Therefore you can't simply do 5*13. You can also see that there's a lil bit missing. On top of the resulting "rectangle". The area of that little missing part is 1.
Slope = rise/run. Right figure slope = .3846. Left figure has 2 slopes; .375 & .400. It is an optical illusion. Look carefully at the segments on each. There is a slight difference. Add them all and voila!
It's so obvious if you look in the top right hand corner. The red area is slightly lower than the orange. Across those 13 squares the total area will add up to that extra piece
The red triangle is 8 high and 3 wide. At the point where the height is 5, the width would be 3 x 5/8 = 15/8 = 1 7/8. They show it as being 2 instead of 1 7/8.
In other words blue/orange 2:5 is not equal to red/green 3:8
so ... the blue and red pieces fit together but are not a triange, and the same for the orange and green. In the figure on the right at the end of the video the slice from the lower left to the upper right is not contiguous or a straight line.
Just a minor correction. dy/dx is change in y over change in x. Thus the slope of the hypotenuse of the red triangle is 3/8, not 8/3. Same for the green. The argumentation presented is fine and still valid.
In order to make the organge side match the slope of the red triganle, the red triagnle's hypotenuse should go through ( 3 ; 6 ), but it doesn't. if you look carefully it goes over it, this means they have different slopes.
It is a trick using Fibonacci numbers to represent the sides of the polygons. This makes no sense the way I said it but the idea is that operations on fibonnacci numbers can be related to rearrangements of the polygons
I recommend this excellent Math channel: ( Mathmatchpoint ) to everyone who wants to become good at Math. He is going to teach you everything about Math the easy way, from the basic to the advanced topics. The great thing is that his videos are categorized within playlists. It is easy to know which video to watch next. This was the least I could do for him (let others know about his videos). Because of this guy I got 97% on my Math test.
For those who want an intelligible and correct solution: the shapes do nit in fact line up when reassembled. Notice that the gradient of the boundary between the red and green pieces is 3/8 but that between orange and blue is 2/5. When they are placed next to one another, they are made to appear to touch but they do not. If you were to try this with paper you would get long, thin holes between red/orange and green/blue which would comprise the extra 1 square unit of area.
Know that when you change the perimeter of of a rectangle, the area changes. The rectangle with the lowest area is a perfect square, which represents the 8X8. When they transform it, now you have a 5X13 rectangle, which is no longer a perfect square, so you have to assume the area will be higher. I applaud this.
Did you notice, that all number used in this trick are Fibonacci numbers?
This is not a pure coincidence, it is related to Casini's identity for Fibonacci numbers F_{n-1}F_{n+1} - F_n^2 = (-1)^n. (You can find it at wikipedia.)
This optical illusion sometimes go by the name Curry's paradox.
the reason is. (the 5X13 boxes. the pieces of box on this on the center diagonal is not 100% maybe 95%.) compare to 8x8 boxes. thats why got extra 1 box on 5x13 boxes..
guys no body notice the changed position of letters typed in figures orange and red which clearly shows the change in size before and after reformation.
Classic mathematical paradox based on a property of the terms of the Fibonacci Sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, ... specifically that each term squared is either one more or one less than the product of the preceding and succeeding terms. Thus 8 squared is one less than the product of 5 and 13, 13 squared is one more than the product of 8 and 21, and so forth. The less/more alternates.
ALL THAT HAS HAPPENED IS THAT THE 8*8 HAS EXPOSED MORE SURFACE AREA BY ROATATING THE COLOURED PIECES TO FIT END TO END IN THE MOST LENGTHIEST WAY TO MAXIMISE THE TOTAL PERIMETER.
@aksy268 the area would always be the same, cuz youre using the same shapes, changing perimeter wont change area.... it's an optical illusion, like many others have said
@PhysicistPL well it acally works, the trick is the inside edges arent exactally a stright line causing a small jap in the middle, which is where the extra square comes from
kann mir das mal jemand auf deutsch erklären ich hab jetzt nicht genau nachgerechnet aber wenn ich mir des nur mal genau anschaue dann schaut des für mich logisch aus aber 64 kann natürlich nicht 65 sein also is irgendwo was getürkt ich erkenn blos nicht wo
This is just an optical illusion. In reality the figure shown is not actually a quadrilateral because the interior angles do not add up to 360. They actually add up to 357.5. This can be derived using tangent ratios of the triangles.
Just do some calculations and you'll realize that in reality it is impossible to create the rectangle to the right (the 5 * 13) because the slope of the orange and blue do not match the slope of the red and green:
DY/DX for red and blur = 8/3 = 2.6666666
DY/DX for blur and orange = 5/2 = 2.5...
As 2.666666 clearly isnt equal to 2.5...
So they have messed with the squares and the shapes... :(
Right on. The only way you can get a sort of "area" creating cutting is using the axiom of choice aka uncountably many cuts... look up Banach-Tarski paradox
@isak885 I was awe-struck a long time ago... I got this as a sort of quiz question... I knew that something was wrong as the slopes were not the same... By the way thanks for the solution. Amazing optical illusion.. ain't it! Near Perfect!
@faisalkfpm Clearly you can see that there are four different reagons. The red and blue make up one triangle, whilst the green and orange make up another. SINCE THE TWO TRIANGLES FIT NICELY TOGETHER CREATING A RECTANGLE (5 * 13) THE SLOPES OF THE SHAPES MUST BE EQUAL!
When I calculated the slope (DY/DX) of both red and green I get: 8/3.
BUT...
When I calculate the slope (DY/DX) of both orange or blue I get: 5/2.
@isak885 okay, we are almost there, good explanation. But I know that slops are calculated if we have a line and i.e. slope=(y2-y1)/(x2-x1). And it's also calculated using derivatives.Clearly that's not the case here, so the point is when you say slop of a shape, what do you mean?
@faisalkfpm Slope is slope :P. No but if you look at the triangles, the red and green shapes, you can clearly count that there are 8 squares along the horizontal edge and 3 along the vertical edge. I must point out that in my first post I have not actually calculated DY/DX, but rather DX/DY, that is if we name horizontal displacement as displacement along the X and vertical as displacement along the Y axes. Whehter you calculate DY/DX or DX/DY doesnt really matter. You would get 3/8 =2/5.
@faisalkfpm So, when calculating slope, you can use either DY/DX or DX/DY. Just make sure that you use the same method whenever you are doing it!
All DY/DX is, is the distance in the y direction (vertical) divided by the distance in x direction (horizontal). I hope you can easily see that DY/DX for the red and green triangles is 3/8, and that the triangle parts of the blur and orange shapes have a DY/DX of 2/5!
@isak885 That is true, but he did not mess with the squares ... regrouping the shapes like that causes the squares to be formed in different ways which will make an oher one appear ... nothing is impossible
Yep, the slope is the key. I already knew because I have seen another video similar but not equal to this one. The guy that solved it talked about changing in the direction of the line, but you put it in clear math way.
@isak885 you are not correct. Derivatives can not be greater than one. It is the slope of the line after all. For red/blue slope = .3846 (right) on the Left there are two slopes; .375 & .400. They messed with the slope to make it appear what they have shown is true - Not!
@menthol5 Derivatives can't be greater than 1? What sort of school did you learn math from?
Very simple counterexample, take equation of line y=5x. Derivative of that is 5. Derivatives can take any value or be any function, or hell, not be functions at all, depending on what you're taking the derivative of.
@SittingOnEdgeman Would you say that the derivative OF A FUNCTION can be not a function? I'm curious I disagree and I think I could prove it but I may be missing something.
exactly! nureddin has erred in the slopes. the 13*5 rectangle isn't a rectangle at all! i've tried this with precision-cut paper shapes. the area of the quadrilateral should be ½*13*5 + ½*12.6*5. by simple ruler measurement in cms.
No it isn't how bad are you at maths, there is no symmetrical degree between the two triangles and when you cut and paste you loose some material to rebuild it!
IF you draw a extra line you see that there is some misses in calculation!
This proves how bad the average person is on math, or your terrible at it, but I guess your a math newbie because you resort to pen and paper instead of the calculator!
Not at all. 6+10 = 8 + 8 does not mean 6*10 = 8*8... thats total nonsense. The answer is what isak states above... the slopes 5/2 and 8/3 do not agree... so the rearrangement is not truly filling the 13*5 space although it appears so (eyesight not so good)
the intersection of triangles r not exact and thus the division of square in smaller squares is an optical illusion. The smaller squares r not same. The traingles r quadrilaterals. The fourth side is very small to be seen with boundaries.
We had this same problem in my geometry book! It got everyone confused until we cheated and looked at the answers. The new shape isn't a perfect rectangle for one of the sides doesn't match up right.(the two shapes aren't scissor congruent) It's very small to see but it is there.
This is an optical illusion. Try it for yourself to draw. Be small slits smaller than a millimeter. They do not notice, but the area will change by 1 unit. Just the area of these cracks is equal to 1.
I think you get 64=65 there because when you change the places of the polygons, there will be one square more/less. Then there will be a "hole" that explains it.
Look at connection between green and red/blue. There is a blank space under green triangle, and its exactly 8 x 1/8 = 1. Make it bigger and very precise and you will see it better.
it's actually MDAS, PEMDAS shortened, or the Order Of Operations. no matter what the equasion is, you MUST solve it in this order:
Parenthesis : [3+4] = 7
Exopnents : 3^3 = 18
Multiply : 4*4 = 16
Divide : 9%3 = 3
Add : 3+4 = 7
Subtract : 3-2 = 1
when you're doing parenthesis, follow the rule until the entire contents of the parenthesis are solved. and one more thing: if you have more than one of the same operation, solve them individually from left to right.
@theyoungster2 Actually, DMAS can be considered correct. Multiplication and Division are interchangeable, as are addition and subtraction. When you have both multiplication and division in an equation, you do the multiplication/division from left to right. So, in an equation such as 3/4*7-5+2=x, you would do the division before the multiplication and the subtraction before the addition. Your way would give: 3/28-7, which is not the same as 21/4-3. By the way, / is division, % means percent.
I dont think it "disobeys" any rules. There is nothing against moving shapes about. The problem is that the gap between shapes after they are shuffled is ignored.
Just Google "fibonacci puzzles". After a while you will get the solution to this problem.
In fact the 2 "triangles" (the red and the green one) are NOT triangles; they are parallelograms.
If you look very close, you can see the triangles are not really "pointy" everywhere.
This way it is just a matter of miscalculation since you are using the wrong formula to calculate the "triangles" (which are in fact parallelograms". :-)
That two of them ARE parallelograms, is VERY obvious! They are represented as parallelograms in both illustrations(as the two triangles are represented as triangles), so what's your point?
It LOOKS like there are only 2 parallellograms and 2 triangles, but in fact there are 4 parallellograms. The 2 triangles are not really triangles, but that is not noticable in this picture/video.
If you want the complete solution, just Google it, it is very easy to understand then. :-)
I've never hseen this before but when i was younger I could some how see this as being possible, not with a square but with a triangle. I'd even tried a couple times but failed :C . You've just confirmed my belief :O
I am a mathematician Blue & Orange shapes are trapezium's Red & Green shapes are right angled triangle's Areas RED = 0.5 * 3 * 8 = 12 GREEN = 0.5 * 3 * 8 = 12 BLUE = 0.5 * (3 + 5) * 5 = 20 ORANGE = 0.5 * (3 + 5) * 5 = 20 12 + 12 + 20 + 20 = 64 Square = 8 * 8 = 64 THE AREA'S OF EACH SHAPE CANNOT BE CHANGED therefore you have not connected the shapes correctly to make a PERFECT RECTANGLE
Your fallacy is in assuming that the slanted side of the red triangle and the slanted side of the blue trapezoid have the same slope (when the short side of the trapezoid is placed against the short leg of the triangle) thus forming a perfect diagonal. However the slopes are not the same. The red triangle's diagonal has a slope of 3/8 while the blue trapezoid's slanted side, in the configuration at the right, has a slope of 2/5. In other words 15/40 for the triangle and 16/40 for the trapezoid.
the error is at 0:16 , the construction uses the contorn of the squares to cheat and make look like the green and the red triangle would fit forming a 1 X 3 rectangle , however the inclination inside this rectangle is 1 / 3 and it would have to be the same as the big red triangle wich is 3 / 8 and the image cheats making look that 1/3 = 1/8 then making its way to 64 = 65
that is just parallelogram .It look like rectangle but angles are not right.
and 64/13= 4,(923076) so angles are not so different as in rectangle
revison97 1 month ago
Put simply looking at the square, the orange and blue shapes have the slope of 2 across for 5 up whereas the red and green shapes have slope 8 across for 3 up. 5/2 is not 8/3 henceforth impossible
speng120 1 month ago
@speng120 that's right,
Thales' theorem :)
pafeuvip 1 month ago
just as everyone pointed out, in one part of the figure, the diagonal goes 2.5 squares right and for 1 square up, and in another part, it goes 3 right for 1 up, therefore it's not the same line
andreirocks1992 2 months ago
middle bit have overlap, not a math trick, just an illusion
Typho0n86 2 months ago
This is a visual trick the angle of the two inclines is not the same one is 2/5 and one is 3/8 so the diagonals are not a straight line and creat a ramboid whose surface area is equal to one.. Therefore 8x8 is not equal to the 5x13.
leanpower 3 months ago
0:22 The square's sides don't coincide exactly. Therefore you can't simply do 5*13. You can also see that there's a lil bit missing. On top of the resulting "rectangle". The area of that little missing part is 1.
raydredX 3 months ago
Math geeks in our presence ><
8RyuRyu8 3 months ago
OMG! A lot of math-troll-geeks here... (including me).
hadesbox 6 months ago
Slope = rise/run. Right figure slope = .3846. Left figure has 2 slopes; .375 & .400. It is an optical illusion. Look carefully at the segments on each. There is a slight difference. Add them all and voila!
menthol5 6 months ago
It's so obvious if you look in the top right hand corner. The red area is slightly lower than the orange. Across those 13 squares the total area will add up to that extra piece
colinluzio 7 months ago
I did the same on my adobe flash software. After I put all the pieces together as in the second picture, I've got a hole in the middle the whole way.
RUL1S88 7 months ago
MR BALCITA RULES!!!!!!!
miestro123xxx 7 months ago
it have tric
natpeera 7 months ago
DAT DIFFERENT IMAGE
muffemod 7 months ago
nice
4theonly1 7 months ago
All who thought, "Really? Cool!" when watching this, just failed Math forever.
mintchocolatebear 8 months ago 2
@mintchocolatebear Can't brain today I havs the dumb.
tonyrandalljonesmead 7 months ago
nnneeeeeeeeeeerrrrrrrrrrrrrrrrrrrrrrrrrrrrrrdddddddddddddddssssssssssssss!!!!!!!!!!!!!
womo1975 8 months ago
The red triangle is 8 high and 3 wide. At the point where the height is 5, the width would be 3 x 5/8 = 15/8 = 1 7/8. They show it as being 2 instead of 1 7/8.
TomKaren1994 8 months ago
In other words blue/orange 2:5 is not equal to red/green 3:8
so ... the blue and red pieces fit together but are not a triange, and the same for the orange and green. In the figure on the right at the end of the video the slice from the lower left to the upper right is not contiguous or a straight line.
justgivemethetruth 8 months ago
You are lying ... the last figure is not a rectangle, so you cannot take its area by multiplying what you are assuming is the base times the height.
justgivemethetruth 8 months ago
face it guys. we have all been mind fucked
conidi1 9 months ago 2
Just a minor correction. dy/dx is change in y over change in x. Thus the slope of the hypotenuse of the red triangle is 3/8, not 8/3. Same for the green. The argumentation presented is fine and still valid.
th30r3m 9 months ago
It is not amazing. There is a very slim parallelogram around the diagonal of the 13x5 rectangle (its area equals 1).
azhari1958 9 months ago
In order to make the organge side match the slope of the red triganle, the red triagnle's hypotenuse should go through ( 3 ; 6 ), but it doesn't. if you look carefully it goes over it, this means they have different slopes.
MathewBilB 10 months ago
Slope of first green triangle: 2.5
Slope of second green triange: 2.66667
They altered the image. Nothing amazing - you've been tricked!
arcza 10 months ago
It is a trick using Fibonacci numbers to represent the sides of the polygons. This makes no sense the way I said it but the idea is that operations on fibonnacci numbers can be related to rearrangements of the polygons
senglord 10 months ago
as you seen red and green beside a small hole, it is 1*1, so why the answer is 64 = 65
wuiyang 10 months ago
i felt something in the middle, between red and green 0:20 :)
Tural192 11 months ago
I recommend this excellent Math channel: ( Mathmatchpoint ) to everyone who wants to become good at Math. He is going to teach you everything about Math the easy way, from the basic to the advanced topics. The great thing is that his videos are categorized within playlists. It is easy to know which video to watch next. This was the least I could do for him (let others know about his videos). Because of this guy I got 97% on my Math test.
Go to his channel: Mathmatchpoint
Math will become easy
1extremepower 11 months ago
i knew numbers dont lie! anyway, who every discovered this illusion, i ask your permision to use this method to fool my teacher and others.
shayorshayorshayor 1 year ago
For those who want an intelligible and correct solution: the shapes do nit in fact line up when reassembled. Notice that the gradient of the boundary between the red and green pieces is 3/8 but that between orange and blue is 2/5. When they are placed next to one another, they are made to appear to touch but they do not. If you were to try this with paper you would get long, thin holes between red/orange and green/blue which would comprise the extra 1 square unit of area.
Lyorias 1 year ago
Know that when you change the perimeter of of a rectangle, the area changes. The rectangle with the lowest area is a perfect square, which represents the 8X8. When they transform it, now you have a 5X13 rectangle, which is no longer a perfect square, so you have to assume the area will be higher. I applaud this.
heromiles 1 year ago
fake
gandhi4unow 1 year ago
This was discovered by puzzle maker and chess master Sam Loyd.
Snootwaller 1 year ago
Notice the big butt parallelogram?
jjovereats 1 year ago
yeah, notice the big ass question mark !?!
ecaple11 1 year ago
The second shape created is just not a quadrilateral as the first. Purely optical and best described by people above ;).
noionxion 1 year ago
don't fuck wid ma head ,,,,
daegracious 1 year ago
this video is wack i need some real math problem
mrproblemsolver89 1 year ago
右邊三角形甲乙交界處有個面積為1的梯形縫隙。
young811019 1 year ago
what an excellent trick!
Its a brilliant example of transpositional entropy.
like when a 1 is divided by 3 the mutliplied by 3 on a calculator. i.e.
1/3=0.333333 x 3 = 0.9999999 : )
krustyegg 1 year ago
the slopes are not the same, the red on it 3/8, the red one is 2/5
pwn493 1 year ago
Did you notice, that all number used in this trick are Fibonacci numbers?
This is not a pure coincidence, it is related to Casini's identity for Fibonacci numbers F_{n-1}F_{n+1} - F_n^2 = (-1)^n. (You can find it at wikipedia.)
This optical illusion sometimes go by the name Curry's paradox.
kompik 1 year ago 2
haha
azmidasimin 1 year ago
It's fake! The diagonal line in the second shape can't be a straight line.
vladkosz 1 year ago
the reason is. (the 5X13 boxes. the pieces of box on this on the center diagonal is not 100% maybe 95%.) compare to 8x8 boxes. thats why got extra 1 box on 5x13 boxes..
ifucusfuror 1 year ago
guys no body notice the changed position of letters typed in figures orange and red which clearly shows the change in size before and after reformation.
rozinashaheen 1 year ago
The slope of the 2 triangles (blue/red and orange/green) are different?
TheTurtleman9 1 year ago
This has been flagged as spam show
Classic mathematical paradox based on a property of the terms of the Fibonacci Sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, ... specifically that each term squared is either one more or one less than the product of the preceding and succeeding terms. Thus 8 squared is one less than the product of 5 and 13, 13 squared is one more than the product of 8 and 21, and so forth. The less/more alternates.
jbmathfun 1 year ago
Comment removed
jbmathfun 1 year ago
That's not math.. that is just some piece of stupidity...
InotablyCrazy 1 year ago
ALL THAT HAS HAPPENED IS THAT THE 8*8 HAS EXPOSED MORE SURFACE AREA BY ROATATING THE COLOURED PIECES TO FIT END TO END IN THE MOST LENGTHIEST WAY TO MAXIMISE THE TOTAL PERIMETER.
aksy268 1 year ago
@aksy268 the area would always be the same, cuz youre using the same shapes, changing perimeter wont change area.... it's an optical illusion, like many others have said
lizziemobley 1 year ago
this picture deceives you
when it is recombined, it is actually making it larger than before.
it's not a maths trick!
kelvinlo125 1 year ago
in the middle have a hole, it is 1*1,so 64 = 64+(1*1)
wuiyang 1 year ago
optical illusion:
the gradient of hypotenuse of green triangle does not match the gradient of slanted edge of the trapezium.
3/8 ≠ 2/5
this is the same for the red and orange too.
hence there is a thick black line to cover up the gap!
PianoKwanMan 1 year ago
Triangles do not share the same angle on their Hypotenuse
dealerwealer 1 year ago
at the 5*13 picture you can clearly see a thicker black line between green and red, that gap is 1.
enkhuizenddg 1 year ago
@PhysicistPL well it acally works, the trick is the inside edges arent exactally a stright line causing a small jap in the middle, which is where the extra square comes from
ChaoMystero 1 year ago
3/8 ≠ 2/5
DrBPhD 1 year ago
also obvious that they are using the longer inside edges to on the outside
powerbuttin888 1 year ago
Lol that's freakin awesome
EpicSqrl 1 year ago
summat like this was on QI wasnt it?
sharpymufc1 1 year ago
@ isak885, i and my lecturer came up with the same proof as you, well done buddy
redjonathan14 1 year ago
kann mir das mal jemand auf deutsch erklären ich hab jetzt nicht genau nachgerechnet aber wenn ich mir des nur mal genau anschaue dann schaut des für mich logisch aus aber 64 kann natürlich nicht 65 sein also is irgendwo was getürkt ich erkenn blos nicht wo
oODeinoOo 1 year ago
Well, the 5*13 one makes little space in the rectangle. the area of the space is exactly 1.
JapanYoshiTheGamer 1 year ago
This is just an optical illusion. In reality the figure shown is not actually a quadrilateral because the interior angles do not add up to 360. They actually add up to 357.5. This can be derived using tangent ratios of the triangles.
clixsyt 1 year ago 9
They have tricked us those fools!!! :P
Just do some calculations and you'll realize that in reality it is impossible to create the rectangle to the right (the 5 * 13) because the slope of the orange and blue do not match the slope of the red and green:
DY/DX for red and blur = 8/3 = 2.6666666
DY/DX for blur and orange = 5/2 = 2.5...
As 2.666666 clearly isnt equal to 2.5...
So they have messed with the squares and the shapes... :(
That is mean!!!! :/
isak885 1 year ago 131
Right on. The only way you can get a sort of "area" creating cutting is using the axiom of choice aka uncountably many cuts... look up Banach-Tarski paradox
zepkid5678 1 year ago
@isak885 I was awe-struck a long time ago... I got this as a sort of quiz question... I knew that something was wrong as the slopes were not the same... By the way thanks for the solution. Amazing optical illusion.. ain't it! Near Perfect!
psycheswirl8 1 year ago
@isak885 can you please re-express that, it's not necessary to be =
faisalkfpm 1 year ago
@faisalkfpm Clearly you can see that there are four different reagons. The red and blue make up one triangle, whilst the green and orange make up another. SINCE THE TWO TRIANGLES FIT NICELY TOGETHER CREATING A RECTANGLE (5 * 13) THE SLOPES OF THE SHAPES MUST BE EQUAL!
When I calculated the slope (DY/DX) of both red and green I get: 8/3.
BUT...
When I calculate the slope (DY/DX) of both orange or blue I get: 5/2.
8/3 = 5/2 ??? Not in my world! ;)
So as BARNEY WOULD SAY!
This is POSSIMPIBLE!
isak885 1 year ago
@isak885 okay, we are almost there, good explanation. But I know that slops are calculated if we have a line and i.e. slope=(y2-y1)/(x2-x1). And it's also calculated using derivatives.Clearly that's not the case here, so the point is when you say slop of a shape, what do you mean?
faisalkfpm 1 year ago
@faisalkfpm Slope is slope :P. No but if you look at the triangles, the red and green shapes, you can clearly count that there are 8 squares along the horizontal edge and 3 along the vertical edge. I must point out that in my first post I have not actually calculated DY/DX, but rather DX/DY, that is if we name horizontal displacement as displacement along the X and vertical as displacement along the Y axes. Whehter you calculate DY/DX or DX/DY doesnt really matter. You would get 3/8 =2/5.
isak885 1 year ago
@faisalkfpm So, when calculating slope, you can use either DY/DX or DX/DY. Just make sure that you use the same method whenever you are doing it!
All DY/DX is, is the distance in the y direction (vertical) divided by the distance in x direction (horizontal). I hope you can easily see that DY/DX for the red and green triangles is 3/8, and that the triangle parts of the blur and orange shapes have a DY/DX of 2/5!
isak885 1 year ago
@isak885 okay got it thanks
faisalkfpm 1 year ago
@isak885 That is true, but he did not mess with the squares ... regrouping the shapes like that causes the squares to be formed in different ways which will make an oher one appear ... nothing is impossible
ThommyTerneborn 1 year ago
@isak885 nice catch :)
seth009eg 1 year ago
@isak885 It's called fuzzy math.
hiloviking 10 months ago
@isak885 you are right~ who gave this video thumbs up FAILED at math, and they are so many :(
dumbnetworks 8 months ago
@isak885
Yep, the slope is the key. I already knew because I have seen another video similar but not equal to this one. The guy that solved it talked about changing in the direction of the line, but you put it in clear math way.
biblia2016 8 months ago
@isak885 you are not correct. Derivatives can not be greater than one. It is the slope of the line after all. For red/blue slope = .3846 (right) on the Left there are two slopes; .375 & .400. They messed with the slope to make it appear what they have shown is true - Not!
menthol5 6 months ago
@menthol5 Derivatives can't be greater than 1? What sort of school did you learn math from?
Very simple counterexample, take equation of line y=5x. Derivative of that is 5. Derivatives can take any value or be any function, or hell, not be functions at all, depending on what you're taking the derivative of.
SittingOnEdgeman 4 months ago
@SittingOnEdgeman Would you say that the derivative OF A FUNCTION can be not a function? I'm curious I disagree and I think I could prove it but I may be missing something.
raydredX 3 months ago
@menthol5 Derivatives cannot be greater than one?....
raydredX 3 months ago
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zambi007i 5 months ago
This has been flagged as spam show
@isak885
exactly! nureddin has erred in the slopes. the 13*5 rectangle isn't a rectangle at all! i've tried this with precision-cut paper shapes. the area of the quadrilateral should be ½*13*5 + ½*12.6*5. by simple ruler measurement in cms.
zambi007i 5 months ago
the blue/orange dont have the same tangent line than green/red ones.
8/3 vs 5/3, so you cant mix them
alej55 1 year ago
for those of you who think this is messing with pixels and crap...make it with paper or something
its real lol
timedstroyer 1 year ago
No it isn't how bad are you at maths, there is no symmetrical degree between the two triangles and when you cut and paste you loose some material to rebuild it!
IF you draw a extra line you see that there is some misses in calculation!
This proves how bad the average person is on math, or your terrible at it, but I guess your a math newbie because you resort to pen and paper instead of the calculator!
coolzed92 1 year ago
@timedstroyer
Look at isak's respond man....
This video messed up with the angles....
amir705 1 year ago
a wise man knows that he know nothing
salvadoraugustus 1 year ago 3
thats why I hate maths!!
schulilaty 1 year ago
That is just an optimization os space. Laplace or Lagrange, my memory on summer sucks.
That doesn't show anything.
64 sq. meters can be rearranged on 65 sq. meters
Kudell46and2 1 year ago
I think the missing part is on the top right corner of the rectangle, the 5X13. I see some pixels missing there.
Kiriiyama 1 year ago
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mircsea 1 year ago
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bsol07 1 year ago
Not at all. 6+10 = 8 + 8 does not mean 6*10 = 8*8... thats total nonsense. The answer is what isak states above... the slopes 5/2 and 8/3 do not agree... so the rearrangement is not truly filling the 13*5 space although it appears so (eyesight not so good)
zepkid5678 1 year ago
the intersection of triangles r not exact and thus the division of square in smaller squares is an optical illusion. The smaller squares r not same. The traingles r quadrilaterals. The fourth side is very small to be seen with boundaries.
amitnarayankar 1 year ago
WTF?
Enperuto 1 year ago
2/5 != 3/8
TfGuy44 1 year ago 2
lame, this is like messing with optimization
12x8=96
11x9 = 99
10x10 = 100 <---max
9x11 = 99
8x12= 96
Kanashto 1 year ago
@Kanashto or maybe im wrong but i know for sure that there is some messing with pixels
Kanashto 1 year ago
the diagonal isnt the same
apple =/= lemon
chamilonster 1 year ago
the squers in the lines of shars are notre realy squers
ZHAROVAN 1 year ago
We had this same problem in my geometry book! It got everyone confused until we cheated and looked at the answers. The new shape isn't a perfect rectangle for one of the sides doesn't match up right.(the two shapes aren't scissor congruent) It's very small to see but it is there.
lullabyexile 1 year ago
This is an optical illusion. Try it for yourself to draw. Be small slits smaller than a millimeter. They do not notice, but the area will change by 1 unit. Just the area of these cracks is equal to 1.
APTYP17 2 years ago 45
@APTYP17 I drew that up in Google Sketch 8' by 8'. I had a massive crack down the middle. It measured 1 1/2 inches. Yes it was entertaining.
startreking2007 2 years ago
@APTYP17
No optical illusion. They just changed the slopes as stated by isak885.
doubleja 10 months ago
why?
omrou 2 years ago
You've got overlap on the diagonal of the rectangle.
mattloops 2 years ago
3/8 ≠ 2/5
buhisensei 2 years ago
Search about the golden number, it's related to that. It's about the slope of the diagonal.
tinic1 2 years ago
Slope!!!
KanYW 2 years ago
Damm u a NERD lah.
BlackWhitephemon 2 years ago
hax0r!!
Extuder 2 years ago 2
I think you get 64=65 there because when you change the places of the polygons, there will be one square more/less. Then there will be a "hole" that explains it.
xBouxBillx 2 years ago
look closely at the rectangle ... the diagonal does't fit. The overlapped area is the missing 1 from 64 to 65.
Kosekans 2 years ago
WTF!!!
He's a witch, get him!!!
gonyea12 2 years ago 6
las pendientes no son las mismas
vatltatl 2 years ago
pff THE VERY MINI PARTICLES ARE DELETED WEN THE COMPUTER FRECTION THE LINES and thats lines = -1
hitmaniori 2 years ago
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bfinn72591 2 years ago
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bfinn72591 2 years ago
Hahaha, what a fake xD
Look at connection between green and red/blue. There is a blank space under green triangle, and its exactly 8 x 1/8 = 1. Make it bigger and very precise and you will see it better.
Tobiasz931 2 years ago 5
guys it simply disobeys the DMAS rule.... :P
frenzy2085 2 years ago
What is DMAS?
CogitoErgoCogitoSum 2 years ago
DMAS is actually WRONG.
it's actually MDAS, PEMDAS shortened, or the Order Of Operations. no matter what the equasion is, you MUST solve it in this order:
Parenthesis : [3+4] = 7
Exopnents : 3^3 = 18
Multiply : 4*4 = 16
Divide : 9%3 = 3
Add : 3+4 = 7
Subtract : 3-2 = 1
when you're doing parenthesis, follow the rule until the entire contents of the parenthesis are solved. and one more thing: if you have more than one of the same operation, solve them individually from left to right.
theyoungster2 2 years ago
? 3^3 = 18 ?
3^3 = 27.. isn't it?
OGSankai 2 years ago
@theyoungster2 Actually, DMAS can be considered correct. Multiplication and Division are interchangeable, as are addition and subtraction. When you have both multiplication and division in an equation, you do the multiplication/division from left to right. So, in an equation such as 3/4*7-5+2=x, you would do the division before the multiplication and the subtraction before the addition. Your way would give: 3/28-7, which is not the same as 21/4-3. By the way, / is division, % means percent.
OrcaV 2 years ago
I dont think it "disobeys" any rules. There is nothing against moving shapes about. The problem is that the gap between shapes after they are shuffled is ignored.
CogitoErgoCogitoSum 2 years ago 4
Math doesn't lie but it sure is shy with revealing itself.
KingDega1 2 years ago
@KingDega1 nice!
psycheswirl8 1 year ago
between AC and BD have hold,the hold totally 1unit so you will see 65
alen921006 2 years ago
Not really: First set of triangles has a slope of 3/8. Second set is 2/5 slope... then do the math ;)
alcamaka 2 years ago
At least you people know what a triangle is - checkout the dumbest USA and UK and German vidz- those people don't even know that!
templarseries 2 years ago
haha i totally agree ;)
badnerd182 2 years ago
for example tg(a)=2/5 tg(a)=3/8 then these can't be equil so it can't make right shape...
Dotastyler 2 years ago
Just Google "fibonacci puzzles". After a while you will get the solution to this problem.
In fact the 2 "triangles" (the red and the green one) are NOT triangles; they are parallelograms.
If you look very close, you can see the triangles are not really "pointy" everywhere.
This way it is just a matter of miscalculation since you are using the wrong formula to calculate the "triangles" (which are in fact parallelograms". :-)
Behindspace90 2 years ago
ur dumb.
prololipop 2 years ago
When speaking of dumb; every sentence starts with a capital letter. And "ur" is spelled "you are" if you want to sound really smart.
Nice try, but you still sounded as dumb as a cheerleading truckdriver.
Behindspace90 2 years ago
Well, i guess you don't know what irony and parallelograms are. Have a nice day.
prololipop 2 years ago
I do know what irony is, and the fact that you wrote "ur dumb" the wrong way is indeed irony, but it made you sound dumb nevertheless. :-)
Thereby, I did use the wrong term; I ment trapezium instead of parallelogram. However, that does not make my solution wrong or dumb as you stated.
Have a nice day, hun. ;-)
Behindspace90 2 years ago
That two of them ARE parallelograms, is VERY obvious! They are represented as parallelograms in both illustrations(as the two triangles are represented as triangles), so what's your point?
MachoKokoa 2 years ago
It LOOKS like there are only 2 parallellograms and 2 triangles, but in fact there are 4 parallellograms. The 2 triangles are not really triangles, but that is not noticable in this picture/video.
If you want the complete solution, just Google it, it is very easy to understand then. :-)
Behindspace90 2 years ago
hey thanks :-)
MachoKokoa 2 years ago
The second shape has an overlapping at the diogonal line
AreSkavlid 2 years ago
Ouch, my brains hurt (if I actually got those)
Extuder 2 years ago
I've never hseen this before but when i was younger I could some how see this as being possible, not with a square but with a triangle. I'd even tried a couple times but failed :C . You've just confirmed my belief :O
1SavageDragon1 2 years ago
danielxxv 2 years ago 10
whoa no comment
manny61s 2 years ago
im not smart no more
martin4rm559 2 years ago
close, but no cigar,
3/8 does not equal 2/5
of course, 65 = 64 mod (1)
but that's just obvious.
FSMGauss 2 years ago
ah yes - top diagonal gradient = 3/8
bottom diagonal = 2/5
so the new rectangle has a wonkey diagonal
This is such a cheat of a problem.
dibbuck 2 years ago
8 x 8 = 12.8 x 5 = 64
alzubir 2 years ago
this is whats know as "Fibonacci Puzzles"
to learn more about it google it :)
HassanAlmuallim 2 years ago
hmm - interesting. I suspect the little squares are not squares.
dibbuck 2 years ago
Short answer:
The diagonal of the rectangle is not a strait line.
36trooper 2 years ago 4
Your fallacy is in assuming that the slanted side of the red triangle and the slanted side of the blue trapezoid have the same slope (when the short side of the trapezoid is placed against the short leg of the triangle) thus forming a perfect diagonal. However the slopes are not the same. The red triangle's diagonal has a slope of 3/8 while the blue trapezoid's slanted side, in the configuration at the right, has a slope of 2/5. In other words 15/40 for the triangle and 16/40 for the trapezoid.
ironclownfish 2 years ago 6
trapeziums? nice. Ever call them trapezoids?
it's an aluminium trapezium it is.
johnqpublic2718 2 years ago
Despite what quite some people say, there is no overlap. Overlap would reduce the perceived area. The thick black line is covering a gap.
Many of these problems exist where the thickness of the lines is used to create a false impression. Very good for sharpening the minds of the young.
I remember my math teacher "proving" that 89.9 degrees is the same as 90 degrees.
Great fun, and we had to use quite some time to find the flaw in the blackboardful of calculations.
moveste 2 years ago
I loved it. It forced me to think about the problem.
DFAWichita 2 years ago
the error is at 0:16 , the construction uses the contorn of the squares to cheat and make look like the green and the red triangle would fit forming a 1 X 3 rectangle , however the inclination inside this rectangle is 1 / 3 and it would have to be the same as the big red triangle wich is 3 / 8 and the image cheats making look that 1/3 = 1/8 then making its way to 64 = 65
TranceDaNight 2 years ago
even the animation shows the excess triangular sections resulting from the diagonal cut that both add to the missing unit
trying to make simple maths seem eroneous must be the new gay thing to do...
usernamepicphail 2 years ago
lol what a scam
soundtrap8 2 years ago
the angle of the green triangle and the triangle inside this orange trapezium is not the same.. so it wouldnt fit like that...
maxmyt412 2 years ago 4
U see "8 x 8 = 64" "64 = 64"
ArmandTV 2 years ago
I only say 64:5=12,8
Tahilles 2 years ago
2/5 slope won't match a 3/8
Andyiron777 2 years ago
True
bhoogeyman 2 years ago
you are right, 3/8 slope of green triangle won't match 2/5 slope of blue triangle of side of trapezium
ariefvankentucky 2 years ago
your gay for posting this
88think 2 years ago
the one thats missing is that when you look closely at the recatangle 5x13 the diagonal its wider so its lost from fucking sight
hectorandrespv 2 years ago
In this case the Whole square is more than the sum of its parts.
Reality has an imaginary irrational component added to it.
Like heaven, its irrational.
myvids6666 2 years ago
1 water droplet + 1 water droplet = 1 water droplet
samerhadionline 2 years ago
that's because water is polar unlike Oil, Oil is hydrophobic and will only mix with non polar substances such as lighter fluid =P
StyxRanger 2 years ago
1 water droplet + 1 water droplet = 1 "bigger" water droplet :p
plataveloz 2 years ago
Visually you can see that the right figure has a thicker centerline. The area of the missing square is smudged in there.
Zoiros85 2 years ago 2
u r sick,,,,,wt d crocodile,,,,,,,,,,
common ...... grow up///////
in dis pattern 5 = 6...and we wud nt be able to build ny missile or nything duffer
robinluvs 2 years ago